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Old page wikitext, before the edit (old_wikitext) | '{{Short description|Fluid flow that occurs due to heterogeneous fluid properties and body forces}}
{{distinguish|Conviction}}
[[File:Convection-snapshot.png|thumb|400px|right|Simulation of thermal convection in the [[Earth's mantle]]. Hot areas are shown in red, cold areas are shown in blue. A hot, less-dense material at the bottom moves upwards, and likewise, cold material from the top moves downwards.]]
'''Convection''' is single or [[Multiphase flow|multiphase]] [[fluid flow]] that occurs [[Spontaneous process|spontaneously]] due to the combined effects of [[material property]] [[heterogeneity]] and [[body forces]] on a [[fluid]], most commonly [[density]] and [[gravity]] (see [[buoyancy]]). When the cause of the convection is unspecified, convection due to the effects of [[thermal expansion]] and buoyancy can be assumed. Convection may also take place in soft [[solids]] or [[mixtures]] where particles can flow.
[[File:Ghillie Kettle Thermal.jpg|thumb|Thermal image of a newly lit [[Kelly Kettle|Ghillie kettle]]. The plume of hot air resulting from the convection current is visible.]]Convective flow may be [[Transient state|transient]] (such as when a [[Multiphasic liquid|multiphase]] [[mixture]] of [[oil]] and [[water]] separates) or [[steady state]] (see [[Convection cell]]). The convection may be due to [[Gravity|gravitational]], [[Electromagnetism|electromagnetic]] or [[Fictitious force|fictitious]] body forces. [[Convection (heat transfer)|Heat transfer by natural convection]] plays a role in the structure of [[Earth's atmosphere]], its [[oceans]], and its [[Earth's mantle|mantle]]. Discrete convective cells in the atmosphere can be identified by [[clouds]], with stronger convection resulting in [[thunderstorm]]s. Natural convection also plays a role in [[stellar physics]]. Convection is often categorised or described by the main effect causing the convective flow; for example, thermal convection.
Convection cannot take place in most solids because neither bulk current flows nor significant [[diffusion]] of matter can take place.
[[Granular convection]] is a similar phenomenon in [[granular material]] instead of fluids.
[[Advection#Distinction between advection and convection|Advection]] is fluid motion created by velocity instead of thermal gradients.
[[Convective heat transfer]] is the intentional use of convection as a method for [[heat transfer]]. Convection is a process in which heat is carried from place to place by the bulk movement of a fluid and gases.
==History==
In the 1830s, in ''[[Bridgewater Treatises|The Bridgewater Treatises]]'', the term ''convection'' is attested in a scientific sense. In treatise VIII by [[William Prout]], in the book on [[chemistry]], it says:<ref>{{Cite book |last=Prout |first=William. |url=http://archive.org/details/chemistrymeteoro00pro |title=Chemistry, meteorology and the function of digestion: considered with reference to natural theology |publisher=William Pickering |year=1834 |series=The Bridgewater Treatises: On the power, wisdom and goodness of God as manifested in the creation. Treatise 8. |volume= |pages=65–66}}</ref>
<blockquote>[[File:Prout William painting (cropped).jpg|alt=Painting of William Prout|thumb|217x217px|William Prout]][[File:Fireplace (60857557) (cropped).jpg|alt=Fireplace with grate|thumb|204x204px|Fireplace, with grate and chimney]][...] This motion of heat takes place in three ways, which a common fire-place very well illustrates. If, for instance, we place a thermometer directly before a fire, it soon begins to rise, indicating an increase of temperature. In this case the heat has made its way through the space between the fire and the thermometer, by the process termed ''[[radiation]]''. If we place a second thermometer in contact with any part of the grate, and away from the direct influence of the fire, we shall find that this thermometer also denotes an increase of temperature; but here the heat must have travelled through the metal of the grate, by what is termed ''[[Thermal conduction|conduction]]''. Lastly, a third thermometer placed in the chimney, away from the direct influence of the fire, will also indicate a considerable increase of temperature; in this case a portion of the air, passing through and near the fire, has become heated, and has ''carried'' up the chimney the temperature acquired from the fire. There is at present no single term in our language employed to denote this third mode of the propagation of heat; but we venture to propose for that purpose, the term ''convection'', [in footnote: [Latin] ''Convectio'', a carrying or conveying] which not only expresses the leading fact, but also accords very well with the two other terms.
</blockquote>
Later, in the same treatise VIII, in the book on [[meteorology]], the concept of convection is also applied to "the process by which heat is communicated through water".
==Terminology==
Today, the word ''convection'' has different but related usages in different scientific or engineering contexts or applications.
In [[fluid mechanics]], ''convection'' has a broader sense: it refers to the motion of fluid driven by density (or other property) difference.<ref>{{cite book| title=Fundamentals of Fluid Mechanics| first= Bruce R. |last=Munson |isbn= 978-0-471-85526-2 |publisher = [[John Wiley & Sons]]| year= 1990 }}</ref><ref>{{cite book|last=Falkovich|first=G.|title=Fluid Mechanics, a short course for physicists|url=http://www.weizmann.ac.il/complex/falkovich/fluid-mechanics|publisher=Cambridge University Press|year=2011|isbn=978-1-107-00575-4|url-status=live|archive-url=https://web.archive.org/web/20120120034443/http://www.weizmann.ac.il/complex/falkovich/fluid-mechanics|archive-date=2012-01-20}}</ref>
In [[thermodynamics]], ''convection'' often refers to [[Convection (heat transfer)|heat transfer by convection]], where the prefixed variant Natural Convection is used to distinguish the fluid mechanics concept of Convection (covered in this article) from convective heat transfer.<ref>{{cite book|title=Thermodynamics:An Engineering Approach|first1= Yunus A. |last1=Çengel |first2= Michael A. |last2 = Boles |year= 2001 |isbn=978-0-07-121688-3 |publisher =[[McGraw-Hill Education]]}}</ref>
Some phenomena which result in an effect superficially similar to that of a convective cell may also be (inaccurately) referred to as a form of convection; for example, [[Marangoni effect|thermo-capillary convection]] and [[granular convection]].
==Mechanisms==
Convection may happen in [[fluids]] at all scales larger than a few atoms. There are a variety of circumstances in which the forces required for convection arise, leading to different types of convection, described below. In broad terms, convection arises because of [[body force]]s acting within the fluid, such as gravity.
===Natural convection===
{{Unreferenced section|date=September 2023}}
[[Image:Bénard cells convection.ogv|thumb|300px|[[Rayleigh–Bénard convection|Rayleigh–Bénard cells]].]]
[[File:Thermal-plume-from-human-hand.jpg|thumb|This color [[schlieren]] image reveals [[thermal convection]] originating from heat conduction from a human hand (in silhouette) to the surrounding still atmosphere, initially by diffusion from the hand to the surrounding air, and subsequently also as advection as the heat causes the air to start to move upwards.]]
'''Natural convection''' is a flow whose motion is caused by some parts of a fluid being heavier than other parts. In most cases this leads to '''natural circulation''': the ability of a fluid in a system to circulate continuously under gravity, with transfer of heat energy.
The driving force for natural convection is gravity. In a column of fluid, pressure increases with depth from the weight of the overlying fluid. The pressure at the bottom of a submerged object then exceeds that at the top, resulting in a net upward [[buoyancy]] force equal to the weight of the displaced fluid. Objects of higher density than that of the displaced fluid then sink. For example, regions of warmer low-density air rise, while those of colder high-density air sink. This creates a circulating flow: convection.
Gravity drives natural convection. Without gravity, convection does not occur, so there is no convection in free-fall ([[inertial]]) environments, such as that of the orbiting International Space Station. Natural convection can occur when there are hot and cold regions of either air or water, because both water and air become less dense as they are heated. But, for example, in the world's oceans it also occurs due to salt water being heavier than fresh water, so a layer of salt water on top of a layer of fresher water will also cause convection.
Natural convection has attracted a great deal of attention from researchers because of its presence both in nature and engineering applications. In nature, convection cells formed from air raising above sunlight-warmed land or water are a major feature of all weather systems. Convection is also seen in the rising plume of hot air from [[fire]], [[plate tectonics]], oceanic currents ([[thermohaline circulation]]) and sea-wind formation (where upward convection is also modified by [[Coriolis force]]s). In engineering applications, convection is commonly visualized in the formation of microstructures during the cooling of molten metals, and fluid flows around shrouded heat-dissipation fins, and solar ponds. A very common industrial application of natural convection is free air cooling without the aid of fans: this can happen on small scales (computer chips) to large scale process equipment.
Natural convection will be more likely and more rapid with a greater variation in density between the two fluids, a larger acceleration due to gravity that drives the convection or a larger distance through the convecting medium. Natural convection will be less likely and less rapid with more rapid diffusion (thereby diffusing away the thermal gradient that is causing the convection) or a more viscous (sticky) fluid.
The onset of natural convection can be determined by the [[Rayleigh number]] ('''Ra''').
Differences in buoyancy within a fluid can arise for reasons other than temperature variations, in which case the fluid motion is called '''gravitational convection''' (see below). However, all types of buoyant convection, including natural convection, do not occur in [[microgravity]] environments. All require the presence of an environment which experiences [[g-force]] ([[proper acceleration]]).
The difference of [[density]] in the fluid is the key driving mechanism. If the differences of density are caused by heat, this force is called as "thermal head" or "thermal driving head." A fluid system designed for natural circulation will have a heat source and a [[heat sink]]. Each of these is in contact with some of the fluid in the system, but not all of it. The heat source is positioned lower than the heat sink.
Most fluids expand when heated, becoming less [[density|dense]], and contract when cooled, becoming denser. At the heat source of a system of natural circulation, the heated fluid becomes lighter than the fluid surrounding it, and thus rises. At the heat sink, the nearby fluid becomes denser as it cools, and is drawn downward by gravity. Together, these effects create a flow of fluid from the heat source to the heat sink and back again.
===Gravitational or buoyant convection===
'''Gravitational convection''' is a type of natural convection induced by buoyancy variations resulting from material properties other than temperature. Typically this is caused by a variable composition of the fluid. If the varying property is a concentration gradient, it is known as '''solutal convection'''.<ref>{{cite journal|citeseerx=10.1.1.15.8288 |title=Pattern Formation in Solutal Convection: Vermiculated Rolls and Isolated Cells |journal=Physica A: Statistical Mechanics and Its Applications |volume=314 |issue=1 |pages=291 |bibcode=2002PhyA..314..291C |last1=Cartwright |first1=Julyan H. E. |author1-link = Julyan Cartwright |last2=Piro |first2=Oreste |last3=Villacampa |first3=Ana I. |year=2002 |doi=10.1016/S0378-4371(02)01080-4 }}</ref> For example, gravitational convection can be seen in the diffusion of a source of dry salt downward into wet soil due to the buoyancy of fresh water in saline.<ref>{{cite journal|last=Raats|first= P. A. C. |year=1969 |title=Steady Gravitational Convection Induced by a Line Source of Salt in a Soil|journal = Soil Science Society of America Proceedings |volume = 33 |pages = 483–487 | doi=10.2136/sssaj1969.03615995003300040005x |issue=4|bibcode=1969SSASJ..33..483R}}</ref>
Variable [[salinity]] in water and variable water content in air masses are frequent causes of convection in the oceans and atmosphere which do not involve heat, or else involve additional compositional density factors other than the density changes from thermal expansion (see ''[[thermohaline circulation]]''). Similarly, variable composition within the Earth's interior which has not yet achieved maximal stability and minimal energy (in other words, with densest parts deepest) continues to cause a fraction of the convection of fluid rock and molten metal within the Earth's interior (see below).
Gravitational convection, like natural thermal convection, also requires a [[g-force]] environment in order to occur.
===Solid-state convection in ice===
[[Sputnik Planitia#Convection cells|Ice convection on Pluto]] is believed to occur in a soft mixture of [[nitrogen ice]] and [[carbon monoxide]] ice. It has also been proposed for [[Europa (moon)|Europa]],<ref name="On convection in ice I shells of ou">{{cite journal| doi=10.1016/j.icarus.2006.03.004 | bibcode=2006Icar..183..435M | volume=183 | issue=2 | title=On convection in ice I shells of outer Solar System bodies, with detailed application to Callisto | year=2006 | journal=Icarus | pages=435–450 | last1 = McKinnon | first1 = William B.}}</ref> and other bodies in the outer Solar System.<ref name="On convection in ice I shells of ou"/>
===Thermomagnetic convection===
{{main|Thermomagnetic convection}}
'''Thermomagnetic convection''' can occur when an external magnetic field is imposed on a [[ferrofluid]] with varying [[magnetic susceptibility]]. In the presence of a temperature gradient this results in a nonuniform magnetic body force, which leads to fluid movement. A ferrofluid is a liquid which becomes strongly magnetized in the presence of a [[magnetic field]].
===Combustion===
In a [[zero-gravity]] environment, there can be no buoyancy forces, and thus no convection possible, so flames in many circumstances without gravity smother in their own waste gases. Thermal expansion and chemical reactions resulting in expansion and contraction gases allows for ventilation of the flame, as waste gases are displaced by cool, fresh, oxygen-rich gas. moves in to take up the low pressure zones created when flame-exhaust water condenses.
==Examples and applications==
Systems of natural circulation include [[tornado]]es and other [[weather|weather systems]], [[ocean current]]s, and household [[Ventilation (architecture)|ventilation]]. Some solar water heaters use natural circulation. The [[Gulf Stream]] circulates as a result of the evaporation of water. In this process, the water increases in salinity and density. In the North Atlantic Ocean, the water becomes so dense that it begins to sink down.
Convection occurs on a large scale in [[Earth atmosphere|atmosphere]]s, oceans, [[planet]]ary [[Mantle (geology)|mantle]]s, and it provides the mechanism of heat transfer for a large fraction of the outermost interiors of the Sun and all stars. Fluid movement during convection may be invisibly slow, or it may be obvious and rapid, as in a [[hurricane]]. On astronomical scales, convection of gas and dust is thought to occur in the accretion disks of [[black hole]]s, at speeds which may closely approach that of light.
===Demonstration experiments===
[[File:Thermal circulation.png|thumb|Thermal circulation of air masses]]
Thermal convection in liquids can be demonstrated by placing a heat source (for example, a [[Bunsen burner]]) at the side of a container with a liquid. Adding a dye to the water (such as food colouring) will enable visualisation of the flow.<ref>{{Citation|title=Convection Experiment - GCSE Physics|url=https://www.youtube.com/watch?v=MBFUfld_5i0| archive-url=https://ghostarchive.org/varchive/youtube/20211211/MBFUfld_5i0| archive-date=2021-12-11 | url-status=live|language=en|access-date=2021-05-11}}{{cbignore}}</ref><ref>{{Citation|title=Convection Experiment|url=https://www.youtube.com/watch?v=B8H06ZA2xmo| archive-url=https://ghostarchive.org/varchive/youtube/20211211/B8H06ZA2xmo| archive-date=2021-12-11 | url-status=live|language=en|access-date=2021-05-11}}{{cbignore}}</ref>
Another common experiment to demonstrate thermal convection in liquids involves submerging open containers of hot and cold liquid coloured with dye into a large container of the same liquid without dye at an intermediate temperature (for example, a jar of hot tap water coloured red, a jar of water chilled in a fridge coloured blue, lowered into a clear tank of water at room temperature).<ref>{{Citation|title=Convection Current Lab Demo|url=https://www.youtube.com/watch?v=JBGT6UPTgWE| archive-url=https://ghostarchive.org/varchive/youtube/20211211/JBGT6UPTgWE| archive-date=2021-12-11 | url-status=live|language=en|access-date=2021-05-11}}{{cbignore}}</ref>
A third approach is to use two identical jars, one filled with hot water dyed one colour, and cold water of another colour. One jar is then temporarily sealed (for example, with a piece of card), inverted and placed on top of the other. When the card is removed, if the jar containing the warmer liquid is placed on top no convection will occur. If the jar containing colder liquid is placed on top, a convection current will form spontaneously.<ref>{{Citation|title=Colorful Convection Currents - Sick Science! #075|url=https://www.youtube.com/watch?v=RCO90hvEL1I| archive-url=https://ghostarchive.org/varchive/youtube/20211211/RCO90hvEL1I| archive-date=2021-12-11 | url-status=live|language=en|access-date=2021-05-11}}{{cbignore}}</ref>
Convection in gases can be demonstrated using a candle in a sealed space with an inlet and exhaust port. The heat from the candle will cause a strong convection current which can be demonstrated with a flow indicator, such as smoke from another candle, being released near the inlet and exhaust areas respectively.<ref>{{Citation|title=Convection in gases|url=https://www.youtube.com/watch?v=6VZZtB7yjmA| archive-url=https://ghostarchive.org/varchive/youtube/20211211/6VZZtB7yjmA| archive-date=2021-12-11 | url-status=live|language=en|access-date=2021-05-11}}{{cbignore}}</ref>
===Double diffusive convection===
{{main|Double diffusive convection}}
===Convection cells===
{{main|Convection cell}}
[[File:ConvectionCells.svg|thumb|right|300px|Convection cells in a gravity field]]
A '''convection cell''', also known as a '''[[Bénard cell]]''', is a characteristic fluid flow pattern in many convection systems. A rising body of fluid typically loses heat because it encounters a colder surface. In liquid, this occurs because it exchanges heat with colder liquid through direct exchange. In the example of the Earth's atmosphere, this occurs because it radiates heat. Because of this heat loss the fluid becomes denser than the fluid underneath it, which is still rising. Since it cannot descend through the rising fluid, it moves to one side. At some distance, its downward force overcomes the rising force beneath it, and the fluid begins to descend. As it descends, it warms again and the cycle repeats itself. Additionally, convection cells can arise due to density variations resulting from differences in the composition of electrolytes.<ref>{{cite journal |last1=Colli |first1=A.N. |last2=Bisang |first2=J.M. |title=Exploring the Impact of Concentration and Temperature Variations on Transient Natural Convection in Metal Electrodeposition: A Finite Volume Method Analysis |journal=Journal of the Electrochemical Society |date=2023 |volume=170 |issue=8 |pages=083505 |doi=10.1149/1945-7111/acef62 |bibcode=2023JElS..170h3505C |s2cid=260857287 |url=https://iopscience.iop.org/article/10.1149/1945-7111/acef62/meta}}</ref>
===Atmospheric convection===
{{main|Atmospheric convection}}
====Atmospheric circulation====
{{main|Atmospheric circulation}}
[[File:Earth Global Circulation.jpg|thumb|300px|left|Idealised depiction of the global circulation on Earth]]
'''Atmospheric circulation''' is the large-scale movement of air, and is a means by which [[thermal energy]] is distributed on the surface of the [[Earth]], together with the much slower (lagged) ocean circulation system. The large-scale structure of the [[atmospheric circulation]] varies from year to year, but the basic climatological structure remains fairly constant.
Latitudinal circulation occurs because incident solar [[radiation]] per unit area is highest at the [[heat equator]], and decreases as the [[latitude]] increases, reaching minima at the poles. It consists of two primary convection cells, the [[Hadley cell]] and the [[polar vortex]], with the [[Hadley cell]] experiencing stronger convection due to the release of [[latent heat]] energy by [[condensation]] of [[water vapor]] at higher altitudes during cloud formation.
Longitudinal circulation, on the other hand, comes about because the [[ocean]] has a higher specific heat capacity than land (and also [[thermal conductivity]], allowing the heat to penetrate further beneath the surface ) and thereby absorbs and releases more [[heat]], but the [[temperature]] changes less than land. This brings the sea breeze, air cooled by the water, ashore in the day, and carries the land breeze, air cooled by contact with the ground, out to sea during the night. Longitudinal circulation consists of two cells, the [[Walker circulation]] and [[El Niño-Southern Oscillation|El Niño / Southern Oscillation]].
{{clear}}
====Weather====
{{see also|Cloud|Thunderstorm|Wind}}
[[File:foehn1.svg|right|thumb|300px|How Foehn is produced]]
Some more localized phenomena than global atmospheric movement are also due to convection, including wind and some of the [[hydrologic cycle]]. For example, a [[foehn wind]] is a down-slope wind which occurs on the downwind side of a mountain range. It results from the [[adiabatic]] warming of air which has dropped most of its moisture on windward slopes.<ref name="MT">{{cite web|first=Michael|last=Pidwirny|year=2008|url=http://www.physicalgeography.net/fundamentals/8e.html|title=CHAPTER 8: Introduction to the Hydrosphere (e). Cloud Formation Processes|publisher=Physical Geography|access-date=2009-01-01|url-status=dead|archive-url=https://web.archive.org/web/20081220230524/http://www.physicalgeography.net/fundamentals/8e.html|archive-date=2008-12-20}}</ref> Because of the different adiabatic lapse rates of moist and dry air, the air on the leeward slopes becomes warmer than at the same height on the windward slopes.
A [[thermal column]] (or thermal) is a vertical section of rising air in the lower altitudes of the Earth's atmosphere. Thermals are created by the uneven heating of the Earth's surface from solar radiation. The Sun warms the ground, which in turn warms the air directly above it. The warmer air expands, becoming less dense than the surrounding air mass, and creating a [[thermal low]].<ref>{{cite web|agency=National Weather Service Forecast Office in [[Tucson, Arizona]]|year=2008|url=http://www.wrh.noaa.gov/twc/monsoon/monsoon_whatis.php|title=What is a monsoon?|publisher=National Weather Service Western Region Headquarters|access-date=2009-03-08|url-status=live|archive-url=https://web.archive.org/web/20120623140647/http://www.wrh.noaa.gov/twc/monsoon/monsoon_whatis.php|archive-date=2012-06-23}}</ref><ref>{{cite journal|first1 = Douglas G. | last1 = Hahn | author2-link = Syukuro Manabe | first2 = Syukuro | last2 = Manabe |year=1975|bibcode=1975JAtS...32.1515H|title=The Role of Mountains in the South Asian Monsoon Circulation|journal=[[Journal of the Atmospheric Sciences]]|volume=32|issue=8|pages=1515–1541|doi=10.1175/1520-0469(1975)032<1515:TROMIT>2.0.CO;2|issn=1520-0469|doi-access=free}}</ref> The mass of lighter air rises, and as it does, it cools by expansion at lower air pressures. It stops rising when it has cooled to the same temperature as the surrounding air. Associated with a thermal is a downward flow surrounding the thermal column. The downward moving exterior is caused by colder air being displaced at the top of the thermal. Another convection-driven weather effect is the [[sea breeze]].<ref>University of Wisconsin. [http://cimss.ssec.wisc.edu/wxwise/seabrz.html Sea and Land Breezes.] {{webarchive|url=https://web.archive.org/web/20120704184333/http://cimss.ssec.wisc.edu/wxwise/seabrz.html |date=2012-07-04 }} Retrieved on 2006-10-24.</ref><ref name="Jet">JetStream: An Online School For Weather (2008). [http://www.srh.weather.gov/srh/jetstream/ocean/seabreezes.htm The Sea Breeze.] {{webarchive|url=https://web.archive.org/web/20060923233344/http://www.srh.weather.gov/srh/jetstream/ocean/seabreezes.htm |date=2006-09-23 }} [[National Weather Service]]. Retrieved on 2006-10-24.</ref>
[[File:Thunderstorm formation.jpg|thumb|500px|Stages of a thunderstorm's life.]]
Warm air has a lower density than cool air, so warm air rises within cooler air,<ref>{{cite book|url=https://books.google.com/books?id=PDtIAAAAIAAJ&pg=PA462 |title=Civil engineers' pocket book: a reference-book for engineers, contractors|first = Albert Irvin | last = Frye|page=462|publisher=D. Van Nostrand Company|year=1913|access-date=2009-08-31}}</ref> similar to [[hot air balloon]]s.<ref>{{cite book
| url = https://books.google.com/books?id=ssO_19TRQ9AC&q=Kongming+balloon&pg=PA112
| title = Ancient Chinese Inventions
| first = Yikne | last = Deng
| publisher = Chinese International Press
| isbn=978-7-5085-0837-5
| year=2005
| pages = 112–13
| access-date = 2009-06-18}}</ref> Clouds form as relatively warmer air carrying moisture rises within cooler air. As the moist air rises, it cools, causing some of the [[water vapor]] in the rising packet of air to [[condensation|condense]].<ref>{{cite web|agency=FMI|year=2007|url=http://www.zamg.ac.at/docu/Manual/SatManu/main.htm?/docu/Manual/SatManu/CMs/FgStr/backgr.htm|title=Fog And Stratus – Meteorological Physical Background|publisher=Zentralanstalt für Meteorologie und Geodynamik|access-date=2009-02-07|url-status=live|archive-url=https://web.archive.org/web/20110706085616/http://www.zamg.ac.at/docu/Manual/SatManu/main.htm?%2Fdocu%2FManual%2FSatManu%2FCMs%2FFgStr%2Fbackgr.htm|archive-date=2011-07-06}}</ref> When the moisture condenses, it releases energy known as [[latent heat]] of condensation which allows the rising packet of air to cool less than its surrounding air,<ref>{{cite book|url=https://books.google.com/books?id=RRSzR4NQdGkC&pg=PA20 |title=Storm world: hurricanes, politics, and the battle over global warming| first = Chris C. | last = Mooney|page=20|isbn=978-0-15-101287-9|publisher=Houghton Mifflin Harcourt|year=2007|access-date=2009-08-31}}</ref> continuing the cloud's ascension. If enough [[Convective available potential energy|instability]] is present in the atmosphere, this process will continue long enough for [[Cumulonimbus|cumulonimbus clouds]] to form, which support lightning and thunder. Generally, thunderstorms require three conditions to form: moisture, an unstable airmass, and a lifting force (heat).
All [[thunderstorm]]s, regardless of type, go through three stages: the '''developing stage''', the '''mature stage''', and the '''dissipation stage'''.<ref name="Extreme Weather">{{cite book |title=Extreme Weather |first=Michael H. |last=Mogil |year=2007 |publisher=Black Dog & Leventhal Publisher |location=New York |isbn=978-1-57912-743-5 |pages=[https://archive.org/details/extremeweatherun0000mogi/page/210 210–211] |url=https://archive.org/details/extremeweatherun0000mogi/page/210 }}</ref> The average thunderstorm has a {{convert|24|km|mi|abbr=on}} diameter. Depending on the conditions present in the atmosphere, these three stages take an average of 30 minutes to go through.<ref name="tsbasics">{{cite web|url=http://www.nssl.noaa.gov/primer/tstorm/tst_basics.html|title=A Severe Weather Primer: Questions and Answers about Thunderstorms|agency=National Severe Storms Laboratory|publisher=[[National Oceanic and Atmospheric Administration]]|date=2006-10-15|access-date=2009-09-01|url-status=dead|archive-url=https://web.archive.org/web/20090825000832/http://www.nssl.noaa.gov/primer/tstorm/tst_basics.html|archive-date=2009-08-25}}</ref>
===Oceanic circulation===
{{Main|Gulf Stream|Thermohaline circulation}}
[[File:Conveyor belt.svg|Ocean currents|thumb|200px|right]]
Solar radiation affects the oceans: warm water from the Equator tends to circulate toward the [[geographical pole|pole]]s, while cold polar water heads towards the Equator. The surface currents are initially dictated by surface wind conditions. The [[trade winds]] blow westward in the tropics,<ref>{{cite web |title=trade winds |work=Glossary of Meteorology |publisher=American Meteorological Society |year=2009 |access-date=2008-09-08 |url=http://amsglossary.allenpress.com/glossary/search?id=trade-winds1 |url-status=dead |archive-url=https://web.archive.org/web/20081211050708/http://amsglossary.allenpress.com/glossary/search?id=trade-winds1 |archive-date=2008-12-11 }}</ref> and the [[westerlies]] blow eastward at mid-latitudes.<ref>Glossary of Meteorology (2009). [http://amsglossary.allenpress.com/glossary/search?id=westerlies1 Westerlies.] {{webarchive|url=https://web.archive.org/web/20100622073904/http://amsglossary.allenpress.com/glossary/search?id=westerlies1 |date=2010-06-22 }} [[American Meteorological Society]]. Retrieved on 2009-04-15.</ref> This wind pattern applies a [[stress (physics)|stress]] to the subtropical ocean surface with negative [[curl (mathematics)|curl]] across the [[Northern Hemisphere]],<ref>Matthias Tomczak and J. Stuart Godfrey (2001). [http://www.es.flinders.edu.au/~mattom/regoc/pdffiles/colour/double/04P-Ekman-left.pdf Regional Oceanography: an Introduction.] {{webarchive|url=https://web.archive.org/web/20090914120630/http://www.es.flinders.edu.au/~mattom/regoc/pdffiles/colour/double/04P-Ekman-left.pdf |date=2009-09-14 }} Matthias Tomczak, pp. 42. {{ISBN|81-7035-306-8}}. Retrieved on 2009-05-06.</ref> and the reverse across the [[Southern Hemisphere]]. The resulting [[Sverdrup transport]] is equatorward.<ref>Earthguide (2007). [http://earthguide.ucsd.edu/parkerprogram/berger/pdf/OcnBasLesson06.pdf Lesson 6: Unraveling the Gulf Stream Puzzle - On a Warm Current Running North.] {{webarchive|url=https://web.archive.org/web/20080723104316/http://earthguide.ucsd.edu/parkerprogram/berger/pdf/OcnBasLesson06.pdf |date=2008-07-23 }} [[University of California]] at San Diego. Retrieved on 2009-05-06.</ref> Because of conservation of [[potential vorticity]] caused by the poleward-moving winds on the [[subtropical ridge]]'s western periphery and the increased relative vorticity of poleward moving water, transport is balanced by a narrow, accelerating poleward current, which flows along the western boundary of the ocean basin, outweighing the effects of friction with the cold western boundary current which originates from high latitudes.<ref>Angela Colling (2001). [https://books.google.com/books?id=tFJRLhSez_YC&pg=PA90 Ocean circulation.] {{webarchive|url=https://web.archive.org/web/20180302144439/https://books.google.com/books?id=tFJRLhSez_YC&pg=PA90 |date=2018-03-02 }} Butterworth-Heinemann, pp. 96. Retrieved on 2009-05-07.</ref> The overall process, known as western intensification, causes currents on the western boundary of an ocean basin to be stronger than those on the eastern boundary.<ref>National Environmental Satellite, Data, and Information Service (2009). [http://www.science-house.org/nesdis/gulf/background.html Investigating the Gulf Stream.] {{webarchive|url=https://web.archive.org/web/20100503013457/http://www.science-house.org/nesdis/gulf/background.html |date=2010-05-03 }} [[North Carolina State University]]. Retrieved on 2009-05-06.</ref>
As it travels poleward, warm water transported by strong warm water current undergoes evaporative cooling. The cooling is wind driven: wind moving over water cools the water and also causes [[evaporation]], leaving a saltier brine. In this process, the water becomes saltier and denser. and decreases in temperature. Once sea ice forms, salts are left out of the ice, a process known as brine exclusion.<ref>{{cite web |last=Russel |first=Randy |title=Thermohaline Ocean Circulation |url=http://www.windows.ucar.edu/tour/link=/earth/Water/thermohaline_ocean_circulation.html |publisher=University Corporation for Atmospheric Research |access-date=2009-01-06 |url-status=live |archive-url=https://web.archive.org/web/20090325062339/http://www.windows.ucar.edu/tour/link=/earth/Water/thermohaline_ocean_circulation.html |archive-date=2009-03-25 }}</ref> These two processes produce water that is denser and colder. The water across the northern [[Atlantic Ocean]] becomes so dense that it begins to sink down through less salty and less dense water. (This [[open ocean convection]] is not unlike that of a [[lava lamp]].) This downdraft of heavy, cold and dense water becomes a part of the [[North Atlantic Deep Water]], a south-going stream.<ref>{{cite web |last=Behl |first=R. |title=Atlantic Ocean water masses |url=http://seis.natsci.csulb.edu/rbehl/NADW.htm |publisher=[[California State University]] Long Beach |access-date=2009-01-06|archive-url = https://web.archive.org/web/20080523170145/http://seis.natsci.csulb.edu/rbehl/NADW.htm |archive-date = May 23, 2008|url-status=dead}}</ref>
{{clear}}
===Mantle convection===
{{main|Mantle convection}}
[[File:Accretion-Subduction.PNG|thumb|right|250px|An [[oceanic plate]] is added to by upwelling (left) and consumed at a [[subduction]] zone (right).]]
'''Mantle convection''' is the slow creeping motion of Earth's rocky mantle caused by convection currents carrying heat from the interior of the Earth to the surface.<ref name="University of Winnipeg">{{cite web | date = 2002-12-16 | last1 = Kobes | first1 = Randy | first2 = Gabor | last2 = Kunstatter | url = http://theory.uwinnipeg.ca/mod_tech/node195.html | title = Mantle Convection | publisher = Physics Department, University of Winnipeg | access-date = 2010-01-03 | url-status = dead | archive-url = https://web.archive.org/web/20110114151750/http://theory.uwinnipeg.ca/mod_tech/node195.html | archive-date = 2011-01-14 }}</ref> It is one of 3 driving forces that causes tectonic plates to move around the Earth's surface.<ref name=Condie>{{cite book |title=Plate tectonics and crustal evolution |first=Kent C. |last=Condie |url=https://books.google.com/books?id=HZrA6OQzsvgC&pg=PA5 |page=5 |isbn=978-0-7506-3386-4 |year=1997 |edition=4th |publisher=Butterworth-Heinemann |url-status=live |archive-url=https://web.archive.org/web/20131029161501/http://books.google.com/books?id=HZrA6OQzsvgC&pg=PA5 |archive-date=2013-10-29 }}</ref>
The Earth's surface is divided into a number of [[tectonic]] plates that are continuously being created and consumed at their opposite plate boundaries. Creation ([[Accretion (geology)|accretion]]) occurs as mantle is added to the growing edges of a plate. This hot added material cools down by conduction and convection of heat. At the consumption edges of the plate, the material has thermally contracted to become dense, and it sinks under its own weight in the process of subduction at an ocean trench. This subducted material sinks to some depth in the Earth's interior where it is prohibited from sinking further. The subducted oceanic crust triggers volcanism.
Convection within [[Earth's mantle]] is the driving force for [[plate tectonics]]. Mantle convection is the result of a thermal gradient: the lower mantle is hotter than the [[upper mantle (Earth)|upper mantle]], and is therefore less dense. This sets up two primary types of instabilities. In the first type, plumes rise from the lower mantle, and corresponding unstable regions of [[lithosphere]] drip back into the mantle. In the second type, subducting oceanic plates (which largely constitute the upper thermal boundary layer of the mantle) plunge back into the mantle and move downwards towards the [[core-mantle boundary]]. Mantle convection occurs at rates of centimeters per year, and it takes on the order of hundreds of millions of years to complete a cycle of convection.
Neutrino flux measurements from the Earth's core (see [[kamLAND]]) show the source of about two-thirds of the heat in the inner core is the [[radioactive decay]] of [[potassium|<sup>40</sup>K]], uranium and thorium. This has allowed plate tectonics on Earth to continue far longer than it would have if it were simply driven by heat left over from Earth's formation; or with heat produced from [[gravitational energy|gravitational potential energy]], as a result of physical rearrangement of denser portions of the Earth's interior toward the center of the planet (that is, a type of prolonged falling and settling).
{{clear}}
===Stack effect===
{{Main|Stack effect}}
The '''Stack effect''' or '''chimney effect''' is the movement of air into and out of buildings, chimneys, flue gas stacks, or other containers due to buoyancy. Buoyancy occurs due to a difference in indoor-to-outdoor air density resulting from temperature and moisture differences. The greater the thermal difference and the height of the structure, the greater the buoyancy force, and thus the stack effect. The stack effect helps drive natural ventilation and infiltration. Some [[cooling tower]]s operate on this principle; similarly the [[solar updraft tower]] is a proposed device to generate electricity based on the stack effect.
===Stellar physics===
{{main|Convection zone|granule (solar physics)}}
[[File:Structure of Stars (artist’s impression).jpg|thumb|right|300px|An illustration of the structure of the [[Sun]] and a [[red giant]] star, showing their convective zones. These are the granular zones in the outer layers of these stars.]]
The convection zone of a star is the range of radii in which energy is transported outward from the [[stellar core|core region]] primarily by convection rather than [[Radiation zone|radiation]]. This occurs at radii which are sufficiently [[Opacity (optics)|opaque]] that convection is more efficient than radiation at transporting energy.<ref>{{cite book
| title=Discovering the Cosmos
| first=Robert C. | last=Bless | year=1996
| page=310 | isbn=9780935702675
| publisher=University Science Books
| url=https://books.google.com/books?id=jC47sk3mfjcC&pg=PA310 }}</ref>
Granules on the [[photosphere]] of the Sun are the visible tops of convection cells in the photosphere, caused by convection of [[plasma (physics)|plasma]] in the photosphere. The rising part of the granules is located in the center where the plasma is hotter. The outer edge of the granules is darker due to the cooler descending plasma. A typical granule has a diameter on the order of 1,000 kilometers and each lasts 8 to 20 minutes before dissipating. Below the photosphere is a layer of much larger "supergranules" up to 30,000 kilometers in diameter, with lifespans of up to 24 hours.
{{clear}}
===Water convection at freezing temperatures===
[[Water]] is a fluid that does not obey the Boussinesq approximation.<ref name=":0">{{Cite journal|last1=Banaszek|first1=J.|last2=Jaluria|first2=Y.|last3=Kowalewski|first3=T. A.|last4=Rebow|first4=M.|date=1999-10-01|journal=Numerical Heat Transfer, Part A: Applications|language=en|volume=36|issue=5|pages=449–472|doi=10.1080/104077899274624|issn=1040-7782|title=Semi-Implicit Fem Analysis of Natural Convection in Freezing Water|bibcode=1999NHTA...36..449B|s2cid=3740709 }}</ref> This is because its density varies nonlinearly with temperature, which causes its thermal expansion coefficient to be inconsistent near freezing temperatures.<ref>{{Cite web|url=https://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html|title=Water - Density, Specific Weight and Thermal Expansion Coefficient|website=www.engineeringtoolbox.com|language=en|access-date=2018-12-01}}</ref><ref name=":1">{{Cite news|url=http://polymer.bu.edu/hes/articles/ds03.pdf |archive-url=https://web.archive.org/web/20060301224729/http://polymer.bu.edu/hes/articles/ds03.pdf |archive-date=2006-03-01 |url-status=live|title=Supercooled and Glassy Water|last1=Debenedetti|first1=Pablo G.|date=June 2003|work=Physics Today|access-date=1 December 2018|last2=Stanley|first2=H. Eugene}}</ref> The [[density of water]] reaches a maximum at 4 °C and decreases as the temperature deviates. This phenomenon is investigated by experiment and numerical methods.<ref name=":0" /> Water is initially stagnant at 10 °C within a square cavity. It is differentially heated between the two vertical walls, where the left and right walls are held at 10 °C and 0 °C, respectively. The density anomaly manifests in its flow pattern.<ref name=":0" /><ref>{{Cite journal|last1=Giangi|first1=Marilena|last2=Stella|first2=Fulvio|last3=Kowalewski|first3=Tomasz A.|date=December 1999|title=Phase change problems with free convection: fixed grid numerical simulation|journal=Computing and Visualization in Science|language=en|volume=2|issue=2–3|pages=123–130|doi=10.1007/s007910050034|issn=1432-9360|citeseerx=10.1.1.31.9300|s2cid=3756976 }}</ref><ref>{{Cite journal|last1=Tong|first1=Wei|last2=Koster|first2=Jean N.|date=December 1993|title=Natural convection of water in a rectangular cavity including density inversion|journal=International Journal of Heat and Fluid Flow|volume=14|issue=4|pages=366–375|doi=10.1016/0142-727x(93)90010-k|issn=0142-727X}}</ref><ref>{{Cite journal|last1=Ezan|first1=Mehmet Akif|last2=Kalfa|first2=Mustafa|date=October 2016|title=Numerical investigation of transient natural convection heat transfer of freezing water in a square cavity|journal=International Journal of Heat and Fluid Flow|volume=61|pages=438–448|doi=10.1016/j.ijheatfluidflow.2016.06.004|issn=0142-727X}}</ref> As the water is cooled at the right wall, the density increases, which accelerates the flow downward. As the flow develops and the water cools further, the decrease in density causes a recirculation current at the bottom right corner of the cavity.
Another case of this phenomenon is the event of [[Supercooling|super-cooling]], where the water is cooled to below freezing temperatures but does not immediately begin to freeze.<ref name=":1" /><ref name=":2">{{Cite journal|last1=Moore|first1=Emily B.|last2=Molinero|first2=Valeria|date=November 2011|title=Structural transformation in supercooled water controls the crystallization rate of ice|journal=Nature|language=En|volume=479|issue=7374|pages=506–508|doi=10.1038/nature10586|pmid=22113691|issn=0028-0836|arxiv=1107.1622|bibcode=2011Natur.479..506M|s2cid=1784703 }}</ref> Under the same conditions as before, the flow is developed. Afterward, the temperature of the right wall is decreased to −10 °C. This causes the water at that wall to become supercooled, create a counter-clockwise flow, and initially overpower the warm current.<ref name=":0" /> This plume is caused by a delay in the [[Nucleation of ice|nucleation of the ice]].<ref name=":0" /><ref name=":1" /><ref name=":2" /> Once ice begins to form, the flow returns to a similar pattern as before and the solidification propagates gradually until the flow is redeveloped.<ref name=":0" />
===Nuclear reactors===
In a [[nuclear reactor]], natural circulation can be a design criterion. It is achieved by reducing turbulence and friction in the fluid flow (that is, minimizing [[head loss]]), and by providing a way to remove any inoperative pumps from the fluid path. Also, the reactor (as the heat source) must be physically lower than the steam generators or turbines (the heat sink). In this way, natural circulation will ensure that the fluid will continue to flow as long as the reactor is hotter than the heat sink, even when power cannot be supplied to the pumps. Notable examples are the [[S5G reactor|S5G]]
<ref>{{cite web| url=http://www.chinfo.navy.mil/navpalib/cno/n87/history/tech-3.html| publisher=Chief of Naval Operations Submarine Warfare Division| title=Technical Innovations of the Submarine Force| access-date=2006-03-12| url-status=dead| archive-url=https://web.archive.org/web/20060127003651/http://www.chinfo.navy.mil/navpalib/cno/n87/history/tech-3.html| archive-date=2006-01-27}}</ref><ref>{{cite web| url=http://ar.inel.gov/images/pdf/200506/2005061600214ALL.pdf| title=Appendix C, Attachment to NR:IBO-05/023, Evaluation of Naval Reactors Facility Radioactive Waste Disposed of at the Radioactive Waste Management Complex| access-date=2006-03-12| archive-url=https://web.archive.org/web/20120204154809/http://ar.inel.gov/images/pdf/200506/2005061600214ALL.pdf| archive-date=2012-02-04| url-status=dead}}</ref><ref>{{cite book |last1=Jones |first1=Edward Monroe |last2=Roderick |first2=Shawn S. |title=Submarine Torpedo Tactics: An American History |date=4 November 2014 |publisher=McFarland |isbn=978-0-7864-9646-4 |page=153 |url=https://books.google.com/books?id=6F6QBQAAQBAJ |language=en}}</ref>
and [[S8G reactor|S8G]]<ref>{{cite web| url=http://ship.bsu.by/main.asp?id=100092| script-title=ru:Энциклопедия кораблей /Ракетные ПЛ /Огайо| access-date=2006-03-12| language=ru| archive-date=2006-07-14| archive-url=https://web.archive.org/web/20060714151444/http://ship.bsu.by/main.asp?id=100092| url-status=dead}}</ref><ref>{{cite web| url=http://www.submarinesonstamps.co.il/openhist.php?ID=269| title=The Ohio, US Navy's nuclear-powered ballistic missile submarine| access-date=2006-03-12 |archive-url = https://web.archive.org/web/20060720075350/http://www.submarinesonstamps.co.il/openhist.php?ID=269 <!-- Bot retrieved archive --> |archive-date = 2006-07-20}}</ref><ref>{{cite web| url=http://tech.military.com/equipment/viewEquipment.do?eq_id=89213| title=Members-only feature, registration required| access-date=2006-03-12| archive-url=https://web.archive.org/web/20070223130956/http://tech.military.com/equipment/viewEquipment.do?eq_id=89213| archive-date=2007-02-23| url-status=dead}}</ref> [[United States Naval reactor]]s, which were designed to operate at a significant fraction of full power under natural circulation, quieting those propulsion plants. The [[S6G reactor]] cannot operate at power under natural circulation, but can use it to maintain emergency cooling while shut down.
By the nature of natural circulation, fluids do not typically move very fast, but this is not necessarily bad, as high flow rates are not essential to safe and effective reactor operation. In modern design nuclear reactors, flow reversal is almost impossible. All nuclear reactors, even ones designed to primarily use natural circulation as the main method of fluid circulation, have pumps that can circulate the fluid in the case that natural circulation is not sufficient.
==Mathematical models of convection==
A number of dimensionless terms have been derived to describe and predict convection, including the [[Archimedes number]], [[Grashof number]], [[Richardson number]], and the [[Rayleigh number]].
In cases of mixed convection (natural and forced occurring together) one would often like to know how much of the convection is due to external constraints, such as the fluid velocity in the pump, and how much is due to natural convection occurring in the system.
The relative magnitudes of the [[Grashof number]] and the square of the [[Reynolds number]] determine which form of convection dominates. If <math>\rm Gr/Re^2 \gg 1 </math>, forced convection may be neglected, whereas if <math>\rm Gr/Re^2 \ll 1 </math>, natural convection may be neglected. If the ratio, known as the [[Richardson number#Thermal convection|Richardson number]], is approximately one, then both forced and natural convection need to be taken into account.
===Onset===
{{See also|Heat transfer}}
The onset of natural convection is determined by the [[Rayleigh number]] ('''Ra'''). This [[dimensionless number]] is given by
:<math>\textbf{Ra} = \frac{\Delta\rho g L^3}{D\mu}</math>
where
*<math>\Delta \rho</math> is the difference in density between the two parcels of material that are mixing
*<math>g</math> is the local [[gravitational acceleration]]
*<math>L</math> is the characteristic length-scale of convection: the depth of the boiling pot, for example
*<math>D</math> is the [[diffusivity]] of the characteristic that is causing the convection, and
*<math>\mu</math> is the [[dynamic viscosity]].
Natural convection will be more likely and/or more rapid with a greater variation in density between the two fluids, a larger acceleration due to gravity that drives the convection, and/or a larger distance through the convecting medium. Convection will be less likely and/or less rapid with more rapid diffusion (thereby diffusing away the gradient that is causing the convection) and/or a more viscous (sticky) fluid.
For thermal convection due to heating from below, as described in the boiling pot above, the equation is modified for thermal expansion and thermal diffusivity. Density variations due to thermal expansion are given by:
:<math>\Delta\rho=\rho_0 \beta \Delta T</math>
where
*<math>\rho_0</math> is the reference density, typically picked to be the average density of the medium,
*<math>\beta</math> is the [[coefficient of thermal expansion]], and
*<math>\Delta T</math> is the temperature difference across the medium.
The general diffusivity, <math>D</math>, is redefined as a [[thermal diffusivity]], <math>\alpha</math>.
:<math>D=\alpha</math>
Inserting these substitutions produces a Rayleigh number that can be used to predict thermal convection.<ref>{{cite book|isbn=978-0-521-66624-4|author1=Donald L. Turcotte |author2=Gerald Schubert. |year=2002|publisher=Cambridge University Press|location=Cambridge|title=Geodynamics}}</ref>
:<math>\textbf{Ra} = \frac{\rho_0 g \beta \Delta T L^3}{\alpha \mu}</math>
===Turbulence===
The tendency of a particular naturally convective system towards turbulence relies on the [[Grashof number]] (Gr).<ref>{{cite book |author1=Kays, William |author2=Crawford, Michael |author3=Weigand, Bernhard | title=Convective Heat and Mass Transfer, 4E | publisher=McGraw-Hill Professional | year=2004 | isbn=978-0072990737}}</ref>
:<math> Gr= \frac{g \beta \Delta T L^3}{\nu^2} </math>
In very sticky, viscous fluids (large ''ν''), fluid motion is restricted, and natural convection will be non-turbulent.
Following the treatment of the previous subsection, the typical fluid velocity is of the order of <math>g \Delta \rho L^2 / \mu</math>, up to a numerical factor depending on the geometry of the system. Therefore, Grashof number can be thought of as [[Reynolds number]] with the velocity of natural convection replacing the velocity in Reynolds number's formula. However In practice, when referring to the Reynolds number, it is understood that one is considering forced convection, and the velocity is taken as the velocity dictated by external constraints (see below).
===Behavior===
The [[Grashof number]] can be formulated for natural convection occurring due to a [[concentration gradient]], sometimes termed thermo-solutal convection. In this case, a concentration of hot fluid diffuses into a cold fluid, in much the same way that ink poured into a container of water diffuses to dye the entire space. Then:
:<math> Gr= \frac{g \beta \Delta C L^3}{\nu^2} </math>
Natural convection is highly dependent on the geometry of the hot surface, various correlations exist in order to determine the heat transfer coefficient.
A general correlation that applies for a variety of geometries is
: <math>Nu = \left[Nu_0^\frac{1}{2} + Ra^ \frac{1}{6} \left(\frac {f_4\left(Pr\right)}{300}\right)^\frac{1}{6} \right]^2 </math>
The value of f<sub>4</sub>(Pr) is calculated using the following formula
: <math>f_4(Pr)= \left[1+ \left ( \frac {0.5}{Pr} \right )^\frac{9}{16} \right]^\frac{-16}{9}</math>
Nu is the [[Nusselt number]] and the values of Nu<sub>0</sub> and the characteristic length used to calculate Re are listed below (see also Discussion):
{| class="wikitable"
|-
! '''Geometry'''
! '''Characteristic length'''
! '''Nu<sub>0</sub>'''
|-
| Inclined plane
| x (Distance along plane)
| 0.68
|-
| Inclined disk
| 9D/11 (D = diameter)
| 0.56
|-
| Vertical cylinder
| x (height of cylinder)
| 0.68
|-
| Cone
| 4x/5 (x = distance along sloping surface)
| 0.54
|-
| Horizontal cylinder
| <math>\pi D/2</math> (D = diameter of cylinder)
| 0.36<math>\pi</math>
|}
'''Warning''': The values indicated for the '''Horizontal cylinder''' are '''wrong'''; see discussion.
==Natural convection from a vertical plate==
One example of natural convection is heat transfer from an isothermal vertical plate immersed in a fluid, causing the fluid to move parallel to the plate. This will occur in any system wherein the density of the moving fluid varies with position. These phenomena will only be of significance when the moving fluid is minimally affected by forced convection.<ref name=unitop>{{cite book | author= W. McCabe J. Smith | title=Unit Operations of Chemical Engineering | publisher=McGraw-Hill | year=1956 | isbn= 978-0-07-044825-4}}</ref>
When considering the flow of fluid is a result of heating, the following correlations can be used, assuming the fluid is an ideal diatomic, has adjacent to a vertical plate at constant temperature and the flow of the fluid is completely laminar.<ref name=bennett>{{cite book | author=Bennett | title=Momentum, Heat and Mass Transfer | url=https://archive.org/details/momentumheatmass00benn | url-access=registration | publisher=McGraw-Hill | year=1962 | isbn = 978-0-07-004667-2 }}</ref>
Nu<sub>m</sub> = 0.478(Gr<sup>0.25</sup>)<ref name=bennett />
Mean [[Nusselt number]] = Nu<sub>m</sub> = h<sub>m</sub>L/k<ref name=bennett />
where
*h<sub>m</sub> = mean coefficient applicable between the lower edge of the plate and any point in a distance L (W/m<sup>2</sup>. K)
*L = height of the vertical surface (m)
*k = thermal conductivity (W/m. K)
[[Grashof number]] = Gr = <math>[gL^3(t_s-t_\infty)]/v^2T</math> <ref name=unitop /><ref name=bennett />
where
*g = gravitational acceleration (m/s<sup>2</sup>)
*L = distance above the lower edge (m)
*t<sub>s</sub> = temperature of the wall (K)
*t∞ = fluid temperature outside the thermal boundary layer (K)
*v = kinematic viscosity of the fluid (m<sup>2</sup>/s)
*T = absolute temperature (K)
When the flow is turbulent different correlations involving the Rayleigh Number (a function of both the [[Grashof number]] and the [[Prandtl number]]) must be used.<ref name=bennett />
Note that the above equation differs from the usual expression for [[Grashof number]] because the value <math>\beta</math> has been replaced by its approximation <math>1/T</math>, which applies for ideal gases only (a reasonable approximation for air at ambient pressure).
==Pattern formation==
[[Image:Convection1.png|thumb|right|A fluid under [[Rayleigh–Bénard convection]]: the left picture represents the thermal field and the right picture its two-dimensional [[Fourier transform]].]]
Convection, especially [[Rayleigh–Bénard convection]], where the convecting fluid is contained by two rigid horizontal plates, is a convenient example of a [[Pattern formation|pattern-forming system]].
When heat is fed into the system from one direction (usually below), at small values it merely diffuses (''conducts'') from below upward, without causing fluid flow. As the heat flow is increased, above a critical value of the [[Rayleigh number]], the system undergoes a [[Bifurcation theory|bifurcation]] from the stable ''conducting'' state to the ''convecting'' state, where bulk motion of the fluid due to heat begins. If fluid parameters other than density do not depend significantly on temperature, the flow profile is symmetric, with the same volume of fluid rising as falling. This is known as [[Boussinesq approximation (buoyancy)|Boussinesq]] convection.
As the temperature difference between the top and bottom of the fluid becomes higher, significant differences in fluid parameters other than density may develop in the fluid due to temperature. An example of such a parameter is [[viscosity]], which may begin to significantly vary horizontally across layers of fluid. This breaks the symmetry of the system, and generally changes the pattern of up- and down-moving fluid from stripes to hexagons, as seen at right. Such hexagons are one example of a [[convection cell]].
As the [[Rayleigh number]] is increased even further above the value where convection cells first appear, the system may undergo other bifurcations, and other more complex patterns, such as [[spiral]]s, may begin to appear.
==See also==
{{cmn|
* [[Convection-diffusion equation]]
* [[Bénard cells]]
* [[Churchill–Bernstein equation]]
* [[Combined forced and natural convection]]
* [[Double diffusive convection]]
* [[Forced convection]]
* [[Fluid dynamics]]
* [[Heat exchanger]]
* [[Heat transfer#Convection|Heat transfer]]
**[[Convection (heat transfer)|Convective heat transfer]]
* [[Laser-heated pedestal growth]]
* [[Natural ventilation]]
* [[Nusselt number]]
* [[Pressure head]]
* [[Thermomagnetic convection]]
* [[Vortex tube]]
* [[Convective mixing]]
}}
==References==
{{Reflist}}
==External links==
{{Commons category|Convection}}
{{Fluid Mechanics}}
{{Meteorological variables}}
{{Portal bar|Physics|Astronomy|Solar System|Weather}}
{{Authority control}}
[[Category:Fluid mechanics]]
[[Category:Physical phenomena]]' |
New page wikitext, after the edit (new_wikitext) | 'Haha do ur own research lazy {{Short description|Fluid flow that occurs due to heterogeneous fluid properties and body forces}}
{{distinguish|Conviction}}
[[File:Convection-snapshot.png|thumb|400px|right|Simulation of thermal convection in the [[Earth's mantle]]. Hot areas are shown in red, cold areas are shown in blue. A hot, less-dense material at the bottom moves upwards, and likewise, cold material from the top moves downwards.]]
'''Convection''' is single or [[Multiphase flow|multiphase]] [[fluid flow]] that occurs [[Spontaneous process|spontaneously]] due to the combined effects of [[material property]] [[heterogeneity]] and [[body forces]] on a [[fluid]], most commonly [[density]] and [[gravity]] (see [[buoyancy]]). When the cause of the convection is unspecified, convection due to the effects of [[thermal expansion]] and buoyancy can be assumed. Convection may also take place in soft [[solids]] or [[mixtures]] where particles can flow.
[[File:Ghillie Kettle Thermal.jpg|thumb|Thermal image of a newly lit [[Kelly Kettle|Ghillie kettle]]. The plume of hot air resulting from the convection current is visible.]]Convective flow may be [[Transient state|transient]] (such as when a [[Multiphasic liquid|multiphase]] [[mixture]] of [[oil]] and [[water]] separates) or [[steady state]] (see [[Convection cell]]). The convection may be due to [[Gravity|gravitational]], [[Electromagnetism|electromagnetic]] or [[Fictitious force|fictitious]] body forces. [[Convection (heat transfer)|Heat transfer by natural convection]] plays a role in the structure of [[Earth's atmosphere]], its [[oceans]], and its [[Earth's mantle|mantle]]. Discrete convective cells in the atmosphere can be identified by [[clouds]], with stronger convection resulting in [[thunderstorm]]s. Natural convection also plays a role in [[stellar physics]]. Convection is often categorised or described by the main effect causing the convective flow; for example, thermal convection.
Convection cannot take place in most solids because neither bulk current flows nor significant [[diffusion]] of matter can take place.
[[Granular convection]] is a similar phenomenon in [[granular material]] instead of fluids.
[[Advection#Distinction between advection and convection|Advection]] is fluid motion created by velocity instead of thermal gradients.
[[Convective heat transfer]] is the intentional use of convection as a method for [[heat transfer]]. Convection is a process in which heat is carried from place to place by the bulk movement of a fluid and gases.
==History==
In the 1830s, in ''[[Bridgewater Treatises|The Bridgewater Treatises]]'', the term ''convection'' is attested in a scientific sense. In treatise VIII by [[William Prout]], in the book on [[chemistry]], it says:<ref>{{Cite book |last=Prout |first=William. |url=http://archive.org/details/chemistrymeteoro00pro |title=Chemistry, meteorology and the function of digestion: considered with reference to natural theology |publisher=William Pickering |year=1834 |series=The Bridgewater Treatises: On the power, wisdom and goodness of God as manifested in the creation. Treatise 8. |volume= |pages=65–66}}</ref>
<blockquote>[[File:Prout William painting (cropped).jpg|alt=Painting of William Prout|thumb|217x217px|William Prout]][[File:Fireplace (60857557) (cropped).jpg|alt=Fireplace with grate|thumb|204x204px|Fireplace, with grate and chimney]][...] This motion of heat takes place in three ways, which a common fire-place very well illustrates. If, for instance, we place a thermometer directly before a fire, it soon begins to rise, indicating an increase of temperature. In this case the heat has made its way through the space between the fire and the thermometer, by the process termed ''[[radiation]]''. If we place a second thermometer in contact with any part of the grate, and away from the direct influence of the fire, we shall find that this thermometer also denotes an increase of temperature; but here the heat must have travelled through the metal of the grate, by what is termed ''[[Thermal conduction|conduction]]''. Lastly, a third thermometer placed in the chimney, away from the direct influence of the fire, will also indicate a considerable increase of temperature; in this case a portion of the air, passing through and near the fire, has become heated, and has ''carried'' up the chimney the temperature acquired from the fire. There is at present no single term in our language employed to denote this third mode of the propagation of heat; but we venture to propose for that purpose, the term ''convection'', [in footnote: [Latin] ''Convectio'', a carrying or conveying] which not only expresses the leading fact, but also accords very well with the two other terms.
</blockquote>
Later, in the same treatise VIII, in the book on [[meteorology]], the concept of convection is also applied to "the process by which heat is communicated through water".
==Terminology==
Today, the word ''convection'' has different but related usages in different scientific or engineering contexts or applications.
In [[fluid mechanics]], ''convection'' has a broader sense: it refers to the motion of fluid driven by density (or other property) difference.<ref>{{cite book| title=Fundamentals of Fluid Mechanics| first= Bruce R. |last=Munson |isbn= 978-0-471-85526-2 |publisher = [[John Wiley & Sons]]| year= 1990 }}</ref><ref>{{cite book|last=Falkovich|first=G.|title=Fluid Mechanics, a short course for physicists|url=http://www.weizmann.ac.il/complex/falkovich/fluid-mechanics|publisher=Cambridge University Press|year=2011|isbn=978-1-107-00575-4|url-status=live|archive-url=https://web.archive.org/web/20120120034443/http://www.weizmann.ac.il/complex/falkovich/fluid-mechanics|archive-date=2012-01-20}}</ref>
In [[thermodynamics]], ''convection'' often refers to [[Convection (heat transfer)|heat transfer by convection]], where the prefixed variant Natural Convection is used to distinguish the fluid mechanics concept of Convection (covered in this article) from convective heat transfer.<ref>{{cite book|title=Thermodynamics:An Engineering Approach|first1= Yunus A. |last1=Çengel |first2= Michael A. |last2 = Boles |year= 2001 |isbn=978-0-07-121688-3 |publisher =[[McGraw-Hill Education]]}}</ref>
Some phenomena which result in an effect superficially similar to that of a convective cell may also be (inaccurately) referred to as a form of convection; for example, [[Marangoni effect|thermo-capillary convection]] and [[granular convection]].
==Mechanisms==
Convection may happen in [[fluids]] at all scales larger than a few atoms. There are a variety of circumstances in which the forces required for convection arise, leading to different types of convection, described below. In broad terms, convection arises because of [[body force]]s acting within the fluid, such as gravity.
===Natural convection===
{{Unreferenced section|date=September 2023}}
[[Image:Bénard cells convection.ogv|thumb|300px|[[Rayleigh–Bénard convection|Rayleigh–Bénard cells]].]]
[[File:Thermal-plume-from-human-hand.jpg|thumb|This color [[schlieren]] image reveals [[thermal convection]] originating from heat conduction from a human hand (in silhouette) to the surrounding still atmosphere, initially by diffusion from the hand to the surrounding air, and subsequently also as advection as the heat causes the air to start to move upwards.]]
'''Natural convection''' is a flow whose motion is caused by some parts of a fluid being heavier than other parts. In most cases this leads to '''natural circulation''': the ability of a fluid in a system to circulate continuously under gravity, with transfer of heat energy.
The driving force for natural convection is gravity. In a column of fluid, pressure increases with depth from the weight of the overlying fluid. The pressure at the bottom of a submerged object then exceeds that at the top, resulting in a net upward [[buoyancy]] force equal to the weight of the displaced fluid. Objects of higher density than that of the displaced fluid then sink. For example, regions of warmer low-density air rise, while those of colder high-density air sink. This creates a circulating flow: convection.
Gravity drives natural convection. Without gravity, convection does not occur, so there is no convection in free-fall ([[inertial]]) environments, such as that of the orbiting International Space Station. Natural convection can occur when there are hot and cold regions of either air or water, because both water and air become less dense as they are heated. But, for example, in the world's oceans it also occurs due to salt water being heavier than fresh water, so a layer of salt water on top of a layer of fresher water will also cause convection.
Natural convection has attracted a great deal of attention from researchers because of its presence both in nature and engineering applications. In nature, convection cells formed from air raising above sunlight-warmed land or water are a major feature of all weather systems. Convection is also seen in the rising plume of hot air from [[fire]], [[plate tectonics]], oceanic currents ([[thermohaline circulation]]) and sea-wind formation (where upward convection is also modified by [[Coriolis force]]s). In engineering applications, convection is commonly visualized in the formation of microstructures during the cooling of molten metals, and fluid flows around shrouded heat-dissipation fins, and solar ponds. A very common industrial application of natural convection is free air cooling without the aid of fans: this can happen on small scales (computer chips) to large scale process equipment.
Natural convection will be more likely and more rapid with a greater variation in density between the two fluids, a larger acceleration due to gravity that drives the convection or a larger distance through the convecting medium. Natural convection will be less likely and less rapid with more rapid diffusion (thereby diffusing away the thermal gradient that is causing the convection) or a more viscous (sticky) fluid.
The onset of natural convection can be determined by the [[Rayleigh number]] ('''Ra''').
Differences in buoyancy within a fluid can arise for reasons other than temperature variations, in which case the fluid motion is called '''gravitational convection''' (see below). However, all types of buoyant convection, including natural convection, do not occur in [[microgravity]] environments. All require the presence of an environment which experiences [[g-force]] ([[proper acceleration]]).
The difference of [[density]] in the fluid is the key driving mechanism. If the differences of density are caused by heat, this force is called as "thermal head" or "thermal driving head." A fluid system designed for natural circulation will have a heat source and a [[heat sink]]. Each of these is in contact with some of the fluid in the system, but not all of it. The heat source is positioned lower than the heat sink.
Most fluids expand when heated, becoming less [[density|dense]], and contract when cooled, becoming denser. At the heat source of a system of natural circulation, the heated fluid becomes lighter than the fluid surrounding it, and thus rises. At the heat sink, the nearby fluid becomes denser as it cools, and is drawn downward by gravity. Together, these effects create a flow of fluid from the heat source to the heat sink and back again.
===Gravitational or buoyant convection===
'''Gravitational convection''' is a type of natural convection induced by buoyancy variations resulting from material properties other than temperature. Typically this is caused by a variable composition of the fluid. If the varying property is a concentration gradient, it is known as '''solutal convection'''.<ref>{{cite journal|citeseerx=10.1.1.15.8288 |title=Pattern Formation in Solutal Convection: Vermiculated Rolls and Isolated Cells |journal=Physica A: Statistical Mechanics and Its Applications |volume=314 |issue=1 |pages=291 |bibcode=2002PhyA..314..291C |last1=Cartwright |first1=Julyan H. E. |author1-link = Julyan Cartwright |last2=Piro |first2=Oreste |last3=Villacampa |first3=Ana I. |year=2002 |doi=10.1016/S0378-4371(02)01080-4 }}</ref> For example, gravitational convection can be seen in the diffusion of a source of dry salt downward into wet soil due to the buoyancy of fresh water in saline.<ref>{{cite journal|last=Raats|first= P. A. C. |year=1969 |title=Steady Gravitational Convection Induced by a Line Source of Salt in a Soil|journal = Soil Science Society of America Proceedings |volume = 33 |pages = 483–487 | doi=10.2136/sssaj1969.03615995003300040005x |issue=4|bibcode=1969SSASJ..33..483R}}</ref>
Variable [[salinity]] in water and variable water content in air masses are frequent causes of convection in the oceans and atmosphere which do not involve heat, or else involve additional compositional density factors other than the density changes from thermal expansion (see ''[[thermohaline circulation]]''). Similarly, variable composition within the Earth's interior which has not yet achieved maximal stability and minimal energy (in other words, with densest parts deepest) continues to cause a fraction of the convection of fluid rock and molten metal within the Earth's interior (see below).
Gravitational convection, like natural thermal convection, also requires a [[g-force]] environment in order to occur.
===Solid-state convection in ice===
[[Sputnik Planitia#Convection cells|Ice convection on Pluto]] is believed to occur in a soft mixture of [[nitrogen ice]] and [[carbon monoxide]] ice. It has also been proposed for [[Europa (moon)|Europa]],<ref name="On convection in ice I shells of ou">{{cite journal| doi=10.1016/j.icarus.2006.03.004 | bibcode=2006Icar..183..435M | volume=183 | issue=2 | title=On convection in ice I shells of outer Solar System bodies, with detailed application to Callisto | year=2006 | journal=Icarus | pages=435–450 | last1 = McKinnon | first1 = William B.}}</ref> and other bodies in the outer Solar System.<ref name="On convection in ice I shells of ou"/>
===Thermomagnetic convection===
{{main|Thermomagnetic convection}}
'''Thermomagnetic convection''' can occur when an external magnetic field is imposed on a [[ferrofluid]] with varying [[magnetic susceptibility]]. In the presence of a temperature gradient this results in a nonuniform magnetic body force, which leads to fluid movement. A ferrofluid is a liquid which becomes strongly magnetized in the presence of a [[magnetic field]].
===Combustion===
In a [[zero-gravity]] environment, there can be no buoyancy forces, and thus no convection possible, so flames in many circumstances without gravity smother in their own waste gases. Thermal expansion and chemical reactions resulting in expansion and contraction gases allows for ventilation of the flame, as waste gases are displaced by cool, fresh, oxygen-rich gas. moves in to take up the low pressure zones created when flame-exhaust water condenses.
==Examples and applications==
Systems of natural circulation include [[tornado]]es and other [[weather|weather systems]], [[ocean current]]s, and household [[Ventilation (architecture)|ventilation]]. Some solar water heaters use natural circulation. The [[Gulf Stream]] circulates as a result of the evaporation of water. In this process, the water increases in salinity and density. In the North Atlantic Ocean, the water becomes so dense that it begins to sink down.
Convection occurs on a large scale in [[Earth atmosphere|atmosphere]]s, oceans, [[planet]]ary [[Mantle (geology)|mantle]]s, and it provides the mechanism of heat transfer for a large fraction of the outermost interiors of the Sun and all stars. Fluid movement during convection may be invisibly slow, or it may be obvious and rapid, as in a [[hurricane]]. On astronomical scales, convection of gas and dust is thought to occur in the accretion disks of [[black hole]]s, at speeds which may closely approach that of light.
===Demonstration experiments===
[[File:Thermal circulation.png|thumb|Thermal circulation of air masses]]
Thermal convection in liquids can be demonstrated by placing a heat source (for example, a [[Bunsen burner]]) at the side of a container with a liquid. Adding a dye to the water (such as food colouring) will enable visualisation of the flow.<ref>{{Citation|title=Convection Experiment - GCSE Physics|url=https://www.youtube.com/watch?v=MBFUfld_5i0| archive-url=https://ghostarchive.org/varchive/youtube/20211211/MBFUfld_5i0| archive-date=2021-12-11 | url-status=live|language=en|access-date=2021-05-11}}{{cbignore}}</ref><ref>{{Citation|title=Convection Experiment|url=https://www.youtube.com/watch?v=B8H06ZA2xmo| archive-url=https://ghostarchive.org/varchive/youtube/20211211/B8H06ZA2xmo| archive-date=2021-12-11 | url-status=live|language=en|access-date=2021-05-11}}{{cbignore}}</ref>
Another common experiment to demonstrate thermal convection in liquids involves submerging open containers of hot and cold liquid coloured with dye into a large container of the same liquid without dye at an intermediate temperature (for example, a jar of hot tap water coloured red, a jar of water chilled in a fridge coloured blue, lowered into a clear tank of water at room temperature).<ref>{{Citation|title=Convection Current Lab Demo|url=https://www.youtube.com/watch?v=JBGT6UPTgWE| archive-url=https://ghostarchive.org/varchive/youtube/20211211/JBGT6UPTgWE| archive-date=2021-12-11 | url-status=live|language=en|access-date=2021-05-11}}{{cbignore}}</ref>
A third approach is to use two identical jars, one filled with hot water dyed one colour, and cold water of another colour. One jar is then temporarily sealed (for example, with a piece of card), inverted and placed on top of the other. When the card is removed, if the jar containing the warmer liquid is placed on top no convection will occur. If the jar containing colder liquid is placed on top, a convection current will form spontaneously.<ref>{{Citation|title=Colorful Convection Currents - Sick Science! #075|url=https://www.youtube.com/watch?v=RCO90hvEL1I| archive-url=https://ghostarchive.org/varchive/youtube/20211211/RCO90hvEL1I| archive-date=2021-12-11 | url-status=live|language=en|access-date=2021-05-11}}{{cbignore}}</ref>
Convection in gases can be demonstrated using a candle in a sealed space with an inlet and exhaust port. The heat from the candle will cause a strong convection current which can be demonstrated with a flow indicator, such as smoke from another candle, being released near the inlet and exhaust areas respectively.<ref>{{Citation|title=Convection in gases|url=https://www.youtube.com/watch?v=6VZZtB7yjmA| archive-url=https://ghostarchive.org/varchive/youtube/20211211/6VZZtB7yjmA| archive-date=2021-12-11 | url-status=live|language=en|access-date=2021-05-11}}{{cbignore}}</ref>
===Double diffusive convection===
{{main|Double diffusive convection}}
===Convection cells===
{{main|Convection cell}}
[[File:ConvectionCells.svg|thumb|right|300px|Convection cells in a gravity field]]
A '''convection cell''', also known as a '''[[Bénard cell]]''', is a characteristic fluid flow pattern in many convection systems. A rising body of fluid typically loses heat because it encounters a colder surface. In liquid, this occurs because it exchanges heat with colder liquid through direct exchange. In the example of the Earth's atmosphere, this occurs because it radiates heat. Because of this heat loss the fluid becomes denser than the fluid underneath it, which is still rising. Since it cannot descend through the rising fluid, it moves to one side. At some distance, its downward force overcomes the rising force beneath it, and the fluid begins to descend. As it descends, it warms again and the cycle repeats itself. Additionally, convection cells can arise due to density variations resulting from differences in the composition of electrolytes.<ref>{{cite journal |last1=Colli |first1=A.N. |last2=Bisang |first2=J.M. |title=Exploring the Impact of Concentration and Temperature Variations on Transient Natural Convection in Metal Electrodeposition: A Finite Volume Method Analysis |journal=Journal of the Electrochemical Society |date=2023 |volume=170 |issue=8 |pages=083505 |doi=10.1149/1945-7111/acef62 |bibcode=2023JElS..170h3505C |s2cid=260857287 |url=https://iopscience.iop.org/article/10.1149/1945-7111/acef62/meta}}</ref>
===Atmospheric convection===
{{main|Atmospheric convection}}
====Atmospheric circulation====
{{main|Atmospheric circulation}}
[[File:Earth Global Circulation.jpg|thumb|300px|left|Idealised depiction of the global circulation on Earth]]
'''Atmospheric circulation''' is the large-scale movement of air, and is a means by which [[thermal energy]] is distributed on the surface of the [[Earth]], together with the much slower (lagged) ocean circulation system. The large-scale structure of the [[atmospheric circulation]] varies from year to year, but the basic climatological structure remains fairly constant.
Latitudinal circulation occurs because incident solar [[radiation]] per unit area is highest at the [[heat equator]], and decreases as the [[latitude]] increases, reaching minima at the poles. It consists of two primary convection cells, the [[Hadley cell]] and the [[polar vortex]], with the [[Hadley cell]] experiencing stronger convection due to the release of [[latent heat]] energy by [[condensation]] of [[water vapor]] at higher altitudes during cloud formation.
Longitudinal circulation, on the other hand, comes about because the [[ocean]] has a higher specific heat capacity than land (and also [[thermal conductivity]], allowing the heat to penetrate further beneath the surface ) and thereby absorbs and releases more [[heat]], but the [[temperature]] changes less than land. This brings the sea breeze, air cooled by the water, ashore in the day, and carries the land breeze, air cooled by contact with the ground, out to sea during the night. Longitudinal circulation consists of two cells, the [[Walker circulation]] and [[El Niño-Southern Oscillation|El Niño / Southern Oscillation]].
{{clear}}
====Weather====
{{see also|Cloud|Thunderstorm|Wind}}
[[File:foehn1.svg|right|thumb|300px|How Foehn is produced]]
Some more localized phenomena than global atmospheric movement are also due to convection, including wind and some of the [[hydrologic cycle]]. For example, a [[foehn wind]] is a down-slope wind which occurs on the downwind side of a mountain range. It results from the [[adiabatic]] warming of air which has dropped most of its moisture on windward slopes.<ref name="MT">{{cite web|first=Michael|last=Pidwirny|year=2008|url=http://www.physicalgeography.net/fundamentals/8e.html|title=CHAPTER 8: Introduction to the Hydrosphere (e). Cloud Formation Processes|publisher=Physical Geography|access-date=2009-01-01|url-status=dead|archive-url=https://web.archive.org/web/20081220230524/http://www.physicalgeography.net/fundamentals/8e.html|archive-date=2008-12-20}}</ref> Because of the different adiabatic lapse rates of moist and dry air, the air on the leeward slopes becomes warmer than at the same height on the windward slopes.
A [[thermal column]] (or thermal) is a vertical section of rising air in the lower altitudes of the Earth's atmosphere. Thermals are created by the uneven heating of the Earth's surface from solar radiation. The Sun warms the ground, which in turn warms the air directly above it. The warmer air expands, becoming less dense than the surrounding air mass, and creating a [[thermal low]].<ref>{{cite web|agency=National Weather Service Forecast Office in [[Tucson, Arizona]]|year=2008|url=http://www.wrh.noaa.gov/twc/monsoon/monsoon_whatis.php|title=What is a monsoon?|publisher=National Weather Service Western Region Headquarters|access-date=2009-03-08|url-status=live|archive-url=https://web.archive.org/web/20120623140647/http://www.wrh.noaa.gov/twc/monsoon/monsoon_whatis.php|archive-date=2012-06-23}}</ref><ref>{{cite journal|first1 = Douglas G. | last1 = Hahn | author2-link = Syukuro Manabe | first2 = Syukuro | last2 = Manabe |year=1975|bibcode=1975JAtS...32.1515H|title=The Role of Mountains in the South Asian Monsoon Circulation|journal=[[Journal of the Atmospheric Sciences]]|volume=32|issue=8|pages=1515–1541|doi=10.1175/1520-0469(1975)032<1515:TROMIT>2.0.CO;2|issn=1520-0469|doi-access=free}}</ref> The mass of lighter air rises, and as it does, it cools by expansion at lower air pressures. It stops rising when it has cooled to the same temperature as the surrounding air. Associated with a thermal is a downward flow surrounding the thermal column. The downward moving exterior is caused by colder air being displaced at the top of the thermal. Another convection-driven weather effect is the [[sea breeze]].<ref>University of Wisconsin. [http://cimss.ssec.wisc.edu/wxwise/seabrz.html Sea and Land Breezes.] {{webarchive|url=https://web.archive.org/web/20120704184333/http://cimss.ssec.wisc.edu/wxwise/seabrz.html |date=2012-07-04 }} Retrieved on 2006-10-24.</ref><ref name="Jet">JetStream: An Online School For Weather (2008). [http://www.srh.weather.gov/srh/jetstream/ocean/seabreezes.htm The Sea Breeze.] {{webarchive|url=https://web.archive.org/web/20060923233344/http://www.srh.weather.gov/srh/jetstream/ocean/seabreezes.htm |date=2006-09-23 }} [[National Weather Service]]. Retrieved on 2006-10-24.</ref>
[[File:Thunderstorm formation.jpg|thumb|500px|Stages of a thunderstorm's life.]]
Warm air has a lower density than cool air, so warm air rises within cooler air,<ref>{{cite book|url=https://books.google.com/books?id=PDtIAAAAIAAJ&pg=PA462 |title=Civil engineers' pocket book: a reference-book for engineers, contractors|first = Albert Irvin | last = Frye|page=462|publisher=D. Van Nostrand Company|year=1913|access-date=2009-08-31}}</ref> similar to [[hot air balloon]]s.<ref>{{cite book
| url = https://books.google.com/books?id=ssO_19TRQ9AC&q=Kongming+balloon&pg=PA112
| title = Ancient Chinese Inventions
| first = Yikne | last = Deng
| publisher = Chinese International Press
| isbn=978-7-5085-0837-5
| year=2005
| pages = 112–13
| access-date = 2009-06-18}}</ref> Clouds form as relatively warmer air carrying moisture rises within cooler air. As the moist air rises, it cools, causing some of the [[water vapor]] in the rising packet of air to [[condensation|condense]].<ref>{{cite web|agency=FMI|year=2007|url=http://www.zamg.ac.at/docu/Manual/SatManu/main.htm?/docu/Manual/SatManu/CMs/FgStr/backgr.htm|title=Fog And Stratus – Meteorological Physical Background|publisher=Zentralanstalt für Meteorologie und Geodynamik|access-date=2009-02-07|url-status=live|archive-url=https://web.archive.org/web/20110706085616/http://www.zamg.ac.at/docu/Manual/SatManu/main.htm?%2Fdocu%2FManual%2FSatManu%2FCMs%2FFgStr%2Fbackgr.htm|archive-date=2011-07-06}}</ref> When the moisture condenses, it releases energy known as [[latent heat]] of condensation which allows the rising packet of air to cool less than its surrounding air,<ref>{{cite book|url=https://books.google.com/books?id=RRSzR4NQdGkC&pg=PA20 |title=Storm world: hurricanes, politics, and the battle over global warming| first = Chris C. | last = Mooney|page=20|isbn=978-0-15-101287-9|publisher=Houghton Mifflin Harcourt|year=2007|access-date=2009-08-31}}</ref> continuing the cloud's ascension. If enough [[Convective available potential energy|instability]] is present in the atmosphere, this process will continue long enough for [[Cumulonimbus|cumulonimbus clouds]] to form, which support lightning and thunder. Generally, thunderstorms require three conditions to form: moisture, an unstable airmass, and a lifting force (heat).
All [[thunderstorm]]s, regardless of type, go through three stages: the '''developing stage''', the '''mature stage''', and the '''dissipation stage'''.<ref name="Extreme Weather">{{cite book |title=Extreme Weather |first=Michael H. |last=Mogil |year=2007 |publisher=Black Dog & Leventhal Publisher |location=New York |isbn=978-1-57912-743-5 |pages=[https://archive.org/details/extremeweatherun0000mogi/page/210 210–211] |url=https://archive.org/details/extremeweatherun0000mogi/page/210 }}</ref> The average thunderstorm has a {{convert|24|km|mi|abbr=on}} diameter. Depending on the conditions present in the atmosphere, these three stages take an average of 30 minutes to go through.<ref name="tsbasics">{{cite web|url=http://www.nssl.noaa.gov/primer/tstorm/tst_basics.html|title=A Severe Weather Primer: Questions and Answers about Thunderstorms|agency=National Severe Storms Laboratory|publisher=[[National Oceanic and Atmospheric Administration]]|date=2006-10-15|access-date=2009-09-01|url-status=dead|archive-url=https://web.archive.org/web/20090825000832/http://www.nssl.noaa.gov/primer/tstorm/tst_basics.html|archive-date=2009-08-25}}</ref>
===Oceanic circulation===
{{Main|Gulf Stream|Thermohaline circulation}}
[[File:Conveyor belt.svg|Ocean currents|thumb|200px|right]]
Solar radiation affects the oceans: warm water from the Equator tends to circulate toward the [[geographical pole|pole]]s, while cold polar water heads towards the Equator. The surface currents are initially dictated by surface wind conditions. The [[trade winds]] blow westward in the tropics,<ref>{{cite web |title=trade winds |work=Glossary of Meteorology |publisher=American Meteorological Society |year=2009 |access-date=2008-09-08 |url=http://amsglossary.allenpress.com/glossary/search?id=trade-winds1 |url-status=dead |archive-url=https://web.archive.org/web/20081211050708/http://amsglossary.allenpress.com/glossary/search?id=trade-winds1 |archive-date=2008-12-11 }}</ref> and the [[westerlies]] blow eastward at mid-latitudes.<ref>Glossary of Meteorology (2009). [http://amsglossary.allenpress.com/glossary/search?id=westerlies1 Westerlies.] {{webarchive|url=https://web.archive.org/web/20100622073904/http://amsglossary.allenpress.com/glossary/search?id=westerlies1 |date=2010-06-22 }} [[American Meteorological Society]]. Retrieved on 2009-04-15.</ref> This wind pattern applies a [[stress (physics)|stress]] to the subtropical ocean surface with negative [[curl (mathematics)|curl]] across the [[Northern Hemisphere]],<ref>Matthias Tomczak and J. Stuart Godfrey (2001). [http://www.es.flinders.edu.au/~mattom/regoc/pdffiles/colour/double/04P-Ekman-left.pdf Regional Oceanography: an Introduction.] {{webarchive|url=https://web.archive.org/web/20090914120630/http://www.es.flinders.edu.au/~mattom/regoc/pdffiles/colour/double/04P-Ekman-left.pdf |date=2009-09-14 }} Matthias Tomczak, pp. 42. {{ISBN|81-7035-306-8}}. Retrieved on 2009-05-06.</ref> and the reverse across the [[Southern Hemisphere]]. The resulting [[Sverdrup transport]] is equatorward.<ref>Earthguide (2007). [http://earthguide.ucsd.edu/parkerprogram/berger/pdf/OcnBasLesson06.pdf Lesson 6: Unraveling the Gulf Stream Puzzle - On a Warm Current Running North.] {{webarchive|url=https://web.archive.org/web/20080723104316/http://earthguide.ucsd.edu/parkerprogram/berger/pdf/OcnBasLesson06.pdf |date=2008-07-23 }} [[University of California]] at San Diego. Retrieved on 2009-05-06.</ref> Because of conservation of [[potential vorticity]] caused by the poleward-moving winds on the [[subtropical ridge]]'s western periphery and the increased relative vorticity of poleward moving water, transport is balanced by a narrow, accelerating poleward current, which flows along the western boundary of the ocean basin, outweighing the effects of friction with the cold western boundary current which originates from high latitudes.<ref>Angela Colling (2001). [https://books.google.com/books?id=tFJRLhSez_YC&pg=PA90 Ocean circulation.] {{webarchive|url=https://web.archive.org/web/20180302144439/https://books.google.com/books?id=tFJRLhSez_YC&pg=PA90 |date=2018-03-02 }} Butterworth-Heinemann, pp. 96. Retrieved on 2009-05-07.</ref> The overall process, known as western intensification, causes currents on the western boundary of an ocean basin to be stronger than those on the eastern boundary.<ref>National Environmental Satellite, Data, and Information Service (2009). [http://www.science-house.org/nesdis/gulf/background.html Investigating the Gulf Stream.] {{webarchive|url=https://web.archive.org/web/20100503013457/http://www.science-house.org/nesdis/gulf/background.html |date=2010-05-03 }} [[North Carolina State University]]. Retrieved on 2009-05-06.</ref>
As it travels poleward, warm water transported by strong warm water current undergoes evaporative cooling. The cooling is wind driven: wind moving over water cools the water and also causes [[evaporation]], leaving a saltier brine. In this process, the water becomes saltier and denser. and decreases in temperature. Once sea ice forms, salts are left out of the ice, a process known as brine exclusion.<ref>{{cite web |last=Russel |first=Randy |title=Thermohaline Ocean Circulation |url=http://www.windows.ucar.edu/tour/link=/earth/Water/thermohaline_ocean_circulation.html |publisher=University Corporation for Atmospheric Research |access-date=2009-01-06 |url-status=live |archive-url=https://web.archive.org/web/20090325062339/http://www.windows.ucar.edu/tour/link=/earth/Water/thermohaline_ocean_circulation.html |archive-date=2009-03-25 }}</ref> These two processes produce water that is denser and colder. The water across the northern [[Atlantic Ocean]] becomes so dense that it begins to sink down through less salty and less dense water. (This [[open ocean convection]] is not unlike that of a [[lava lamp]].) This downdraft of heavy, cold and dense water becomes a part of the [[North Atlantic Deep Water]], a south-going stream.<ref>{{cite web |last=Behl |first=R. |title=Atlantic Ocean water masses |url=http://seis.natsci.csulb.edu/rbehl/NADW.htm |publisher=[[California State University]] Long Beach |access-date=2009-01-06|archive-url = https://web.archive.org/web/20080523170145/http://seis.natsci.csulb.edu/rbehl/NADW.htm |archive-date = May 23, 2008|url-status=dead}}</ref>
{{clear}}
===Mantle convection===
{{main|Mantle convection}}
[[File:Accretion-Subduction.PNG|thumb|right|250px|An [[oceanic plate]] is added to by upwelling (left) and consumed at a [[subduction]] zone (right).]]
'''Mantle convection''' is the slow creeping motion of Earth's rocky mantle caused by convection currents carrying heat from the interior of the Earth to the surface.<ref name="University of Winnipeg">{{cite web | date = 2002-12-16 | last1 = Kobes | first1 = Randy | first2 = Gabor | last2 = Kunstatter | url = http://theory.uwinnipeg.ca/mod_tech/node195.html | title = Mantle Convection | publisher = Physics Department, University of Winnipeg | access-date = 2010-01-03 | url-status = dead | archive-url = https://web.archive.org/web/20110114151750/http://theory.uwinnipeg.ca/mod_tech/node195.html | archive-date = 2011-01-14 }}</ref> It is one of 3 driving forces that causes tectonic plates to move around the Earth's surface.<ref name=Condie>{{cite book |title=Plate tectonics and crustal evolution |first=Kent C. |last=Condie |url=https://books.google.com/books?id=HZrA6OQzsvgC&pg=PA5 |page=5 |isbn=978-0-7506-3386-4 |year=1997 |edition=4th |publisher=Butterworth-Heinemann |url-status=live |archive-url=https://web.archive.org/web/20131029161501/http://books.google.com/books?id=HZrA6OQzsvgC&pg=PA5 |archive-date=2013-10-29 }}</ref>
The Earth's surface is divided into a number of [[tectonic]] plates that are continuously being created and consumed at their opposite plate boundaries. Creation ([[Accretion (geology)|accretion]]) occurs as mantle is added to the growing edges of a plate. This hot added material cools down by conduction and convection of heat. At the consumption edges of the plate, the material has thermally contracted to become dense, and it sinks under its own weight in the process of subduction at an ocean trench. This subducted material sinks to some depth in the Earth's interior where it is prohibited from sinking further. The subducted oceanic crust triggers volcanism.
Convection within [[Earth's mantle]] is the driving force for [[plate tectonics]]. Mantle convection is the result of a thermal gradient: the lower mantle is hotter than the [[upper mantle (Earth)|upper mantle]], and is therefore less dense. This sets up two primary types of instabilities. In the first type, plumes rise from the lower mantle, and corresponding unstable regions of [[lithosphere]] drip back into the mantle. In the second type, subducting oceanic plates (which largely constitute the upper thermal boundary layer of the mantle) plunge back into the mantle and move downwards towards the [[core-mantle boundary]]. Mantle convection occurs at rates of centimeters per year, and it takes on the order of hundreds of millions of years to complete a cycle of convection.
Neutrino flux measurements from the Earth's core (see [[kamLAND]]) show the source of about two-thirds of the heat in the inner core is the [[radioactive decay]] of [[potassium|<sup>40</sup>K]], uranium and thorium. This has allowed plate tectonics on Earth to continue far longer than it would have if it were simply driven by heat left over from Earth's formation; or with heat produced from [[gravitational energy|gravitational potential energy]], as a result of physical rearrangement of denser portions of the Earth's interior toward the center of the planet (that is, a type of prolonged falling and settling).
{{clear}}
===Stack effect===
{{Main|Stack effect}}
The '''Stack effect''' or '''chimney effect''' is the movement of air into and out of buildings, chimneys, flue gas stacks, or other containers due to buoyancy. Buoyancy occurs due to a difference in indoor-to-outdoor air density resulting from temperature and moisture differences. The greater the thermal difference and the height of the structure, the greater the buoyancy force, and thus the stack effect. The stack effect helps drive natural ventilation and infiltration. Some [[cooling tower]]s operate on this principle; similarly the [[solar updraft tower]] is a proposed device to generate electricity based on the stack effect.
===Stellar physics===
{{main|Convection zone|granule (solar physics)}}
[[File:Structure of Stars (artist’s impression).jpg|thumb|right|300px|An illustration of the structure of the [[Sun]] and a [[red giant]] star, showing their convective zones. These are the granular zones in the outer layers of these stars.]]
The convection zone of a star is the range of radii in which energy is transported outward from the [[stellar core|core region]] primarily by convection rather than [[Radiation zone|radiation]]. This occurs at radii which are sufficiently [[Opacity (optics)|opaque]] that convection is more efficient than radiation at transporting energy.<ref>{{cite book
| title=Discovering the Cosmos
| first=Robert C. | last=Bless | year=1996
| page=310 | isbn=9780935702675
| publisher=University Science Books
| url=https://books.google.com/books?id=jC47sk3mfjcC&pg=PA310 }}</ref>
Granules on the [[photosphere]] of the Sun are the visible tops of convection cells in the photosphere, caused by convection of [[plasma (physics)|plasma]] in the photosphere. The rising part of the granules is located in the center where the plasma is hotter. The outer edge of the granules is darker due to the cooler descending plasma. A typical granule has a diameter on the order of 1,000 kilometers and each lasts 8 to 20 minutes before dissipating. Below the photosphere is a layer of much larger "supergranules" up to 30,000 kilometers in diameter, with lifespans of up to 24 hours.
{{clear}}
===Water convection at freezing temperatures===
[[Water]] is a fluid that does not obey the Boussinesq approximation.<ref name=":0">{{Cite journal|last1=Banaszek|first1=J.|last2=Jaluria|first2=Y.|last3=Kowalewski|first3=T. A.|last4=Rebow|first4=M.|date=1999-10-01|journal=Numerical Heat Transfer, Part A: Applications|language=en|volume=36|issue=5|pages=449–472|doi=10.1080/104077899274624|issn=1040-7782|title=Semi-Implicit Fem Analysis of Natural Convection in Freezing Water|bibcode=1999NHTA...36..449B|s2cid=3740709 }}</ref> This is because its density varies nonlinearly with temperature, which causes its thermal expansion coefficient to be inconsistent near freezing temperatures.<ref>{{Cite web|url=https://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html|title=Water - Density, Specific Weight and Thermal Expansion Coefficient|website=www.engineeringtoolbox.com|language=en|access-date=2018-12-01}}</ref><ref name=":1">{{Cite news|url=http://polymer.bu.edu/hes/articles/ds03.pdf |archive-url=https://web.archive.org/web/20060301224729/http://polymer.bu.edu/hes/articles/ds03.pdf |archive-date=2006-03-01 |url-status=live|title=Supercooled and Glassy Water|last1=Debenedetti|first1=Pablo G.|date=June 2003|work=Physics Today|access-date=1 December 2018|last2=Stanley|first2=H. Eugene}}</ref> The [[density of water]] reaches a maximum at 4 °C and decreases as the temperature deviates. This phenomenon is investigated by experiment and numerical methods.<ref name=":0" /> Water is initially stagnant at 10 °C within a square cavity. It is differentially heated between the two vertical walls, where the left and right walls are held at 10 °C and 0 °C, respectively. The density anomaly manifests in its flow pattern.<ref name=":0" /><ref>{{Cite journal|last1=Giangi|first1=Marilena|last2=Stella|first2=Fulvio|last3=Kowalewski|first3=Tomasz A.|date=December 1999|title=Phase change problems with free convection: fixed grid numerical simulation|journal=Computing and Visualization in Science|language=en|volume=2|issue=2–3|pages=123–130|doi=10.1007/s007910050034|issn=1432-9360|citeseerx=10.1.1.31.9300|s2cid=3756976 }}</ref><ref>{{Cite journal|last1=Tong|first1=Wei|last2=Koster|first2=Jean N.|date=December 1993|title=Natural convection of water in a rectangular cavity including density inversion|journal=International Journal of Heat and Fluid Flow|volume=14|issue=4|pages=366–375|doi=10.1016/0142-727x(93)90010-k|issn=0142-727X}}</ref><ref>{{Cite journal|last1=Ezan|first1=Mehmet Akif|last2=Kalfa|first2=Mustafa|date=October 2016|title=Numerical investigation of transient natural convection heat transfer of freezing water in a square cavity|journal=International Journal of Heat and Fluid Flow|volume=61|pages=438–448|doi=10.1016/j.ijheatfluidflow.2016.06.004|issn=0142-727X}}</ref> As the water is cooled at the right wall, the density increases, which accelerates the flow downward. As the flow develops and the water cools further, the decrease in density causes a recirculation current at the bottom right corner of the cavity.
Another case of this phenomenon is the event of [[Supercooling|super-cooling]], where the water is cooled to below freezing temperatures but does not immediately begin to freeze.<ref name=":1" /><ref name=":2">{{Cite journal|last1=Moore|first1=Emily B.|last2=Molinero|first2=Valeria|date=November 2011|title=Structural transformation in supercooled water controls the crystallization rate of ice|journal=Nature|language=En|volume=479|issue=7374|pages=506–508|doi=10.1038/nature10586|pmid=22113691|issn=0028-0836|arxiv=1107.1622|bibcode=2011Natur.479..506M|s2cid=1784703 }}</ref> Under the same conditions as before, the flow is developed. Afterward, the temperature of the right wall is decreased to −10 °C. This causes the water at that wall to become supercooled, create a counter-clockwise flow, and initially overpower the warm current.<ref name=":0" /> This plume is caused by a delay in the [[Nucleation of ice|nucleation of the ice]].<ref name=":0" /><ref name=":1" /><ref name=":2" /> Once ice begins to form, the flow returns to a similar pattern as before and the solidification propagates gradually until the flow is redeveloped.<ref name=":0" />
===Nuclear reactors===
In a [[nuclear reactor]], natural circulation can be a design criterion. It is achieved by reducing turbulence and friction in the fluid flow (that is, minimizing [[head loss]]), and by providing a way to remove any inoperative pumps from the fluid path. Also, the reactor (as the heat source) must be physically lower than the steam generators or turbines (the heat sink). In this way, natural circulation will ensure that the fluid will continue to flow as long as the reactor is hotter than the heat sink, even when power cannot be supplied to the pumps. Notable examples are the [[S5G reactor|S5G]]
<ref>{{cite web| url=http://www.chinfo.navy.mil/navpalib/cno/n87/history/tech-3.html| publisher=Chief of Naval Operations Submarine Warfare Division| title=Technical Innovations of the Submarine Force| access-date=2006-03-12| url-status=dead| archive-url=https://web.archive.org/web/20060127003651/http://www.chinfo.navy.mil/navpalib/cno/n87/history/tech-3.html| archive-date=2006-01-27}}</ref><ref>{{cite web| url=http://ar.inel.gov/images/pdf/200506/2005061600214ALL.pdf| title=Appendix C, Attachment to NR:IBO-05/023, Evaluation of Naval Reactors Facility Radioactive Waste Disposed of at the Radioactive Waste Management Complex| access-date=2006-03-12| archive-url=https://web.archive.org/web/20120204154809/http://ar.inel.gov/images/pdf/200506/2005061600214ALL.pdf| archive-date=2012-02-04| url-status=dead}}</ref><ref>{{cite book |last1=Jones |first1=Edward Monroe |last2=Roderick |first2=Shawn S. |title=Submarine Torpedo Tactics: An American History |date=4 November 2014 |publisher=McFarland |isbn=978-0-7864-9646-4 |page=153 |url=https://books.google.com/books?id=6F6QBQAAQBAJ |language=en}}</ref>
and [[S8G reactor|S8G]]<ref>{{cite web| url=http://ship.bsu.by/main.asp?id=100092| script-title=ru:Энциклопедия кораблей /Ракетные ПЛ /Огайо| access-date=2006-03-12| language=ru| archive-date=2006-07-14| archive-url=https://web.archive.org/web/20060714151444/http://ship.bsu.by/main.asp?id=100092| url-status=dead}}</ref><ref>{{cite web| url=http://www.submarinesonstamps.co.il/openhist.php?ID=269| title=The Ohio, US Navy's nuclear-powered ballistic missile submarine| access-date=2006-03-12 |archive-url = https://web.archive.org/web/20060720075350/http://www.submarinesonstamps.co.il/openhist.php?ID=269 <!-- Bot retrieved archive --> |archive-date = 2006-07-20}}</ref><ref>{{cite web| url=http://tech.military.com/equipment/viewEquipment.do?eq_id=89213| title=Members-only feature, registration required| access-date=2006-03-12| archive-url=https://web.archive.org/web/20070223130956/http://tech.military.com/equipment/viewEquipment.do?eq_id=89213| archive-date=2007-02-23| url-status=dead}}</ref> [[United States Naval reactor]]s, which were designed to operate at a significant fraction of full power under natural circulation, quieting those propulsion plants. The [[S6G reactor]] cannot operate at power under natural circulation, but can use it to maintain emergency cooling while shut down.
By the nature of natural circulation, fluids do not typically move very fast, but this is not necessarily bad, as high flow rates are not essential to safe and effective reactor operation. In modern design nuclear reactors, flow reversal is almost impossible. All nuclear reactors, even ones designed to primarily use natural circulation as the main method of fluid circulation, have pumps that can circulate the fluid in the case that natural circulation is not sufficient.
==Mathematical models of convection==
A number of dimensionless terms have been derived to describe and predict convection, including the [[Archimedes number]], [[Grashof number]], [[Richardson number]], and the [[Rayleigh number]].
In cases of mixed convection (natural and forced occurring together) one would often like to know how much of the convection is due to external constraints, such as the fluid velocity in the pump, and how much is due to natural convection occurring in the system.
The relative magnitudes of the [[Grashof number]] and the square of the [[Reynolds number]] determine which form of convection dominates. If <math>\rm Gr/Re^2 \gg 1 </math>, forced convection may be neglected, whereas if <math>\rm Gr/Re^2 \ll 1 </math>, natural convection may be neglected. If the ratio, known as the [[Richardson number#Thermal convection|Richardson number]], is approximately one, then both forced and natural convection need to be taken into account.
===Onset===
{{See also|Heat transfer}}
The onset of natural convection is determined by the [[Rayleigh number]] ('''Ra'''). This [[dimensionless number]] is given by
:<math>\textbf{Ra} = \frac{\Delta\rho g L^3}{D\mu}</math>
where
*<math>\Delta \rho</math> is the difference in density between the two parcels of material that are mixing
*<math>g</math> is the local [[gravitational acceleration]]
*<math>L</math> is the characteristic length-scale of convection: the depth of the boiling pot, for example
*<math>D</math> is the [[diffusivity]] of the characteristic that is causing the convection, and
*<math>\mu</math> is the [[dynamic viscosity]].
Natural convection will be more likely and/or more rapid with a greater variation in density between the two fluids, a larger acceleration due to gravity that drives the convection, and/or a larger distance through the convecting medium. Convection will be less likely and/or less rapid with more rapid diffusion (thereby diffusing away the gradient that is causing the convection) and/or a more viscous (sticky) fluid.
For thermal convection due to heating from below, as described in the boiling pot above, the equation is modified for thermal expansion and thermal diffusivity. Density variations due to thermal expansion are given by:
:<math>\Delta\rho=\rho_0 \beta \Delta T</math>
where
*<math>\rho_0</math> is the reference density, typically picked to be the average density of the medium,
*<math>\beta</math> is the [[coefficient of thermal expansion]], and
*<math>\Delta T</math> is the temperature difference across the medium.
The general diffusivity, <math>D</math>, is redefined as a [[thermal diffusivity]], <math>\alpha</math>.
:<math>D=\alpha</math>
Inserting these substitutions produces a Rayleigh number that can be used to predict thermal convection.<ref>{{cite book|isbn=978-0-521-66624-4|author1=Donald L. Turcotte |author2=Gerald Schubert. |year=2002|publisher=Cambridge University Press|location=Cambridge|title=Geodynamics}}</ref>
:<math>\textbf{Ra} = \frac{\rho_0 g \beta \Delta T L^3}{\alpha \mu}</math>
===Turbulence===
The tendency of a particular naturally convective system towards turbulence relies on the [[Grashof number]] (Gr).<ref>{{cite book |author1=Kays, William |author2=Crawford, Michael |author3=Weigand, Bernhard | title=Convective Heat and Mass Transfer, 4E | publisher=McGraw-Hill Professional | year=2004 | isbn=978-0072990737}}</ref>
:<math> Gr= \frac{g \beta \Delta T L^3}{\nu^2} </math>
In very sticky, viscous fluids (large ''ν''), fluid motion is restricted, and natural convection will be non-turbulent.
Following the treatment of the previous subsection, the typical fluid velocity is of the order of <math>g \Delta \rho L^2 / \mu</math>, up to a numerical factor depending on the geometry of the system. Therefore, Grashof number can be thought of as [[Reynolds number]] with the velocity of natural convection replacing the velocity in Reynolds number's formula. However In practice, when referring to the Reynolds number, it is understood that one is considering forced convection, and the velocity is taken as the velocity dictated by external constraints (see below).
===Behavior===
The [[Grashof number]] can be formulated for natural convection occurring due to a [[concentration gradient]], sometimes termed thermo-solutal convection. In this case, a concentration of hot fluid diffuses into a cold fluid, in much the same way that ink poured into a container of water diffuses to dye the entire space. Then:
:<math> Gr= \frac{g \beta \Delta C L^3}{\nu^2} </math>
Natural convection is highly dependent on the geometry of the hot surface, various correlations exist in order to determine the heat transfer coefficient.
A general correlation that applies for a variety of geometries is
: <math>Nu = \left[Nu_0^\frac{1}{2} + Ra^ \frac{1}{6} \left(\frac {f_4\left(Pr\right)}{300}\right)^\frac{1}{6} \right]^2 </math>
The value of f<sub>4</sub>(Pr) is calculated using the following formula
: <math>f_4(Pr)= \left[1+ \left ( \frac {0.5}{Pr} \right )^\frac{9}{16} \right]^\frac{-16}{9}</math>
Nu is the [[Nusselt number]] and the values of Nu<sub>0</sub> and the characteristic length used to calculate Re are listed below (see also Discussion):
{| class="wikitable"
|-
! '''Geometry'''
! '''Characteristic length'''
! '''Nu<sub>0</sub>'''
|-
| Inclined plane
| x (Distance along plane)
| 0.68
|-
| Inclined disk
| 9D/11 (D = diameter)
| 0.56
|-
| Vertical cylinder
| x (height of cylinder)
| 0.68
|-
| Cone
| 4x/5 (x = distance along sloping surface)
| 0.54
|-
| Horizontal cylinder
| <math>\pi D/2</math> (D = diameter of cylinder)
| 0.36<math>\pi</math>
|}
'''Warning''': The values indicated for the '''Horizontal cylinder''' are '''wrong'''; see discussion.
==Natural convection from a vertical plate==
One example of natural convection is heat transfer from an isothermal vertical plate immersed in a fluid, causing the fluid to move parallel to the plate. This will occur in any system wherein the density of the moving fluid varies with position. These phenomena will only be of significance when the moving fluid is minimally affected by forced convection.<ref name=unitop>{{cite book | author= W. McCabe J. Smith | title=Unit Operations of Chemical Engineering | publisher=McGraw-Hill | year=1956 | isbn= 978-0-07-044825-4}}</ref>
When considering the flow of fluid is a result of heating, the following correlations can be used, assuming the fluid is an ideal diatomic, has adjacent to a vertical plate at constant temperature and the flow of the fluid is completely laminar.<ref name=bennett>{{cite book | author=Bennett | title=Momentum, Heat and Mass Transfer | url=https://archive.org/details/momentumheatmass00benn | url-access=registration | publisher=McGraw-Hill | year=1962 | isbn = 978-0-07-004667-2 }}</ref>
Nu<sub>m</sub> = 0.478(Gr<sup>0.25</sup>)<ref name=bennett />
Mean [[Nusselt number]] = Nu<sub>m</sub> = h<sub>m</sub>L/k<ref name=bennett />
where
*h<sub>m</sub> = mean coefficient applicable between the lower edge of the plate and any point in a distance L (W/m<sup>2</sup>. K)
*L = height of the vertical surface (m)
*k = thermal conductivity (W/m. K)
[[Grashof number]] = Gr = <math>[gL^3(t_s-t_\infty)]/v^2T</math> <ref name=unitop /><ref name=bennett />
where
*g = gravitational acceleration (m/s<sup>2</sup>)
*L = distance above the lower edge (m)
*t<sub>s</sub> = temperature of the wall (K)
*t∞ = fluid temperature outside the thermal boundary layer (K)
*v = kinematic viscosity of the fluid (m<sup>2</sup>/s)
*T = absolute temperature (K)
When the flow is turbulent different correlations involving the Rayleigh Number (a function of both the [[Grashof number]] and the [[Prandtl number]]) must be used.<ref name=bennett />
Note that the above equation differs from the usual expression for [[Grashof number]] because the value <math>\beta</math> has been replaced by its approximation <math>1/T</math>, which applies for ideal gases only (a reasonable approximation for air at ambient pressure).
==Pattern formation==
[[Image:Convection1.png|thumb|right|A fluid under [[Rayleigh–Bénard convection]]: the left picture represents the thermal field and the right picture its two-dimensional [[Fourier transform]].]]
Convection, especially [[Rayleigh–Bénard convection]], where the convecting fluid is contained by two rigid horizontal plates, is a convenient example of a [[Pattern formation|pattern-forming system]].
When heat is fed into the system from one direction (usually below), at small values it merely diffuses (''conducts'') from below upward, without causing fluid flow. As the heat flow is increased, above a critical value of the [[Rayleigh number]], the system undergoes a [[Bifurcation theory|bifurcation]] from the stable ''conducting'' state to the ''convecting'' state, where bulk motion of the fluid due to heat begins. If fluid parameters other than density do not depend significantly on temperature, the flow profile is symmetric, with the same volume of fluid rising as falling. This is known as [[Boussinesq approximation (buoyancy)|Boussinesq]] convection.
As the temperature difference between the top and bottom of the fluid becomes higher, significant differences in fluid parameters other than density may develop in the fluid due to temperature. An example of such a parameter is [[viscosity]], which may begin to significantly vary horizontally across layers of fluid. This breaks the symmetry of the system, and generally changes the pattern of up- and down-moving fluid from stripes to hexagons, as seen at right. Such hexagons are one example of a [[convection cell]].
As the [[Rayleigh number]] is increased even further above the value where convection cells first appear, the system may undergo other bifurcations, and other more complex patterns, such as [[spiral]]s, may begin to appear.
==See also==
{{cmn|
* [[Convection-diffusion equation]]
* [[Bénard cells]]
* [[Churchill–Bernstein equation]]
* [[Combined forced and natural convection]]
* [[Double diffusive convection]]
* [[Forced convection]]
* [[Fluid dynamics]]
* [[Heat exchanger]]
* [[Heat transfer#Convection|Heat transfer]]
**[[Convection (heat transfer)|Convective heat transfer]]
* [[Laser-heated pedestal growth]]
* [[Natural ventilation]]
* [[Nusselt number]]
* [[Pressure head]]
* [[Thermomagnetic convection]]
* [[Vortex tube]]
* [[Convective mixing]]
}}
==References==
{{Reflist}}
==External links==
{{Commons category|Convection}}
{{Fluid Mechanics}}
{{Meteorological variables}}
{{Portal bar|Physics|Astronomy|Solar System|Weather}}
{{Authority control}}
[[Category:Fluid mechanics]]
[[Category:Physical phenomena]]' |
Unified diff of changes made by edit (edit_diff) | '@@ -1,3 +1,3 @@
-{{Short description|Fluid flow that occurs due to heterogeneous fluid properties and body forces}}
+Haha do ur own research lazy {{Short description|Fluid flow that occurs due to heterogeneous fluid properties and body forces}}
{{distinguish|Conviction}}
[[File:Convection-snapshot.png|thumb|400px|right|Simulation of thermal convection in the [[Earth's mantle]]. Hot areas are shown in red, cold areas are shown in blue. A hot, less-dense material at the bottom moves upwards, and likewise, cold material from the top moves downwards.]]
' |
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Parsed HTML source of the new revision (new_html) | '<div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p>Haha do ur own research lazy </p><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Fluid flow that occurs due to heterogeneous fluid properties and body forces</div>
<style data-mw-deduplicate="TemplateStyles:r1033289096">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Conviction" title="Conviction">Conviction</a>.</div>
<figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Convection-snapshot.png" class="mw-file-description"><img src="/media/wikipedia/commons/thumb/0/01/Convection-snapshot.png/400px-Convection-snapshot.png" decoding="async" width="400" height="159" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/0/01/Convection-snapshot.png/600px-Convection-snapshot.png 1.5x, /media/wikipedia/commons/0/01/Convection-snapshot.png 2x" data-file-width="689" data-file-height="274" /></a><figcaption>Simulation of thermal convection in the <a href="/wiki/Earth%27s_mantle" title="Earth's mantle">Earth's mantle</a>. Hot areas are shown in red, cold areas are shown in blue. A hot, less-dense material at the bottom moves upwards, and likewise, cold material from the top moves downwards.</figcaption></figure>
<p><b>Convection</b> is single or <a href="/wiki/Multiphase_flow" title="Multiphase flow">multiphase</a> <a href="/wiki/Fluid_flow" class="mw-redirect" title="Fluid flow">fluid flow</a> that occurs <a href="/wiki/Spontaneous_process" title="Spontaneous process">spontaneously</a> due to the combined effects of <a href="/wiki/Material_property" class="mw-redirect" title="Material property">material property</a> <a href="/wiki/Heterogeneity" class="mw-redirect" title="Heterogeneity">heterogeneity</a> and <a href="/wiki/Body_forces" class="mw-redirect" title="Body forces">body forces</a> on a <a href="/wiki/Fluid" title="Fluid">fluid</a>, most commonly <a href="/wiki/Density" title="Density">density</a> and <a href="/wiki/Gravity" title="Gravity">gravity</a> (see <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a>). When the cause of the convection is unspecified, convection due to the effects of <a href="/wiki/Thermal_expansion" title="Thermal expansion">thermal expansion</a> and buoyancy can be assumed. Convection may also take place in soft <a href="/wiki/Solids" class="mw-redirect" title="Solids">solids</a> or <a href="/wiki/Mixtures" class="mw-redirect" title="Mixtures">mixtures</a> where particles can flow.
</p>
<figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Ghillie_Kettle_Thermal.jpg" class="mw-file-description"><img src="/media/wikipedia/commons/thumb/d/d8/Ghillie_Kettle_Thermal.jpg/220px-Ghillie_Kettle_Thermal.jpg" decoding="async" width="220" height="225" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/d/d8/Ghillie_Kettle_Thermal.jpg/330px-Ghillie_Kettle_Thermal.jpg 1.5x, /media/wikipedia/commons/thumb/d/d8/Ghillie_Kettle_Thermal.jpg/440px-Ghillie_Kettle_Thermal.jpg 2x" data-file-width="449" data-file-height="460" /></a><figcaption>Thermal image of a newly lit <a href="/wiki/Kelly_Kettle" title="Kelly Kettle">Ghillie kettle</a>. The plume of hot air resulting from the convection current is visible.</figcaption></figure><p>Convective flow may be <a href="/wiki/Transient_state" title="Transient state">transient</a> (such as when a <a href="/wiki/Multiphasic_liquid" title="Multiphasic liquid">multiphase</a> <a href="/wiki/Mixture" title="Mixture">mixture</a> of <a href="/wiki/Oil" title="Oil">oil</a> and <a href="/wiki/Water" title="Water">water</a> separates) or <a href="/wiki/Steady_state" title="Steady state">steady state</a> (see <a href="/wiki/Convection_cell" title="Convection cell">Convection cell</a>). The convection may be due to <a href="/wiki/Gravity" title="Gravity">gravitational</a>, <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetic</a> or <a href="/wiki/Fictitious_force" title="Fictitious force">fictitious</a> body forces. <a href="/wiki/Convection_(heat_transfer)" title="Convection (heat transfer)">Heat transfer by natural convection</a> plays a role in the structure of <a href="/wiki/Earth%27s_atmosphere" class="mw-redirect" title="Earth's atmosphere">Earth's atmosphere</a>, its <a href="/wiki/Oceans" class="mw-redirect" title="Oceans">oceans</a>, and its <a href="/wiki/Earth%27s_mantle" title="Earth's mantle">mantle</a>. Discrete convective cells in the atmosphere can be identified by <a href="/wiki/Clouds" class="mw-redirect" title="Clouds">clouds</a>, with stronger convection resulting in <a href="/wiki/Thunderstorm" title="Thunderstorm">thunderstorms</a>. Natural convection also plays a role in <a href="/wiki/Stellar_physics" class="mw-redirect" title="Stellar physics">stellar physics</a>. Convection is often categorised or described by the main effect causing the convective flow; for example, thermal convection.
</p><p>Convection cannot take place in most solids because neither bulk current flows nor significant <a href="/wiki/Diffusion" title="Diffusion">diffusion</a> of matter can take place.
<a href="/wiki/Granular_convection" title="Granular convection">Granular convection</a> is a similar phenomenon in <a href="/wiki/Granular_material" title="Granular material">granular material</a> instead of fluids.
<a href="/wiki/Advection#Distinction_between_advection_and_convection" title="Advection">Advection</a> is fluid motion created by velocity instead of thermal gradients.
<a href="/wiki/Convective_heat_transfer" class="mw-redirect" title="Convective heat transfer">Convective heat transfer</a> is the intentional use of convection as a method for <a href="/wiki/Heat_transfer" title="Heat transfer">heat transfer</a>. Convection is a process in which heat is carried from place to place by the bulk movement of a fluid and gases.
</p>
<div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div>
<ul>
<li class="toclevel-1 tocsection-1"><a href="#History"><span class="tocnumber">1</span> <span class="toctext">History</span></a></li>
<li class="toclevel-1 tocsection-2"><a href="#Terminology"><span class="tocnumber">2</span> <span class="toctext">Terminology</span></a></li>
<li class="toclevel-1 tocsection-3"><a href="#Mechanisms"><span class="tocnumber">3</span> <span class="toctext">Mechanisms</span></a>
<ul>
<li class="toclevel-2 tocsection-4"><a href="#Natural_convection"><span class="tocnumber">3.1</span> <span class="toctext">Natural convection</span></a></li>
<li class="toclevel-2 tocsection-5"><a href="#Gravitational_or_buoyant_convection"><span class="tocnumber">3.2</span> <span class="toctext">Gravitational or buoyant convection</span></a></li>
<li class="toclevel-2 tocsection-6"><a href="#Solid-state_convection_in_ice"><span class="tocnumber">3.3</span> <span class="toctext">Solid-state convection in ice</span></a></li>
<li class="toclevel-2 tocsection-7"><a href="#Thermomagnetic_convection"><span class="tocnumber">3.4</span> <span class="toctext">Thermomagnetic convection</span></a></li>
<li class="toclevel-2 tocsection-8"><a href="#Combustion"><span class="tocnumber">3.5</span> <span class="toctext">Combustion</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-9"><a href="#Examples_and_applications"><span class="tocnumber">4</span> <span class="toctext">Examples and applications</span></a>
<ul>
<li class="toclevel-2 tocsection-10"><a href="#Demonstration_experiments"><span class="tocnumber">4.1</span> <span class="toctext">Demonstration experiments</span></a></li>
<li class="toclevel-2 tocsection-11"><a href="#Double_diffusive_convection"><span class="tocnumber">4.2</span> <span class="toctext">Double diffusive convection</span></a></li>
<li class="toclevel-2 tocsection-12"><a href="#Convection_cells"><span class="tocnumber">4.3</span> <span class="toctext">Convection cells</span></a></li>
<li class="toclevel-2 tocsection-13"><a href="#Atmospheric_convection"><span class="tocnumber">4.4</span> <span class="toctext">Atmospheric convection</span></a>
<ul>
<li class="toclevel-3 tocsection-14"><a href="#Atmospheric_circulation"><span class="tocnumber">4.4.1</span> <span class="toctext">Atmospheric circulation</span></a></li>
<li class="toclevel-3 tocsection-15"><a href="#Weather"><span class="tocnumber">4.4.2</span> <span class="toctext">Weather</span></a></li>
</ul>
</li>
<li class="toclevel-2 tocsection-16"><a href="#Oceanic_circulation"><span class="tocnumber">4.5</span> <span class="toctext">Oceanic circulation</span></a></li>
<li class="toclevel-2 tocsection-17"><a href="#Mantle_convection"><span class="tocnumber">4.6</span> <span class="toctext">Mantle convection</span></a></li>
<li class="toclevel-2 tocsection-18"><a href="#Stack_effect"><span class="tocnumber">4.7</span> <span class="toctext">Stack effect</span></a></li>
<li class="toclevel-2 tocsection-19"><a href="#Stellar_physics"><span class="tocnumber">4.8</span> <span class="toctext">Stellar physics</span></a></li>
<li class="toclevel-2 tocsection-20"><a href="#Water_convection_at_freezing_temperatures"><span class="tocnumber">4.9</span> <span class="toctext">Water convection at freezing temperatures</span></a></li>
<li class="toclevel-2 tocsection-21"><a href="#Nuclear_reactors"><span class="tocnumber">4.10</span> <span class="toctext">Nuclear reactors</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-22"><a href="#Mathematical_models_of_convection"><span class="tocnumber">5</span> <span class="toctext">Mathematical models of convection</span></a>
<ul>
<li class="toclevel-2 tocsection-23"><a href="#Onset"><span class="tocnumber">5.1</span> <span class="toctext">Onset</span></a></li>
<li class="toclevel-2 tocsection-24"><a href="#Turbulence"><span class="tocnumber">5.2</span> <span class="toctext">Turbulence</span></a></li>
<li class="toclevel-2 tocsection-25"><a href="#Behavior"><span class="tocnumber">5.3</span> <span class="toctext">Behavior</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-26"><a href="#Natural_convection_from_a_vertical_plate"><span class="tocnumber">6</span> <span class="toctext">Natural convection from a vertical plate</span></a></li>
<li class="toclevel-1 tocsection-27"><a href="#Pattern_formation"><span class="tocnumber">7</span> <span class="toctext">Pattern formation</span></a></li>
<li class="toclevel-1 tocsection-28"><a href="#See_also"><span class="tocnumber">8</span> <span class="toctext">See also</span></a></li>
<li class="toclevel-1 tocsection-29"><a href="#References"><span class="tocnumber">9</span> <span class="toctext">References</span></a></li>
<li class="toclevel-1 tocsection-30"><a href="#External_links"><span class="tocnumber">10</span> <span class="toctext">External links</span></a></li>
</ul>
</div>
<h2><span class="mw-headline" id="History">History</span><span class="mw-editsection">
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<p>In the 1830s, in <i><a href="/wiki/Bridgewater_Treatises" title="Bridgewater Treatises">The Bridgewater Treatises</a></i>, the term <i>convection</i> is attested in a scientific sense. In treatise VIII by <a href="/wiki/William_Prout" title="William Prout">William Prout</a>, in the book on <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, it says:<sup id="cite_ref-1" class="reference"><a href="#cite_note-1">[1]</a></sup>
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<blockquote><figure typeof="mw:File/Thumb"><a href="/wiki/File:Prout_William_painting_(cropped).jpg" class="mw-file-description"><img alt="Painting of William Prout" src="/media/wikipedia/commons/thumb/2/21/Prout_William_painting_%28cropped%29.jpg/170px-Prout_William_painting_%28cropped%29.jpg" decoding="async" width="170" height="217" class="mw-file-element" srcset="/media/wikipedia/commons/2/21/Prout_William_painting_%28cropped%29.jpg 1.5x" data-file-width="246" data-file-height="314" /></a><figcaption>William Prout</figcaption></figure><figure typeof="mw:File/Thumb"><a href="/wiki/File:Fireplace_(60857557)_(cropped).jpg" class="mw-file-description"><img alt="Fireplace with grate" src="/media/wikipedia/commons/thumb/f/ff/Fireplace_%2860857557%29_%28cropped%29.jpg/170px-Fireplace_%2860857557%29_%28cropped%29.jpg" decoding="async" width="170" height="204" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/f/ff/Fireplace_%2860857557%29_%28cropped%29.jpg/255px-Fireplace_%2860857557%29_%28cropped%29.jpg 1.5x, /media/wikipedia/commons/thumb/f/ff/Fireplace_%2860857557%29_%28cropped%29.jpg/339px-Fireplace_%2860857557%29_%28cropped%29.jpg 2x" data-file-width="779" data-file-height="936" /></a><figcaption>Fireplace, with grate and chimney</figcaption></figure><p>[...] This motion of heat takes place in three ways, which a common fire-place very well illustrates. If, for instance, we place a thermometer directly before a fire, it soon begins to rise, indicating an increase of temperature. In this case the heat has made its way through the space between the fire and the thermometer, by the process termed <i><a href="/wiki/Radiation" title="Radiation">radiation</a></i>. If we place a second thermometer in contact with any part of the grate, and away from the direct influence of the fire, we shall find that this thermometer also denotes an increase of temperature; but here the heat must have travelled through the metal of the grate, by what is termed <i><a href="/wiki/Thermal_conduction" title="Thermal conduction">conduction</a></i>. Lastly, a third thermometer placed in the chimney, away from the direct influence of the fire, will also indicate a considerable increase of temperature; in this case a portion of the air, passing through and near the fire, has become heated, and has <i>carried</i> up the chimney the temperature acquired from the fire. There is at present no single term in our language employed to denote this third mode of the propagation of heat; but we venture to propose for that purpose, the term <i>convection</i>, [in footnote: [Latin] <i>Convectio</i>, a carrying or conveying] which not only expresses the leading fact, but also accords very well with the two other terms.
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<p>Later, in the same treatise VIII, in the book on <a href="/wiki/Meteorology" title="Meteorology">meteorology</a>, the concept of convection is also applied to "the process by which heat is communicated through water".
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<h2><span class="mw-headline" id="Terminology">Terminology</span><span class="mw-editsection">
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<p>Today, the word <i>convection</i> has different but related usages in different scientific or engineering contexts or applications.
</p><p>In <a href="/wiki/Fluid_mechanics" title="Fluid mechanics">fluid mechanics</a>, <i>convection</i> has a broader sense: it refers to the motion of fluid driven by density (or other property) difference.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3">[3]</a></sup>
</p><p>In <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>, <i>convection</i> often refers to <a href="/wiki/Convection_(heat_transfer)" title="Convection (heat transfer)">heat transfer by convection</a>, where the prefixed variant Natural Convection is used to distinguish the fluid mechanics concept of Convection (covered in this article) from convective heat transfer.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4">[4]</a></sup>
</p><p>Some phenomena which result in an effect superficially similar to that of a convective cell may also be (inaccurately) referred to as a form of convection; for example, <a href="/wiki/Marangoni_effect" title="Marangoni effect">thermo-capillary convection</a> and <a href="/wiki/Granular_convection" title="Granular convection">granular convection</a>.
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<h2><span class="mw-headline" id="Mechanisms">Mechanisms</span><span class="mw-editsection">
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<p>Convection may happen in <a href="/wiki/Fluids" class="mw-redirect" title="Fluids">fluids</a> at all scales larger than a few atoms. There are a variety of circumstances in which the forces required for convection arise, leading to different types of convection, described below. In broad terms, convection arises because of <a href="/wiki/Body_force" title="Body force">body forces</a> acting within the fluid, such as gravity.
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<h3><span class="mw-headline" id="Natural_convection">Natural convection</span><span class="mw-editsection">
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<figure typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="/media/wikipedia/commons/thumb/3/37/B%C3%A9nard_cells_convection.ogv/300px--B%C3%A9nard_cells_convection.ogv.jpg" controls="" preload="none" class="mw-file-element" width="300" height="225" data-durationhint="27" data-mwtitle="Bénard_cells_convection.ogv" data-mwprovider="wikimediacommons" resource="/wiki/File:B%C3%A9nard_cells_convection.ogv"><source src="/media/wikipedia/commons/transcoded/3/37/B%C3%A9nard_cells_convection.ogv/B%C3%A9nard_cells_convection.ogv.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="640" data-height="480" /><source src="/media/wikipedia/commons/3/37/B%C3%A9nard_cells_convection.ogv" type="video/ogg; codecs="theora, vorbis"" data-width="640" data-height="480" /><source src="/media/wikipedia/commons/transcoded/3/37/B%C3%A9nard_cells_convection.ogv/B%C3%A9nard_cells_convection.ogv.m3u8" type="application/vnd.apple.mpegurl" data-transcodekey="m3u8" data-width="0" data-height="0" /><source src="/media/wikipedia/commons/transcoded/3/37/B%C3%A9nard_cells_convection.ogv/B%C3%A9nard_cells_convection.ogv.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="320" data-height="240" /><source src="/media/wikipedia/commons/transcoded/3/37/B%C3%A9nard_cells_convection.ogv/B%C3%A9nard_cells_convection.ogv.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="480" data-height="360" /><source src="/media/wikipedia/commons/transcoded/3/37/B%C3%A9nard_cells_convection.ogv/B%C3%A9nard_cells_convection.ogv.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="480" data-height="360" /></video></span><figcaption><a href="/wiki/Rayleigh%E2%80%93B%C3%A9nard_convection" title="Rayleigh–Bénard convection">Rayleigh–Bénard cells</a>.</figcaption></figure>
<figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Thermal-plume-from-human-hand.jpg" class="mw-file-description"><img src="/media/wikipedia/commons/thumb/9/90/Thermal-plume-from-human-hand.jpg/220px-Thermal-plume-from-human-hand.jpg" decoding="async" width="220" height="251" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/9/90/Thermal-plume-from-human-hand.jpg/330px-Thermal-plume-from-human-hand.jpg 1.5x, /media/wikipedia/commons/thumb/9/90/Thermal-plume-from-human-hand.jpg/440px-Thermal-plume-from-human-hand.jpg 2x" data-file-width="667" data-file-height="760" /></a><figcaption>This color <a href="/wiki/Schlieren" title="Schlieren">schlieren</a> image reveals <a href="/wiki/Thermal_convection" class="mw-redirect" title="Thermal convection">thermal convection</a> originating from heat conduction from a human hand (in silhouette) to the surrounding still atmosphere, initially by diffusion from the hand to the surrounding air, and subsequently also as advection as the heat causes the air to start to move upwards.</figcaption></figure>
<p><b>Natural convection</b> is a flow whose motion is caused by some parts of a fluid being heavier than other parts. In most cases this leads to <b>natural circulation</b>: the ability of a fluid in a system to circulate continuously under gravity, with transfer of heat energy.
</p><p>The driving force for natural convection is gravity. In a column of fluid, pressure increases with depth from the weight of the overlying fluid. The pressure at the bottom of a submerged object then exceeds that at the top, resulting in a net upward <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a> force equal to the weight of the displaced fluid. Objects of higher density than that of the displaced fluid then sink. For example, regions of warmer low-density air rise, while those of colder high-density air sink. This creates a circulating flow: convection.
</p><p>Gravity drives natural convection. Without gravity, convection does not occur, so there is no convection in free-fall (<a href="/wiki/Inertial" class="mw-redirect" title="Inertial">inertial</a>) environments, such as that of the orbiting International Space Station. Natural convection can occur when there are hot and cold regions of either air or water, because both water and air become less dense as they are heated. But, for example, in the world's oceans it also occurs due to salt water being heavier than fresh water, so a layer of salt water on top of a layer of fresher water will also cause convection.
</p><p>Natural convection has attracted a great deal of attention from researchers because of its presence both in nature and engineering applications. In nature, convection cells formed from air raising above sunlight-warmed land or water are a major feature of all weather systems. Convection is also seen in the rising plume of hot air from <a href="/wiki/Fire" title="Fire">fire</a>, <a href="/wiki/Plate_tectonics" title="Plate tectonics">plate tectonics</a>, oceanic currents (<a href="/wiki/Thermohaline_circulation" title="Thermohaline circulation">thermohaline circulation</a>) and sea-wind formation (where upward convection is also modified by <a href="/wiki/Coriolis_force" title="Coriolis force">Coriolis forces</a>). In engineering applications, convection is commonly visualized in the formation of microstructures during the cooling of molten metals, and fluid flows around shrouded heat-dissipation fins, and solar ponds. A very common industrial application of natural convection is free air cooling without the aid of fans: this can happen on small scales (computer chips) to large scale process equipment.
</p><p>Natural convection will be more likely and more rapid with a greater variation in density between the two fluids, a larger acceleration due to gravity that drives the convection or a larger distance through the convecting medium. Natural convection will be less likely and less rapid with more rapid diffusion (thereby diffusing away the thermal gradient that is causing the convection) or a more viscous (sticky) fluid.
</p><p>The onset of natural convection can be determined by the <a href="/wiki/Rayleigh_number" title="Rayleigh number">Rayleigh number</a> (<b>Ra</b>).
</p><p>Differences in buoyancy within a fluid can arise for reasons other than temperature variations, in which case the fluid motion is called <b>gravitational convection</b> (see below). However, all types of buoyant convection, including natural convection, do not occur in <a href="/wiki/Microgravity" class="mw-redirect" title="Microgravity">microgravity</a> environments. All require the presence of an environment which experiences <a href="/wiki/G-force" title="G-force">g-force</a> (<a href="/wiki/Proper_acceleration" title="Proper acceleration">proper acceleration</a>).
</p><p>The difference of <a href="/wiki/Density" title="Density">density</a> in the fluid is the key driving mechanism. If the differences of density are caused by heat, this force is called as "thermal head" or "thermal driving head." A fluid system designed for natural circulation will have a heat source and a <a href="/wiki/Heat_sink" title="Heat sink">heat sink</a>. Each of these is in contact with some of the fluid in the system, but not all of it. The heat source is positioned lower than the heat sink.
</p><p>Most fluids expand when heated, becoming less <a href="/wiki/Density" title="Density">dense</a>, and contract when cooled, becoming denser. At the heat source of a system of natural circulation, the heated fluid becomes lighter than the fluid surrounding it, and thus rises. At the heat sink, the nearby fluid becomes denser as it cools, and is drawn downward by gravity. Together, these effects create a flow of fluid from the heat source to the heat sink and back again.
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<h3><span class="mw-headline" id="Gravitational_or_buoyant_convection">Gravitational or buoyant convection</span><span class="mw-editsection">
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<p><b>Gravitational convection</b> is a type of natural convection induced by buoyancy variations resulting from material properties other than temperature. Typically this is caused by a variable composition of the fluid. If the varying property is a concentration gradient, it is known as <b>solutal convection</b>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5">[5]</a></sup> For example, gravitational convection can be seen in the diffusion of a source of dry salt downward into wet soil due to the buoyancy of fresh water in saline.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6">[6]</a></sup>
</p><p>Variable <a href="/wiki/Salinity" title="Salinity">salinity</a> in water and variable water content in air masses are frequent causes of convection in the oceans and atmosphere which do not involve heat, or else involve additional compositional density factors other than the density changes from thermal expansion (see <i><a href="/wiki/Thermohaline_circulation" title="Thermohaline circulation">thermohaline circulation</a></i>). Similarly, variable composition within the Earth's interior which has not yet achieved maximal stability and minimal energy (in other words, with densest parts deepest) continues to cause a fraction of the convection of fluid rock and molten metal within the Earth's interior (see below).
</p><p>Gravitational convection, like natural thermal convection, also requires a <a href="/wiki/G-force" title="G-force">g-force</a> environment in order to occur.
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<p><a href="/wiki/Sputnik_Planitia#Convection_cells" title="Sputnik Planitia">Ice convection on Pluto</a> is believed to occur in a soft mixture of <a href="/wiki/Nitrogen_ice" class="mw-redirect" title="Nitrogen ice">nitrogen ice</a> and <a href="/wiki/Carbon_monoxide" title="Carbon monoxide">carbon monoxide</a> ice. It has also been proposed for <a href="/wiki/Europa_(moon)" title="Europa (moon)">Europa</a>,<sup id="cite_ref-On_convection_in_ice_I_shells_of_ou_7-0" class="reference"><a href="#cite_note-On_convection_in_ice_I_shells_of_ou-7">[7]</a></sup> and other bodies in the outer Solar System.<sup id="cite_ref-On_convection_in_ice_I_shells_of_ou_7-1" class="reference"><a href="#cite_note-On_convection_in_ice_I_shells_of_ou-7">[7]</a></sup>
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<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033289096"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Thermomagnetic_convection" title="Thermomagnetic convection">Thermomagnetic convection</a></div>
<p><b>Thermomagnetic convection</b> can occur when an external magnetic field is imposed on a <a href="/wiki/Ferrofluid" title="Ferrofluid">ferrofluid</a> with varying <a href="/wiki/Magnetic_susceptibility" title="Magnetic susceptibility">magnetic susceptibility</a>. In the presence of a temperature gradient this results in a nonuniform magnetic body force, which leads to fluid movement. A ferrofluid is a liquid which becomes strongly magnetized in the presence of a <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a>.
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<h3><span class="mw-headline" id="Combustion">Combustion</span><span class="mw-editsection">
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<p>In a <a href="/wiki/Zero-gravity" class="mw-redirect" title="Zero-gravity">zero-gravity</a> environment, there can be no buoyancy forces, and thus no convection possible, so flames in many circumstances without gravity smother in their own waste gases. Thermal expansion and chemical reactions resulting in expansion and contraction gases allows for ventilation of the flame, as waste gases are displaced by cool, fresh, oxygen-rich gas. moves in to take up the low pressure zones created when flame-exhaust water condenses.
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<h2><span class="mw-headline" id="Examples_and_applications">Examples and applications</span><span class="mw-editsection">
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<p>Systems of natural circulation include <a href="/wiki/Tornado" title="Tornado">tornadoes</a> and other <a href="/wiki/Weather" title="Weather">weather systems</a>, <a href="/wiki/Ocean_current" title="Ocean current">ocean currents</a>, and household <a href="/wiki/Ventilation_(architecture)" title="Ventilation (architecture)">ventilation</a>. Some solar water heaters use natural circulation. The <a href="/wiki/Gulf_Stream" title="Gulf Stream">Gulf Stream</a> circulates as a result of the evaporation of water. In this process, the water increases in salinity and density. In the North Atlantic Ocean, the water becomes so dense that it begins to sink down.
</p><p>Convection occurs on a large scale in <a href="/wiki/Earth_atmosphere" class="mw-redirect" title="Earth atmosphere">atmospheres</a>, oceans, <a href="/wiki/Planet" title="Planet">planetary</a> <a href="/wiki/Mantle_(geology)" title="Mantle (geology)">mantles</a>, and it provides the mechanism of heat transfer for a large fraction of the outermost interiors of the Sun and all stars. Fluid movement during convection may be invisibly slow, or it may be obvious and rapid, as in a <a href="/wiki/Hurricane" class="mw-redirect" title="Hurricane">hurricane</a>. On astronomical scales, convection of gas and dust is thought to occur in the accretion disks of <a href="/wiki/Black_hole" title="Black hole">black holes</a>, at speeds which may closely approach that of light.
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<h3><span class="mw-headline" id="Demonstration_experiments">Demonstration experiments</span><span class="mw-editsection">
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<figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Thermal_circulation.png" class="mw-file-description"><img src="/media/wikipedia/commons/thumb/7/74/Thermal_circulation.png/220px-Thermal_circulation.png" decoding="async" width="220" height="160" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/7/74/Thermal_circulation.png/330px-Thermal_circulation.png 1.5x, /media/wikipedia/commons/thumb/7/74/Thermal_circulation.png/440px-Thermal_circulation.png 2x" data-file-width="1148" data-file-height="834" /></a><figcaption>Thermal circulation of air masses</figcaption></figure>
<p>Thermal convection in liquids can be demonstrated by placing a heat source (for example, a <a href="/wiki/Bunsen_burner" title="Bunsen burner">Bunsen burner</a>) at the side of a container with a liquid. Adding a dye to the water (such as food colouring) will enable visualisation of the flow.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8">[8]</a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9">[9]</a></sup>
</p><p>Another common experiment to demonstrate thermal convection in liquids involves submerging open containers of hot and cold liquid coloured with dye into a large container of the same liquid without dye at an intermediate temperature (for example, a jar of hot tap water coloured red, a jar of water chilled in a fridge coloured blue, lowered into a clear tank of water at room temperature).<sup id="cite_ref-10" class="reference"><a href="#cite_note-10">[10]</a></sup>
</p><p>A third approach is to use two identical jars, one filled with hot water dyed one colour, and cold water of another colour. One jar is then temporarily sealed (for example, with a piece of card), inverted and placed on top of the other. When the card is removed, if the jar containing the warmer liquid is placed on top no convection will occur. If the jar containing colder liquid is placed on top, a convection current will form spontaneously.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11">[11]</a></sup>
</p><p>Convection in gases can be demonstrated using a candle in a sealed space with an inlet and exhaust port. The heat from the candle will cause a strong convection current which can be demonstrated with a flow indicator, such as smoke from another candle, being released near the inlet and exhaust areas respectively.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12">[12]</a></sup>
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<h3><span class="mw-headline" id="Double_diffusive_convection">Double diffusive convection</span><span class="mw-editsection">
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<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033289096"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Double_diffusive_convection" title="Double diffusive convection">Double diffusive convection</a></div>
<h3><span class="mw-headline" id="Convection_cells">Convection cells</span><span class="mw-editsection">
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<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033289096"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Convection_cell" title="Convection cell">Convection cell</a></div>
<figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:ConvectionCells.svg" class="mw-file-description"><img src="/media/wikipedia/commons/thumb/f/f5/ConvectionCells.svg/300px-ConvectionCells.svg.png" decoding="async" width="300" height="216" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/f/f5/ConvectionCells.svg/450px-ConvectionCells.svg.png 1.5x, /media/wikipedia/commons/thumb/f/f5/ConvectionCells.svg/600px-ConvectionCells.svg.png 2x" data-file-width="500" data-file-height="360" /></a><figcaption>Convection cells in a gravity field</figcaption></figure>
<p>A <b>convection cell</b>, also known as a <b><a href="/wiki/B%C3%A9nard_cell" class="mw-redirect" title="Bénard cell">Bénard cell</a></b>, is a characteristic fluid flow pattern in many convection systems. A rising body of fluid typically loses heat because it encounters a colder surface. In liquid, this occurs because it exchanges heat with colder liquid through direct exchange. In the example of the Earth's atmosphere, this occurs because it radiates heat. Because of this heat loss the fluid becomes denser than the fluid underneath it, which is still rising. Since it cannot descend through the rising fluid, it moves to one side. At some distance, its downward force overcomes the rising force beneath it, and the fluid begins to descend. As it descends, it warms again and the cycle repeats itself. Additionally, convection cells can arise due to density variations resulting from differences in the composition of electrolytes.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13">[13]</a></sup>
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<h3><span class="mw-headline" id="Atmospheric_convection">Atmospheric convection</span><span class="mw-editsection">
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<h4><span class="mw-headline" id="Atmospheric_circulation">Atmospheric circulation</span><span class="mw-editsection">
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<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033289096"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Atmospheric_circulation" title="Atmospheric circulation">Atmospheric circulation</a></div>
<figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Earth_Global_Circulation.jpg" class="mw-file-description"><img src="/media/wikipedia/commons/thumb/6/6d/Earth_Global_Circulation.jpg/300px-Earth_Global_Circulation.jpg" decoding="async" width="300" height="257" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/6/6d/Earth_Global_Circulation.jpg/450px-Earth_Global_Circulation.jpg 1.5x, /media/wikipedia/commons/6/6d/Earth_Global_Circulation.jpg 2x" data-file-width="556" data-file-height="477" /></a><figcaption>Idealised depiction of the global circulation on Earth</figcaption></figure>
<p><b>Atmospheric circulation</b> is the large-scale movement of air, and is a means by which <a href="/wiki/Thermal_energy" title="Thermal energy">thermal energy</a> is distributed on the surface of the <a href="/wiki/Earth" title="Earth">Earth</a>, together with the much slower (lagged) ocean circulation system. The large-scale structure of the <a href="/wiki/Atmospheric_circulation" title="Atmospheric circulation">atmospheric circulation</a> varies from year to year, but the basic climatological structure remains fairly constant.
</p><p>Latitudinal circulation occurs because incident solar <a href="/wiki/Radiation" title="Radiation">radiation</a> per unit area is highest at the <a href="/wiki/Heat_equator" class="mw-redirect" title="Heat equator">heat equator</a>, and decreases as the <a href="/wiki/Latitude" title="Latitude">latitude</a> increases, reaching minima at the poles. It consists of two primary convection cells, the <a href="/wiki/Hadley_cell" title="Hadley cell">Hadley cell</a> and the <a href="/wiki/Polar_vortex" title="Polar vortex">polar vortex</a>, with the <a href="/wiki/Hadley_cell" title="Hadley cell">Hadley cell</a> experiencing stronger convection due to the release of <a href="/wiki/Latent_heat" title="Latent heat">latent heat</a> energy by <a href="/wiki/Condensation" title="Condensation">condensation</a> of <a href="/wiki/Water_vapor" title="Water vapor">water vapor</a> at higher altitudes during cloud formation.
</p><p>Longitudinal circulation, on the other hand, comes about because the <a href="/wiki/Ocean" title="Ocean">ocean</a> has a higher specific heat capacity than land (and also <a href="/wiki/Thermal_conductivity" class="mw-redirect" title="Thermal conductivity">thermal conductivity</a>, allowing the heat to penetrate further beneath the surface ) and thereby absorbs and releases more <a href="/wiki/Heat" title="Heat">heat</a>, but the <a href="/wiki/Temperature" title="Temperature">temperature</a> changes less than land. This brings the sea breeze, air cooled by the water, ashore in the day, and carries the land breeze, air cooled by contact with the ground, out to sea during the night. Longitudinal circulation consists of two cells, the <a href="/wiki/Walker_circulation" title="Walker circulation">Walker circulation</a> and <a href="/wiki/El_Ni%C3%B1o-Southern_Oscillation" class="mw-redirect" title="El Niño-Southern Oscillation">El Niño / Southern Oscillation</a>.
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<h4><span class="mw-headline" id="Weather">Weather</span><span class="mw-editsection">
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<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033289096"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Cloud" title="Cloud">Cloud</a>, <a href="/wiki/Thunderstorm" title="Thunderstorm">Thunderstorm</a>, and <a href="/wiki/Wind" title="Wind">Wind</a></div>
<figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Foehn1.svg" class="mw-file-description"><img src="/media/wikipedia/commons/thumb/a/aa/Foehn1.svg/300px-Foehn1.svg.png" decoding="async" width="300" height="211" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/a/aa/Foehn1.svg/450px-Foehn1.svg.png 1.5x, /media/wikipedia/commons/thumb/a/aa/Foehn1.svg/600px-Foehn1.svg.png 2x" data-file-width="512" data-file-height="360" /></a><figcaption>How Foehn is produced</figcaption></figure>
<p>Some more localized phenomena than global atmospheric movement are also due to convection, including wind and some of the <a href="/wiki/Hydrologic_cycle" class="mw-redirect" title="Hydrologic cycle">hydrologic cycle</a>. For example, a <a href="/wiki/Foehn_wind" title="Foehn wind">foehn wind</a> is a down-slope wind which occurs on the downwind side of a mountain range. It results from the <a href="/wiki/Adiabatic" class="mw-redirect" title="Adiabatic">adiabatic</a> warming of air which has dropped most of its moisture on windward slopes.<sup id="cite_ref-MT_14-0" class="reference"><a href="#cite_note-MT-14">[14]</a></sup> Because of the different adiabatic lapse rates of moist and dry air, the air on the leeward slopes becomes warmer than at the same height on the windward slopes.
</p><p>A <a href="/wiki/Thermal_column" class="mw-redirect" title="Thermal column">thermal column</a> (or thermal) is a vertical section of rising air in the lower altitudes of the Earth's atmosphere. Thermals are created by the uneven heating of the Earth's surface from solar radiation. The Sun warms the ground, which in turn warms the air directly above it. The warmer air expands, becoming less dense than the surrounding air mass, and creating a <a href="/wiki/Thermal_low" title="Thermal low">thermal low</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15">[15]</a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16">[16]</a></sup> The mass of lighter air rises, and as it does, it cools by expansion at lower air pressures. It stops rising when it has cooled to the same temperature as the surrounding air. Associated with a thermal is a downward flow surrounding the thermal column. The downward moving exterior is caused by colder air being displaced at the top of the thermal. Another convection-driven weather effect is the <a href="/wiki/Sea_breeze" title="Sea breeze">sea breeze</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17">[17]</a></sup><sup id="cite_ref-Jet_18-0" class="reference"><a href="#cite_note-Jet-18">[18]</a></sup>
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<figure typeof="mw:File/Thumb"><a href="/wiki/File:Thunderstorm_formation.jpg" class="mw-file-description"><img src="/media/wikipedia/commons/thumb/c/c8/Thunderstorm_formation.jpg/500px-Thunderstorm_formation.jpg" decoding="async" width="500" height="255" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/c/c8/Thunderstorm_formation.jpg/750px-Thunderstorm_formation.jpg 1.5x, /media/wikipedia/commons/thumb/c/c8/Thunderstorm_formation.jpg/1000px-Thunderstorm_formation.jpg 2x" data-file-width="1087" data-file-height="554" /></a><figcaption>Stages of a thunderstorm's life.</figcaption></figure>
<p>Warm air has a lower density than cool air, so warm air rises within cooler air,<sup id="cite_ref-19" class="reference"><a href="#cite_note-19">[19]</a></sup> similar to <a href="/wiki/Hot_air_balloon" title="Hot air balloon">hot air balloons</a>.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20">[20]</a></sup> Clouds form as relatively warmer air carrying moisture rises within cooler air. As the moist air rises, it cools, causing some of the <a href="/wiki/Water_vapor" title="Water vapor">water vapor</a> in the rising packet of air to <a href="/wiki/Condensation" title="Condensation">condense</a>.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21">[21]</a></sup> When the moisture condenses, it releases energy known as <a href="/wiki/Latent_heat" title="Latent heat">latent heat</a> of condensation which allows the rising packet of air to cool less than its surrounding air,<sup id="cite_ref-22" class="reference"><a href="#cite_note-22">[22]</a></sup> continuing the cloud's ascension. If enough <a href="/wiki/Convective_available_potential_energy" title="Convective available potential energy">instability</a> is present in the atmosphere, this process will continue long enough for <a href="/wiki/Cumulonimbus" class="mw-redirect" title="Cumulonimbus">cumulonimbus clouds</a> to form, which support lightning and thunder. Generally, thunderstorms require three conditions to form: moisture, an unstable airmass, and a lifting force (heat).
</p><p>All <a href="/wiki/Thunderstorm" title="Thunderstorm">thunderstorms</a>, regardless of type, go through three stages: the <b>developing stage</b>, the <b>mature stage</b>, and the <b>dissipation stage</b>.<sup id="cite_ref-Extreme_Weather_23-0" class="reference"><a href="#cite_note-Extreme_Weather-23">[23]</a></sup> The average thunderstorm has a 24 km (15 mi) diameter. Depending on the conditions present in the atmosphere, these three stages take an average of 30 minutes to go through.<sup id="cite_ref-tsbasics_24-0" class="reference"><a href="#cite_note-tsbasics-24">[24]</a></sup>
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<h3><span class="mw-headline" id="Oceanic_circulation">Oceanic circulation</span><span class="mw-editsection">
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<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033289096"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Gulf_Stream" title="Gulf Stream">Gulf Stream</a> and <a href="/wiki/Thermohaline_circulation" title="Thermohaline circulation">Thermohaline circulation</a></div>
<figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Conveyor_belt.svg" class="mw-file-description"><img src="/media/wikipedia/commons/thumb/a/a6/Conveyor_belt.svg/200px-Conveyor_belt.svg.png" decoding="async" width="200" height="206" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/a/a6/Conveyor_belt.svg/300px-Conveyor_belt.svg.png 1.5x, /media/wikipedia/commons/thumb/a/a6/Conveyor_belt.svg/400px-Conveyor_belt.svg.png 2x" data-file-width="313" data-file-height="322" /></a><figcaption>Ocean currents</figcaption></figure>
<p>Solar radiation affects the oceans: warm water from the Equator tends to circulate toward the <a href="/wiki/Geographical_pole" title="Geographical pole">poles</a>, while cold polar water heads towards the Equator. The surface currents are initially dictated by surface wind conditions. The <a href="/wiki/Trade_winds" title="Trade winds">trade winds</a> blow westward in the tropics,<sup id="cite_ref-25" class="reference"><a href="#cite_note-25">[25]</a></sup> and the <a href="/wiki/Westerlies" title="Westerlies">westerlies</a> blow eastward at mid-latitudes.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26">[26]</a></sup> This wind pattern applies a <a href="/wiki/Stress_(physics)" class="mw-redirect" title="Stress (physics)">stress</a> to the subtropical ocean surface with negative <a href="/wiki/Curl_(mathematics)" title="Curl (mathematics)">curl</a> across the <a href="/wiki/Northern_Hemisphere" title="Northern Hemisphere">Northern Hemisphere</a>,<sup id="cite_ref-27" class="reference"><a href="#cite_note-27">[27]</a></sup> and the reverse across the <a href="/wiki/Southern_Hemisphere" title="Southern Hemisphere">Southern Hemisphere</a>. The resulting <a href="/wiki/Sverdrup_transport" class="mw-redirect" title="Sverdrup transport">Sverdrup transport</a> is equatorward.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28">[28]</a></sup> Because of conservation of <a href="/wiki/Potential_vorticity" title="Potential vorticity">potential vorticity</a> caused by the poleward-moving winds on the <a href="/wiki/Subtropical_ridge" class="mw-redirect" title="Subtropical ridge">subtropical ridge</a>'s western periphery and the increased relative vorticity of poleward moving water, transport is balanced by a narrow, accelerating poleward current, which flows along the western boundary of the ocean basin, outweighing the effects of friction with the cold western boundary current which originates from high latitudes.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29">[29]</a></sup> The overall process, known as western intensification, causes currents on the western boundary of an ocean basin to be stronger than those on the eastern boundary.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30">[30]</a></sup>
</p><p>As it travels poleward, warm water transported by strong warm water current undergoes evaporative cooling. The cooling is wind driven: wind moving over water cools the water and also causes <a href="/wiki/Evaporation" title="Evaporation">evaporation</a>, leaving a saltier brine. In this process, the water becomes saltier and denser. and decreases in temperature. Once sea ice forms, salts are left out of the ice, a process known as brine exclusion.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31">[31]</a></sup> These two processes produce water that is denser and colder. The water across the northern <a href="/wiki/Atlantic_Ocean" title="Atlantic Ocean">Atlantic Ocean</a> becomes so dense that it begins to sink down through less salty and less dense water. (This <a href="/wiki/Open_ocean_convection" title="Open ocean convection">open ocean convection</a> is not unlike that of a <a href="/wiki/Lava_lamp" title="Lava lamp">lava lamp</a>.) This downdraft of heavy, cold and dense water becomes a part of the <a href="/wiki/North_Atlantic_Deep_Water" title="North Atlantic Deep Water">North Atlantic Deep Water</a>, a south-going stream.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32">[32]</a></sup>
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<h3><span class="mw-headline" id="Mantle_convection">Mantle convection</span><span class="mw-editsection">
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<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033289096"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Mantle_convection" title="Mantle convection">Mantle convection</a></div>
<figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Accretion-Subduction.PNG" class="mw-file-description"><img src="/media/wikipedia/commons/thumb/6/62/Accretion-Subduction.PNG/250px-Accretion-Subduction.PNG" decoding="async" width="250" height="129" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/6/62/Accretion-Subduction.PNG/375px-Accretion-Subduction.PNG 1.5x, /media/wikipedia/commons/thumb/6/62/Accretion-Subduction.PNG/500px-Accretion-Subduction.PNG 2x" data-file-width="751" data-file-height="388" /></a><figcaption>An <a href="/wiki/Oceanic_plate" class="mw-redirect" title="Oceanic plate">oceanic plate</a> is added to by upwelling (left) and consumed at a <a href="/wiki/Subduction" title="Subduction">subduction</a> zone (right).</figcaption></figure>
<p><b>Mantle convection</b> is the slow creeping motion of Earth's rocky mantle caused by convection currents carrying heat from the interior of the Earth to the surface.<sup id="cite_ref-University_of_Winnipeg_33-0" class="reference"><a href="#cite_note-University_of_Winnipeg-33">[33]</a></sup> It is one of 3 driving forces that causes tectonic plates to move around the Earth's surface.<sup id="cite_ref-Condie_34-0" class="reference"><a href="#cite_note-Condie-34">[34]</a></sup>
</p><p>The Earth's surface is divided into a number of <a href="/wiki/Tectonic" class="mw-redirect" title="Tectonic">tectonic</a> plates that are continuously being created and consumed at their opposite plate boundaries. Creation (<a href="/wiki/Accretion_(geology)" title="Accretion (geology)">accretion</a>) occurs as mantle is added to the growing edges of a plate. This hot added material cools down by conduction and convection of heat. At the consumption edges of the plate, the material has thermally contracted to become dense, and it sinks under its own weight in the process of subduction at an ocean trench. This subducted material sinks to some depth in the Earth's interior where it is prohibited from sinking further. The subducted oceanic crust triggers volcanism.
</p><p>Convection within <a href="/wiki/Earth%27s_mantle" title="Earth's mantle">Earth's mantle</a> is the driving force for <a href="/wiki/Plate_tectonics" title="Plate tectonics">plate tectonics</a>. Mantle convection is the result of a thermal gradient: the lower mantle is hotter than the <a href="/wiki/Upper_mantle_(Earth)" class="mw-redirect" title="Upper mantle (Earth)">upper mantle</a>, and is therefore less dense. This sets up two primary types of instabilities. In the first type, plumes rise from the lower mantle, and corresponding unstable regions of <a href="/wiki/Lithosphere" title="Lithosphere">lithosphere</a> drip back into the mantle. In the second type, subducting oceanic plates (which largely constitute the upper thermal boundary layer of the mantle) plunge back into the mantle and move downwards towards the <a href="/wiki/Core-mantle_boundary" class="mw-redirect" title="Core-mantle boundary">core-mantle boundary</a>. Mantle convection occurs at rates of centimeters per year, and it takes on the order of hundreds of millions of years to complete a cycle of convection.
</p><p>Neutrino flux measurements from the Earth's core (see <a href="/wiki/KamLAND" class="mw-redirect" title="KamLAND">kamLAND</a>) show the source of about two-thirds of the heat in the inner core is the <a href="/wiki/Radioactive_decay" title="Radioactive decay">radioactive decay</a> of <a href="/wiki/Potassium" title="Potassium"><sup>40</sup>K</a>, uranium and thorium. This has allowed plate tectonics on Earth to continue far longer than it would have if it were simply driven by heat left over from Earth's formation; or with heat produced from <a href="/wiki/Gravitational_energy" title="Gravitational energy">gravitational potential energy</a>, as a result of physical rearrangement of denser portions of the Earth's interior toward the center of the planet (that is, a type of prolonged falling and settling).
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<h3><span class="mw-headline" id="Stack_effect">Stack effect</span><span class="mw-editsection">
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<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033289096"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Stack_effect" title="Stack effect">Stack effect</a></div>
<p>The <b>Stack effect</b> or <b>chimney effect</b> is the movement of air into and out of buildings, chimneys, flue gas stacks, or other containers due to buoyancy. Buoyancy occurs due to a difference in indoor-to-outdoor air density resulting from temperature and moisture differences. The greater the thermal difference and the height of the structure, the greater the buoyancy force, and thus the stack effect. The stack effect helps drive natural ventilation and infiltration. Some <a href="/wiki/Cooling_tower" title="Cooling tower">cooling towers</a> operate on this principle; similarly the <a href="/wiki/Solar_updraft_tower" title="Solar updraft tower">solar updraft tower</a> is a proposed device to generate electricity based on the stack effect.
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<h3><span class="mw-headline" id="Stellar_physics">Stellar physics</span><span class="mw-editsection">
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<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033289096"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Convection_zone" title="Convection zone">Convection zone</a> and <a href="/wiki/Granule_(solar_physics)" class="mw-redirect" title="Granule (solar physics)">granule (solar physics)</a></div>
<figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Structure_of_Stars_(artist%E2%80%99s_impression).jpg" class="mw-file-description"><img src="/media/wikipedia/commons/thumb/c/c3/Structure_of_Stars_%28artist%E2%80%99s_impression%29.jpg/300px-Structure_of_Stars_%28artist%E2%80%99s_impression%29.jpg" decoding="async" width="300" height="227" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/c/c3/Structure_of_Stars_%28artist%E2%80%99s_impression%29.jpg/450px-Structure_of_Stars_%28artist%E2%80%99s_impression%29.jpg 1.5x, /media/wikipedia/commons/thumb/c/c3/Structure_of_Stars_%28artist%E2%80%99s_impression%29.jpg/600px-Structure_of_Stars_%28artist%E2%80%99s_impression%29.jpg 2x" data-file-width="5176" data-file-height="3910" /></a><figcaption>An illustration of the structure of the <a href="/wiki/Sun" title="Sun">Sun</a> and a <a href="/wiki/Red_giant" title="Red giant">red giant</a> star, showing their convective zones. These are the granular zones in the outer layers of these stars.</figcaption></figure>
<p>The convection zone of a star is the range of radii in which energy is transported outward from the <a href="/wiki/Stellar_core" title="Stellar core">core region</a> primarily by convection rather than <a href="/wiki/Radiation_zone" title="Radiation zone">radiation</a>. This occurs at radii which are sufficiently <a href="/wiki/Opacity_(optics)" title="Opacity (optics)">opaque</a> that convection is more efficient than radiation at transporting energy.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35">[35]</a></sup>
</p><p>Granules on the <a href="/wiki/Photosphere" title="Photosphere">photosphere</a> of the Sun are the visible tops of convection cells in the photosphere, caused by convection of <a href="/wiki/Plasma_(physics)" title="Plasma (physics)">plasma</a> in the photosphere. The rising part of the granules is located in the center where the plasma is hotter. The outer edge of the granules is darker due to the cooler descending plasma. A typical granule has a diameter on the order of 1,000 kilometers and each lasts 8 to 20 minutes before dissipating. Below the photosphere is a layer of much larger "supergranules" up to 30,000 kilometers in diameter, with lifespans of up to 24 hours.
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<h3><span class="mw-headline" id="Water_convection_at_freezing_temperatures">Water convection at freezing temperatures</span><span class="mw-editsection">
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<p><a href="/wiki/Water" title="Water">Water</a> is a fluid that does not obey the Boussinesq approximation.<sup id="cite_ref-:0_36-0" class="reference"><a href="#cite_note-:0-36">[36]</a></sup> This is because its density varies nonlinearly with temperature, which causes its thermal expansion coefficient to be inconsistent near freezing temperatures.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37">[37]</a></sup><sup id="cite_ref-:1_38-0" class="reference"><a href="#cite_note-:1-38">[38]</a></sup> The <a href="/wiki/Density_of_water" class="mw-redirect" title="Density of water">density of water</a> reaches a maximum at 4 °C and decreases as the temperature deviates. This phenomenon is investigated by experiment and numerical methods.<sup id="cite_ref-:0_36-1" class="reference"><a href="#cite_note-:0-36">[36]</a></sup> Water is initially stagnant at 10 °C within a square cavity. It is differentially heated between the two vertical walls, where the left and right walls are held at 10 °C and 0 °C, respectively. The density anomaly manifests in its flow pattern.<sup id="cite_ref-:0_36-2" class="reference"><a href="#cite_note-:0-36">[36]</a></sup><sup id="cite_ref-39" class="reference"><a href="#cite_note-39">[39]</a></sup><sup id="cite_ref-40" class="reference"><a href="#cite_note-40">[40]</a></sup><sup id="cite_ref-41" class="reference"><a href="#cite_note-41">[41]</a></sup> As the water is cooled at the right wall, the density increases, which accelerates the flow downward. As the flow develops and the water cools further, the decrease in density causes a recirculation current at the bottom right corner of the cavity.
</p><p>Another case of this phenomenon is the event of <a href="/wiki/Supercooling" title="Supercooling">super-cooling</a>, where the water is cooled to below freezing temperatures but does not immediately begin to freeze.<sup id="cite_ref-:1_38-1" class="reference"><a href="#cite_note-:1-38">[38]</a></sup><sup id="cite_ref-:2_42-0" class="reference"><a href="#cite_note-:2-42">[42]</a></sup> Under the same conditions as before, the flow is developed. Afterward, the temperature of the right wall is decreased to −10 °C. This causes the water at that wall to become supercooled, create a counter-clockwise flow, and initially overpower the warm current.<sup id="cite_ref-:0_36-3" class="reference"><a href="#cite_note-:0-36">[36]</a></sup> This plume is caused by a delay in the <a href="/wiki/Nucleation_of_ice" class="mw-redirect" title="Nucleation of ice">nucleation of the ice</a>.<sup id="cite_ref-:0_36-4" class="reference"><a href="#cite_note-:0-36">[36]</a></sup><sup id="cite_ref-:1_38-2" class="reference"><a href="#cite_note-:1-38">[38]</a></sup><sup id="cite_ref-:2_42-1" class="reference"><a href="#cite_note-:2-42">[42]</a></sup> Once ice begins to form, the flow returns to a similar pattern as before and the solidification propagates gradually until the flow is redeveloped.<sup id="cite_ref-:0_36-5" class="reference"><a href="#cite_note-:0-36">[36]</a></sup>
</p>
<h3><span class="mw-headline" id="Nuclear_reactors">Nuclear reactors</span><span class="mw-editsection">
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<p>In a <a href="/wiki/Nuclear_reactor" title="Nuclear reactor">nuclear reactor</a>, natural circulation can be a design criterion. It is achieved by reducing turbulence and friction in the fluid flow (that is, minimizing <a href="/wiki/Head_loss" class="mw-redirect" title="Head loss">head loss</a>), and by providing a way to remove any inoperative pumps from the fluid path. Also, the reactor (as the heat source) must be physically lower than the steam generators or turbines (the heat sink). In this way, natural circulation will ensure that the fluid will continue to flow as long as the reactor is hotter than the heat sink, even when power cannot be supplied to the pumps. Notable examples are the <a href="/wiki/S5G_reactor" title="S5G reactor">S5G</a>
<sup id="cite_ref-43" class="reference"><a href="#cite_note-43">[43]</a></sup><sup id="cite_ref-44" class="reference"><a href="#cite_note-44">[44]</a></sup><sup id="cite_ref-45" class="reference"><a href="#cite_note-45">[45]</a></sup>
and <a href="/wiki/S8G_reactor" title="S8G reactor">S8G</a><sup id="cite_ref-46" class="reference"><a href="#cite_note-46">[46]</a></sup><sup id="cite_ref-47" class="reference"><a href="#cite_note-47">[47]</a></sup><sup id="cite_ref-48" class="reference"><a href="#cite_note-48">[48]</a></sup> <a href="/wiki/United_States_Naval_reactor" class="mw-redirect" title="United States Naval reactor">United States Naval reactors</a>, which were designed to operate at a significant fraction of full power under natural circulation, quieting those propulsion plants. The <a href="/wiki/S6G_reactor" title="S6G reactor">S6G reactor</a> cannot operate at power under natural circulation, but can use it to maintain emergency cooling while shut down.
</p><p>By the nature of natural circulation, fluids do not typically move very fast, but this is not necessarily bad, as high flow rates are not essential to safe and effective reactor operation. In modern design nuclear reactors, flow reversal is almost impossible. All nuclear reactors, even ones designed to primarily use natural circulation as the main method of fluid circulation, have pumps that can circulate the fluid in the case that natural circulation is not sufficient.
</p>
<h2><span class="mw-headline" id="Mathematical_models_of_convection">Mathematical models of convection</span><span class="mw-editsection">
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<p>A number of dimensionless terms have been derived to describe and predict convection, including the <a href="/wiki/Archimedes_number" title="Archimedes number">Archimedes number</a>, <a href="/wiki/Grashof_number" title="Grashof number">Grashof number</a>, <a href="/wiki/Richardson_number" title="Richardson number">Richardson number</a>, and the <a href="/wiki/Rayleigh_number" title="Rayleigh number">Rayleigh number</a>.
</p><p>In cases of mixed convection (natural and forced occurring together) one would often like to know how much of the convection is due to external constraints, such as the fluid velocity in the pump, and how much is due to natural convection occurring in the system.
</p><p>The relative magnitudes of the <a href="/wiki/Grashof_number" title="Grashof number">Grashof number</a> and the square of the <a href="/wiki/Reynolds_number" title="Reynolds number">Reynolds number</a> determine which form of convection dominates. If <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {Gr/Re^{2}\gg 1}}}">
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<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
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<mi mathvariant="normal">R</mi>
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</math></span><img src="/media/api/rest_v1/media/math/render/svg/c5b2bad4051fee9a3135dfc442c662d9bbe4ade4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.472ex; height:3.176ex;" alt="{\displaystyle {\rm {Gr/Re^{2}\gg 1}}}"></span>, forced convection may be neglected, whereas if <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {Gr/Re^{2}\ll 1}}}">
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<mi mathvariant="normal">R</mi>
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<annotation encoding="application/x-tex">{\displaystyle {\rm {Gr/Re^{2}\ll 1}}}</annotation>
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</math></span><img src="/media/api/rest_v1/media/math/render/svg/d784c76d32aebefbac7931a256745d5f09ffd951" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.472ex; height:3.176ex;" alt="{\displaystyle {\rm {Gr/Re^{2}\ll 1}}}"></span>, natural convection may be neglected. If the ratio, known as the <a href="/wiki/Richardson_number#Thermal_convection" title="Richardson number">Richardson number</a>, is approximately one, then both forced and natural convection need to be taken into account.
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<h3><span class="mw-headline" id="Onset">Onset</span><span class="mw-editsection">
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<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033289096"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Heat_transfer" title="Heat transfer">Heat transfer</a></div>
<p>The onset of natural convection is determined by the <a href="/wiki/Rayleigh_number" title="Rayleigh number">Rayleigh number</a> (<b>Ra</b>). This <a href="/wiki/Dimensionless_number" class="mw-redirect" title="Dimensionless number">dimensionless number</a> is given by
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\textbf {Ra}}={\frac {\Delta \rho gL^{3}}{D\mu }}}">
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<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mtext mathvariant="bold">Ra</mtext>
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<mi mathvariant="normal">Δ<!-- Δ --></mi>
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<annotation encoding="application/x-tex">{\displaystyle {\textbf {Ra}}={\frac {\Delta \rho gL^{3}}{D\mu }}}</annotation>
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</math></span><img src="/media/api/rest_v1/media/math/render/svg/da497f9649d280d113f7f2994d7283d6ff97f601" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.128ex; height:6.176ex;" alt="{\displaystyle {\textbf {Ra}}={\frac {\Delta \rho gL^{3}}{D\mu }}}"></span></dd></dl>
<p>where
</p>
<ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \rho }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>ρ<!-- ρ --></mi>
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<annotation encoding="application/x-tex">{\displaystyle \Delta \rho }</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/9ac7403b36530639e4330396cb1a8264b5c08693" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.138ex; height:2.676ex;" alt="{\displaystyle \Delta \rho }"></span> is the difference in density between the two parcels of material that are mixing</li>
<li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g}">
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<mi>g</mi>
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<annotation encoding="application/x-tex">{\displaystyle g}</annotation>
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</math></span><img src="/media/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.116ex; height:2.009ex;" alt="{\displaystyle g}"></span> is the local <a href="/wiki/Gravitational_acceleration" title="Gravitational acceleration">gravitational acceleration</a></li>
<li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L}">
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<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>L</mi>
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<annotation encoding="application/x-tex">{\displaystyle L}</annotation>
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</math></span><img src="/media/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span> is the characteristic length-scale of convection: the depth of the boiling pot, for example</li>
<li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">
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<mi>D</mi>
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<annotation encoding="application/x-tex">{\displaystyle D}</annotation>
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</math></span><img src="/media/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></span> is the <a href="/wiki/Diffusivity" title="Diffusivity">diffusivity</a> of the characteristic that is causing the convection, and</li>
<li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu }">
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<mi>μ<!-- μ --></mi>
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<annotation encoding="application/x-tex">{\displaystyle \mu }</annotation>
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</math></span><img src="/media/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> is the <a href="/wiki/Dynamic_viscosity" class="mw-redirect" title="Dynamic viscosity">dynamic viscosity</a>.</li></ul>
<p>Natural convection will be more likely and/or more rapid with a greater variation in density between the two fluids, a larger acceleration due to gravity that drives the convection, and/or a larger distance through the convecting medium. Convection will be less likely and/or less rapid with more rapid diffusion (thereby diffusing away the gradient that is causing the convection) and/or a more viscous (sticky) fluid.
</p><p>For thermal convection due to heating from below, as described in the boiling pot above, the equation is modified for thermal expansion and thermal diffusivity. Density variations due to thermal expansion are given by:
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \rho =\rho _{0}\beta \Delta T}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>ρ<!-- ρ --></mi>
<mo>=</mo>
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<mi>ρ<!-- ρ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
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<mi>β<!-- β --></mi>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>T</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Delta \rho =\rho _{0}\beta \Delta T}</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/303a2ba3b8d843bd9c9daf854873d5c9b1336f37" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.397ex; height:2.676ex;" alt="{\displaystyle \Delta \rho =\rho _{0}\beta \Delta T}"></span></dd></dl>
<p>where
</p>
<ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{0}}">
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<mi>ρ<!-- ρ --></mi>
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<annotation encoding="application/x-tex">{\displaystyle \rho _{0}}</annotation>
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</math></span><img src="/media/api/rest_v1/media/math/render/svg/d9c04a9d26b86af8c6205ba2a6287fd655b6b714" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.256ex; height:2.176ex;" alt="{\displaystyle \rho _{0}}"></span> is the reference density, typically picked to be the average density of the medium,</li>
<li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>β<!-- β --></mi>
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<annotation encoding="application/x-tex">{\displaystyle \beta }</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> is the <a href="/wiki/Coefficient_of_thermal_expansion" class="mw-redirect" title="Coefficient of thermal expansion">coefficient of thermal expansion</a>, and</li>
<li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta T}">
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<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>T</mi>
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<annotation encoding="application/x-tex">{\displaystyle \Delta T}</annotation>
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</math></span><img src="/media/api/rest_v1/media/math/render/svg/e61e7deb9c7c7b7dda762b0935e757add2acc559" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.572ex; height:2.176ex;" alt="{\displaystyle \Delta T}"></span> is the temperature difference across the medium.</li></ul>
<p>The general diffusivity, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>D</mi>
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<annotation encoding="application/x-tex">{\displaystyle D}</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></span>, is redefined as a <a href="/wiki/Thermal_diffusivity" title="Thermal diffusivity">thermal diffusivity</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }">
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<mrow class="MJX-TeXAtom-ORD">
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<mi>α<!-- α --></mi>
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<annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span>.
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D=\alpha }">
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<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>D</mi>
<mo>=</mo>
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<annotation encoding="application/x-tex">{\displaystyle D=\alpha }</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/e97b4bb5b4df2d84fd4d9bf90bbe3b76cae6e63c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.51ex; height:2.176ex;" alt="{\displaystyle D=\alpha }"></span></dd></dl>
<p>Inserting these substitutions produces a Rayleigh number that can be used to predict thermal convection.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49">[49]</a></sup>
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\textbf {Ra}}={\frac {\rho _{0}g\beta \Delta TL^{3}}{\alpha \mu }}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
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<mtext mathvariant="bold">Ra</mtext>
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<mo>=</mo>
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<mfrac>
<mrow>
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<mi>ρ<!-- ρ --></mi>
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<mn>0</mn>
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<mrow class="MJX-TeXAtom-ORD">
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</mfrac>
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<annotation encoding="application/x-tex">{\displaystyle {\textbf {Ra}}={\frac {\rho _{0}g\beta \Delta TL^{3}}{\alpha \mu }}}</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/23280142cb108f2b3aed074796d502833392e704" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.151ex; height:6.176ex;" alt="{\displaystyle {\textbf {Ra}}={\frac {\rho _{0}g\beta \Delta TL^{3}}{\alpha \mu }}}"></span></dd></dl>
<h3><span class="mw-headline" id="Turbulence">Turbulence</span><span class="mw-editsection">
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<p>The tendency of a particular naturally convective system towards turbulence relies on the <a href="/wiki/Grashof_number" title="Grashof number">Grashof number</a> (Gr).<sup id="cite_ref-50" class="reference"><a href="#cite_note-50">[50]</a></sup>
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Gr={\frac {g\beta \Delta TL^{3}}{\nu ^{2}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>G</mi>
<mi>r</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>g</mi>
<mi>β<!-- β --></mi>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>T</mi>
<msup>
<mi>L</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
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</msup>
</mrow>
<msup>
<mi>ν<!-- ν --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
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</msup>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle Gr={\frac {g\beta \Delta TL^{3}}{\nu ^{2}}}}</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/a7a0e8ef300dd43e003fa0d93939f402554d9d3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.467ex; height:5.843ex;" alt="{\displaystyle Gr={\frac {g\beta \Delta TL^{3}}{\nu ^{2}}}}"></span></dd></dl>
<p>In very sticky, viscous fluids (large <i>ν</i>), fluid motion is restricted, and natural convection will be non-turbulent.
</p><p>Following the treatment of the previous subsection, the typical fluid velocity is of the order of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g\Delta \rho L^{2}/\mu }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>g</mi>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>ρ<!-- ρ --></mi>
<msup>
<mi>L</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
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<mo>/</mo>
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<mi>μ<!-- μ --></mi>
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<annotation encoding="application/x-tex">{\displaystyle g\Delta \rho L^{2}/\mu }</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/28fe931daf9bedb4ccd5916b1aef9ef8f7ad59bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.455ex; height:3.176ex;" alt="{\displaystyle g\Delta \rho L^{2}/\mu }"></span>, up to a numerical factor depending on the geometry of the system. Therefore, Grashof number can be thought of as <a href="/wiki/Reynolds_number" title="Reynolds number">Reynolds number</a> with the velocity of natural convection replacing the velocity in Reynolds number's formula. However In practice, when referring to the Reynolds number, it is understood that one is considering forced convection, and the velocity is taken as the velocity dictated by external constraints (see below).
</p>
<h3><span class="mw-headline" id="Behavior">Behavior</span><span class="mw-editsection">
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<p>The <a href="/wiki/Grashof_number" title="Grashof number">Grashof number</a> can be formulated for natural convection occurring due to a <a href="/wiki/Concentration_gradient" class="mw-redirect" title="Concentration gradient">concentration gradient</a>, sometimes termed thermo-solutal convection. In this case, a concentration of hot fluid diffuses into a cold fluid, in much the same way that ink poured into a container of water diffuses to dye the entire space. Then:
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Gr={\frac {g\beta \Delta CL^{3}}{\nu ^{2}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>G</mi>
<mi>r</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>g</mi>
<mi>β<!-- β --></mi>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>C</mi>
<msup>
<mi>L</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msup>
</mrow>
<msup>
<mi>ν<!-- ν --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
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</msup>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle Gr={\frac {g\beta \Delta CL^{3}}{\nu ^{2}}}}</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/f4359a6e1df57a3a2a901bca54a1aa6935a06162" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.597ex; height:5.843ex;" alt="{\displaystyle Gr={\frac {g\beta \Delta CL^{3}}{\nu ^{2}}}}"></span></dd></dl>
<p>Natural convection is highly dependent on the geometry of the hot surface, various correlations exist in order to determine the heat transfer coefficient.
A general correlation that applies for a variety of geometries is
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Nu=\left[Nu_{0}^{\frac {1}{2}}+Ra^{\frac {1}{6}}\left({\frac {f_{4}\left(Pr\right)}{300}}\right)^{\frac {1}{6}}\right]^{2}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>N</mi>
<mi>u</mi>
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<mo>[</mo>
<mrow>
<mi>N</mi>
<msubsup>
<mi>u</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
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<mn>1</mn>
<mn>2</mn>
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<mo>+</mo>
<mi>R</mi>
<msup>
<mi>a</mi>
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<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
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<msup>
<mrow>
<mo>(</mo>
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<mfrac>
<mrow>
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
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</msub>
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<mo>(</mo>
<mrow>
<mi>P</mi>
<mi>r</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>300</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
</mrow>
</msup>
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<mo>]</mo>
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<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
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</mrow>
<annotation encoding="application/x-tex">{\displaystyle Nu=\left[Nu_{0}^{\frac {1}{2}}+Ra^{\frac {1}{6}}\left({\frac {f_{4}\left(Pr\right)}{300}}\right)^{\frac {1}{6}}\right]^{2}}</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/5c796fe28809788aeefc2f78744547847689eae8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:36.523ex; height:9.009ex;" alt="{\displaystyle Nu=\left[Nu_{0}^{\frac {1}{2}}+Ra^{\frac {1}{6}}\left({\frac {f_{4}\left(Pr\right)}{300}}\right)^{\frac {1}{6}}\right]^{2}}"></span></dd></dl>
<p>The value of f<sub>4</sub>(Pr) is calculated using the following formula
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{4}(Pr)=\left[1+\left({\frac {0.5}{Pr}}\right)^{\frac {9}{16}}\right]^{\frac {-16}{9}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mi>P</mi>
<mi>r</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<msup>
<mrow>
<mo>[</mo>
<mrow>
<mn>1</mn>
<mo>+</mo>
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<mo>(</mo>
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<mn>0.5</mn>
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<mo>)</mo>
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<mfrac>
<mn>9</mn>
<mn>16</mn>
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<annotation encoding="application/x-tex">{\displaystyle f_{4}(Pr)=\left[1+\left({\frac {0.5}{Pr}}\right)^{\frac {9}{16}}\right]^{\frac {-16}{9}}}</annotation>
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</math></span><img src="/media/api/rest_v1/media/math/render/svg/4a50d2a430fbd1360680d731061cbf11728ac1ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:30.072ex; height:9.676ex;" alt="{\displaystyle f_{4}(Pr)=\left[1+\left({\frac {0.5}{Pr}}\right)^{\frac {9}{16}}\right]^{\frac {-16}{9}}}"></span></dd></dl>
<p>Nu is the <a href="/wiki/Nusselt_number" title="Nusselt number">Nusselt number</a> and the values of Nu<sub>0</sub> and the characteristic length used to calculate Re are listed below (see also Discussion):
</p>
<table class="wikitable">
<tbody><tr>
<th><b>Geometry</b>
</th>
<th><b>Characteristic length</b>
</th>
<th><b>Nu<sub>0</sub></b>
</th></tr>
<tr>
<td>Inclined plane
</td>
<td>x (Distance along plane)
</td>
<td>0.68
</td></tr>
<tr>
<td>Inclined disk
</td>
<td>9D/11 (D = diameter)
</td>
<td>0.56
</td></tr>
<tr>
<td>Vertical cylinder
</td>
<td>x (height of cylinder)
</td>
<td>0.68
</td></tr>
<tr>
<td>Cone
</td>
<td>4x/5 (x = distance along sloping surface)
</td>
<td>0.54
</td></tr>
<tr>
<td>Horizontal cylinder
</td>
<td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi D/2}">
<semantics>
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<mstyle displaystyle="true" scriptlevel="0">
<mi>π<!-- π --></mi>
<mi>D</mi>
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<mo>/</mo>
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<mn>2</mn>
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</mrow>
<annotation encoding="application/x-tex">{\displaystyle \pi D/2}</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/ec91bb758addc81cc81f5caeaac67b593c1196db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.581ex; height:2.843ex;" alt="{\displaystyle \pi D/2}"></span> (D = diameter of cylinder)
</td>
<td>0.36<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>π<!-- π --></mi>
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<annotation encoding="application/x-tex">{\displaystyle \pi }</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span>
</td></tr></tbody></table>
<p><b>Warning</b>: The values indicated for the <b>Horizontal cylinder</b> are <b>wrong</b>; see discussion.
</p>
<h2><span class="mw-headline" id="Natural_convection_from_a_vertical_plate">Natural convection from a vertical plate</span><span class="mw-editsection">
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<p>One example of natural convection is heat transfer from an isothermal vertical plate immersed in a fluid, causing the fluid to move parallel to the plate. This will occur in any system wherein the density of the moving fluid varies with position. These phenomena will only be of significance when the moving fluid is minimally affected by forced convection.<sup id="cite_ref-unitop_51-0" class="reference"><a href="#cite_note-unitop-51">[51]</a></sup>
</p><p>When considering the flow of fluid is a result of heating, the following correlations can be used, assuming the fluid is an ideal diatomic, has adjacent to a vertical plate at constant temperature and the flow of the fluid is completely laminar.<sup id="cite_ref-bennett_52-0" class="reference"><a href="#cite_note-bennett-52">[52]</a></sup>
</p><p>Nu<sub>m</sub> = 0.478(Gr<sup>0.25</sup>)<sup id="cite_ref-bennett_52-1" class="reference"><a href="#cite_note-bennett-52">[52]</a></sup>
</p><p>Mean <a href="/wiki/Nusselt_number" title="Nusselt number">Nusselt number</a> = Nu<sub>m</sub> = h<sub>m</sub>L/k<sup id="cite_ref-bennett_52-2" class="reference"><a href="#cite_note-bennett-52">[52]</a></sup>
</p><p>where
</p>
<ul><li>h<sub>m</sub> = mean coefficient applicable between the lower edge of the plate and any point in a distance L (W/m<sup>2</sup>. K)</li>
<li>L = height of the vertical surface (m)</li>
<li>k = thermal conductivity (W/m. K)</li></ul>
<p><a href="/wiki/Grashof_number" title="Grashof number">Grashof number</a> = Gr = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [gL^{3}(t_{s}-t_{\infty })]/v^{2}T}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo stretchy="false">[</mo>
<mi>g</mi>
<msup>
<mi>L</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msup>
<mo stretchy="false">(</mo>
<msub>
<mi>t</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>s</mi>
</mrow>
</msub>
<mo>−<!-- − --></mo>
<msub>
<mi>t</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">∞<!-- ∞ --></mi>
</mrow>
</msub>
<mo stretchy="false">)</mo>
<mo stretchy="false">]</mo>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<msup>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
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</msup>
<mi>T</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle [gL^{3}(t_{s}-t_{\infty })]/v^{2}T}</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/7cefc61521e7ee2bbcd5874caa3ea5fc54cdcada" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.235ex; height:3.176ex;" alt="{\displaystyle [gL^{3}(t_{s}-t_{\infty })]/v^{2}T}"></span> <sup id="cite_ref-unitop_51-1" class="reference"><a href="#cite_note-unitop-51">[51]</a></sup><sup id="cite_ref-bennett_52-3" class="reference"><a href="#cite_note-bennett-52">[52]</a></sup>
</p><p>where
</p>
<ul><li>g = gravitational acceleration (m/s<sup>2</sup>)</li>
<li>L = distance above the lower edge (m)</li>
<li>t<sub>s</sub> = temperature of the wall (K)</li>
<li>t∞ = fluid temperature outside the thermal boundary layer (K)</li>
<li>v = kinematic viscosity of the fluid (m<sup>2</sup>/s)</li>
<li>T = absolute temperature (K)</li></ul>
<p>When the flow is turbulent different correlations involving the Rayleigh Number (a function of both the <a href="/wiki/Grashof_number" title="Grashof number">Grashof number</a> and the <a href="/wiki/Prandtl_number" title="Prandtl number">Prandtl number</a>) must be used.<sup id="cite_ref-bennett_52-4" class="reference"><a href="#cite_note-bennett-52">[52]</a></sup>
</p><p>Note that the above equation differs from the usual expression for <a href="/wiki/Grashof_number" title="Grashof number">Grashof number</a> because the value <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>β<!-- β --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \beta }</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> has been replaced by its approximation <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1/T}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mn>1</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mi>T</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle 1/T}</annotation>
</semantics>
</math></span><img src="/media/api/rest_v1/media/math/render/svg/ee06bfe8f48b840ea1c11f78977a90f661f2375e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.961ex; height:2.843ex;" alt="{\displaystyle 1/T}"></span>, which applies for ideal gases only (a reasonable approximation for air at ambient pressure).
</p>
<h2><span class="mw-headline" id="Pattern_formation">Pattern formation</span><span class="mw-editsection">
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<figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Convection1.png" class="mw-file-description"><img src="/media/wikipedia/commons/thumb/2/2e/Convection1.png/220px-Convection1.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/2/2e/Convection1.png/330px-Convection1.png 1.5x, /media/wikipedia/commons/thumb/2/2e/Convection1.png/440px-Convection1.png 2x" data-file-width="720" data-file-height="540" /></a><figcaption>A fluid under <a href="/wiki/Rayleigh%E2%80%93B%C3%A9nard_convection" title="Rayleigh–Bénard convection">Rayleigh–Bénard convection</a>: the left picture represents the thermal field and the right picture its two-dimensional <a href="/wiki/Fourier_transform" title="Fourier transform">Fourier transform</a>.</figcaption></figure>
<p>Convection, especially <a href="/wiki/Rayleigh%E2%80%93B%C3%A9nard_convection" title="Rayleigh–Bénard convection">Rayleigh–Bénard convection</a>, where the convecting fluid is contained by two rigid horizontal plates, is a convenient example of a <a href="/wiki/Pattern_formation" title="Pattern formation">pattern-forming system</a>.
</p><p>When heat is fed into the system from one direction (usually below), at small values it merely diffuses (<i>conducts</i>) from below upward, without causing fluid flow. As the heat flow is increased, above a critical value of the <a href="/wiki/Rayleigh_number" title="Rayleigh number">Rayleigh number</a>, the system undergoes a <a href="/wiki/Bifurcation_theory" title="Bifurcation theory">bifurcation</a> from the stable <i>conducting</i> state to the <i>convecting</i> state, where bulk motion of the fluid due to heat begins. If fluid parameters other than density do not depend significantly on temperature, the flow profile is symmetric, with the same volume of fluid rising as falling. This is known as <a href="/wiki/Boussinesq_approximation_(buoyancy)" title="Boussinesq approximation (buoyancy)">Boussinesq</a> convection.
</p><p>As the temperature difference between the top and bottom of the fluid becomes higher, significant differences in fluid parameters other than density may develop in the fluid due to temperature. An example of such a parameter is <a href="/wiki/Viscosity" title="Viscosity">viscosity</a>, which may begin to significantly vary horizontally across layers of fluid. This breaks the symmetry of the system, and generally changes the pattern of up- and down-moving fluid from stripes to hexagons, as seen at right. Such hexagons are one example of a <a href="/wiki/Convection_cell" title="Convection cell">convection cell</a>.
</p><p>As the <a href="/wiki/Rayleigh_number" title="Rayleigh number">Rayleigh number</a> is increased even further above the value where convection cells first appear, the system may undergo other bifurcations, and other more complex patterns, such as <a href="/wiki/Spiral" title="Spiral">spirals</a>, may begin to appear.
</p>
<h2><span class="mw-headline" id="See_also">See also</span><span class="mw-editsection">
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<ul><li><a href="/wiki/Convection-diffusion_equation" class="mw-redirect" title="Convection-diffusion equation">Convection-diffusion equation</a></li>
<li><a href="/wiki/B%C3%A9nard_cells" class="mw-redirect" title="Bénard cells">Bénard cells</a></li>
<li><a href="/wiki/Churchill%E2%80%93Bernstein_equation" title="Churchill–Bernstein equation">Churchill–Bernstein equation</a></li>
<li><a href="/wiki/Combined_forced_and_natural_convection" title="Combined forced and natural convection">Combined forced and natural convection</a></li>
<li><a href="/wiki/Double_diffusive_convection" title="Double diffusive convection">Double diffusive convection</a></li>
<li><a href="/wiki/Forced_convection" title="Forced convection">Forced convection</a></li>
<li><a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Fluid dynamics</a></li>
<li><a href="/wiki/Heat_exchanger" title="Heat exchanger">Heat exchanger</a></li>
<li><a href="/wiki/Heat_transfer#Convection" title="Heat transfer">Heat transfer</a>
<ul><li><a href="/wiki/Convection_(heat_transfer)" title="Convection (heat transfer)">Convective heat transfer</a></li></ul></li>
<li><a href="/wiki/Laser-heated_pedestal_growth" title="Laser-heated pedestal growth">Laser-heated pedestal growth</a></li>
<li><a href="/wiki/Natural_ventilation" class="mw-redirect" title="Natural ventilation">Natural ventilation</a></li>
<li><a href="/wiki/Nusselt_number" title="Nusselt number">Nusselt number</a></li>
<li><a href="/wiki/Pressure_head" title="Pressure head">Pressure head</a></li>
<li><a href="/wiki/Thermomagnetic_convection" title="Thermomagnetic convection">Thermomagnetic convection</a></li>
<li><a href="/wiki/Vortex_tube" title="Vortex tube">Vortex tube</a></li>
<li><a href="/wiki/Convective_mixing" title="Convective mixing">Convective mixing</a></li></ul></div>
<h2><span class="mw-headline" id="References">References</span><span class="mw-editsection">
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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFFalkovich2011" class="citation book cs1">Falkovich, G. (2011). <a rel="nofollow" class="external text" href="http://www.weizmann.ac.il/complex/falkovich/fluid-mechanics"><i>Fluid Mechanics, a short course for physicists</i></a>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-107-00575-4" title="Special:BookSources/978-1-107-00575-4"><bdi>978-1-107-00575-4</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120120034443/http://www.weizmann.ac.il/complex/falkovich/fluid-mechanics">Archived</a> from the original on 2012-01-20.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fluid+Mechanics%2C+a+short+course+for+physicists&rft.pub=Cambridge+University+Press&rft.date=2011&rft.isbn=978-1-107-00575-4&rft.aulast=Falkovich&rft.aufirst=G.&rft_id=http%3A%2F%2Fwww.weizmann.ac.il%2Fcomplex%2Ffalkovich%2Ffluid-mechanics&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFÇengelBoles2001" class="citation book cs1">Çengel, Yunus A.; Boles, Michael A. (2001). <i>Thermodynamics:An Engineering Approach</i>. <a href="/wiki/McGraw-Hill_Education" class="mw-redirect" title="McGraw-Hill Education">McGraw-Hill Education</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-121688-3" title="Special:BookSources/978-0-07-121688-3"><bdi>978-0-07-121688-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics%3AAn+Engineering+Approach&rft.pub=McGraw-Hill+Education&rft.date=2001&rft.isbn=978-0-07-121688-3&rft.aulast=%C3%87engel&rft.aufirst=Yunus+A.&rft.au=Boles%2C+Michael+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFCartwrightPiroVillacampa2002" class="citation journal cs1"><a href="/wiki/Julyan_Cartwright" title="Julyan Cartwright">Cartwright, Julyan H. E.</a>; Piro, Oreste; Villacampa, Ana I. (2002). "Pattern Formation in Solutal Convection: Vermiculated Rolls and Isolated Cells". <i>Physica A: Statistical Mechanics and Its Applications</i>. <b>314</b> (1): 291. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002PhyA..314..291C">2002PhyA..314..291C</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.8288">10.1.1.15.8288</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0378-4371%2802%2901080-4">10.1016/S0378-4371(02)01080-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physica+A%3A+Statistical+Mechanics+and+Its+Applications&rft.atitle=Pattern+Formation+in+Solutal+Convection%3A+Vermiculated+Rolls+and+Isolated+Cells&rft.volume=314&rft.issue=1&rft.pages=291&rft.date=2002&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.15.8288%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1016%2FS0378-4371%2802%2901080-4&rft_id=info%3Abibcode%2F2002PhyA..314..291C&rft.aulast=Cartwright&rft.aufirst=Julyan+H.+E.&rft.au=Piro%2C+Oreste&rft.au=Villacampa%2C+Ana+I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFRaats1969" class="citation journal cs1">Raats, P. A. C. (1969). "Steady Gravitational Convection Induced by a Line Source of Salt in a Soil". <i>Soil Science Society of America Proceedings</i>. <b>33</b> (4): 483–487. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1969SSASJ..33..483R">1969SSASJ..33..483R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2136%2Fsssaj1969.03615995003300040005x">10.2136/sssaj1969.03615995003300040005x</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Soil+Science+Society+of+America+Proceedings&rft.atitle=Steady+Gravitational+Convection+Induced+by+a+Line+Source+of+Salt+in+a+Soil&rft.volume=33&rft.issue=4&rft.pages=483-487&rft.date=1969&rft_id=info%3Adoi%2F10.2136%2Fsssaj1969.03615995003300040005x&rft_id=info%3Abibcode%2F1969SSASJ..33..483R&rft.aulast=Raats&rft.aufirst=P.+A.+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-On_convection_in_ice_I_shells_of_ou-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-On_convection_in_ice_I_shells_of_ou_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-On_convection_in_ice_I_shells_of_ou_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFMcKinnon2006" class="citation journal cs1">McKinnon, William B. (2006). "On convection in ice I shells of outer Solar System bodies, with detailed application to Callisto". <i>Icarus</i>. <b>183</b> (2): 435–450. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006Icar..183..435M">2006Icar..183..435M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.icarus.2006.03.004">10.1016/j.icarus.2006.03.004</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Icarus&rft.atitle=On+convection+in+ice+I+shells+of+outer+Solar+System+bodies%2C+with+detailed+application+to+Callisto&rft.volume=183&rft.issue=2&rft.pages=435-450&rft.date=2006&rft_id=info%3Adoi%2F10.1016%2Fj.icarus.2006.03.004&rft_id=info%3Abibcode%2F2006Icar..183..435M&rft.aulast=McKinnon&rft.aufirst=William+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=MBFUfld_5i0"><i>Convection Experiment - GCSE Physics</i></a>, <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211211/MBFUfld_5i0">archived</a> from the original on 2021-12-11<span class="reference-accessdate">, retrieved <span class="nowrap">2021-05-11</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Convection+Experiment+-+GCSE+Physics&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DMBFUfld_5i0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=B8H06ZA2xmo"><i>Convection Experiment</i></a>, <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211211/B8H06ZA2xmo">archived</a> from the original on 2021-12-11<span class="reference-accessdate">, retrieved <span class="nowrap">2021-05-11</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Convection+Experiment&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DB8H06ZA2xmo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=JBGT6UPTgWE"><i>Convection Current Lab Demo</i></a>, <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211211/JBGT6UPTgWE">archived</a> from the original on 2021-12-11<span class="reference-accessdate">, retrieved <span class="nowrap">2021-05-11</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Convection+Current+Lab+Demo&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DJBGT6UPTgWE&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=RCO90hvEL1I"><i>Colorful Convection Currents - Sick Science! #075</i></a>, <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211211/RCO90hvEL1I">archived</a> from the original on 2021-12-11<span class="reference-accessdate">, retrieved <span class="nowrap">2021-05-11</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Colorful+Convection+Currents+-+Sick+Science%21+%23075&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DRCO90hvEL1I&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=6VZZtB7yjmA"><i>Convection in gases</i></a>, <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211211/6VZZtB7yjmA">archived</a> from the original on 2021-12-11<span class="reference-accessdate">, retrieved <span class="nowrap">2021-05-11</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Convection+in+gases&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D6VZZtB7yjmA&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFColliBisang2023" class="citation journal cs1">Colli, A.N.; Bisang, J.M. (2023). <a rel="nofollow" class="external text" href="https://iopscience.iop.org/article/10.1149/1945-7111/acef62/meta">"Exploring the Impact of Concentration and Temperature Variations on Transient Natural Convection in Metal Electrodeposition: A Finite Volume Method Analysis"</a>. <i>Journal of the Electrochemical Society</i>. <b>170</b> (8): 083505. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2023JElS..170h3505C">2023JElS..170h3505C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1149%2F1945-7111%2Facef62">10.1149/1945-7111/acef62</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:260857287">260857287</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Electrochemical+Society&rft.atitle=Exploring+the+Impact+of+Concentration+and+Temperature+Variations+on+Transient+Natural+Convection+in+Metal+Electrodeposition%3A+A+Finite+Volume+Method+Analysis&rft.volume=170&rft.issue=8&rft.pages=083505&rft.date=2023&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A260857287%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1149%2F1945-7111%2Facef62&rft_id=info%3Abibcode%2F2023JElS..170h3505C&rft.aulast=Colli&rft.aufirst=A.N.&rft.au=Bisang%2C+J.M.&rft_id=https%3A%2F%2Fiopscience.iop.org%2Farticle%2F10.1149%2F1945-7111%2Facef62%2Fmeta&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-MT-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-MT_14-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFPidwirny2008" class="citation web cs1">Pidwirny, Michael (2008). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081220230524/http://www.physicalgeography.net/fundamentals/8e.html">"CHAPTER 8: Introduction to the Hydrosphere (e). Cloud Formation Processes"</a>. Physical Geography. Archived from <a rel="nofollow" class="external text" href="http://www.physicalgeography.net/fundamentals/8e.html">the original</a> on 2008-12-20<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-01-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=CHAPTER+8%3A+Introduction+to+the+Hydrosphere+%28e%29.+Cloud+Formation+Processes&rft.pub=Physical+Geography&rft.date=2008&rft.aulast=Pidwirny&rft.aufirst=Michael&rft_id=http%3A%2F%2Fwww.physicalgeography.net%2Ffundamentals%2F8e.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.wrh.noaa.gov/twc/monsoon/monsoon_whatis.php">"What is a monsoon?"</a>. National Weather Service Western Region Headquarters. National Weather Service Forecast Office in <a href="/wiki/Tucson,_Arizona" title="Tucson, Arizona">Tucson, Arizona</a>. 2008. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120623140647/http://www.wrh.noaa.gov/twc/monsoon/monsoon_whatis.php">Archived</a> from the original on 2012-06-23<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-03-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=What+is+a+monsoon%3F&rft.pub=National+Weather+Service+Western+Region+Headquarters&rft.date=2008&rft_id=http%3A%2F%2Fwww.wrh.noaa.gov%2Ftwc%2Fmonsoon%2Fmonsoon_whatis.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFHahnManabe1975" class="citation journal cs1">Hahn, Douglas G.; <a href="/wiki/Syukuro_Manabe" title="Syukuro Manabe">Manabe, Syukuro</a> (1975). <a rel="nofollow" class="external text" href="https://doi.org/10.1175%2F1520-0469%281975%29032%3C1515%3ATROMIT%3E2.0.CO%3B2">"The Role of Mountains in the South Asian Monsoon Circulation"</a>. <i><a href="/wiki/Journal_of_the_Atmospheric_Sciences" title="Journal of the Atmospheric Sciences">Journal of the Atmospheric Sciences</a></i>. <b>32</b> (8): 1515–1541. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1975JAtS...32.1515H">1975JAtS...32.1515H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1175%2F1520-0469%281975%29032%3C1515%3ATROMIT%3E2.0.CO%3B2">10.1175/1520-0469(1975)032<1515:TROMIT>2.0.CO;2</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/issn/1520-0469">1520-0469</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Atmospheric+Sciences&rft.atitle=The+Role+of+Mountains+in+the+South+Asian+Monsoon+Circulation&rft.volume=32&rft.issue=8&rft.pages=1515-1541&rft.date=1975&rft.issn=1520-0469&rft_id=info%3Adoi%2F10.1175%2F1520-0469%281975%29032%3C1515%3ATROMIT%3E2.0.CO%3B2&rft_id=info%3Abibcode%2F1975JAtS...32.1515H&rft.aulast=Hahn&rft.aufirst=Douglas+G.&rft.au=Manabe%2C+Syukuro&rft_id=https%3A%2F%2Fdoi.org%2F10.1175%252F1520-0469%25281975%2529032%253C1515%253ATROMIT%253E2.0.CO%253B2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">University of Wisconsin. <a rel="nofollow" class="external text" href="http://cimss.ssec.wisc.edu/wxwise/seabrz.html">Sea and Land Breezes.</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120704184333/http://cimss.ssec.wisc.edu/wxwise/seabrz.html">Archived</a> 2012-07-04 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> Retrieved on 2006-10-24.</span>
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<li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.zamg.ac.at/docu/Manual/SatManu/main.htm?/docu/Manual/SatManu/CMs/FgStr/backgr.htm">"Fog And Stratus – Meteorological Physical Background"</a>. Zentralanstalt für Meteorologie und Geodynamik. FMI. 2007. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110706085616/http://www.zamg.ac.at/docu/Manual/SatManu/main.htm?%2Fdocu%2FManual%2FSatManu%2FCMs%2FFgStr%2Fbackgr.htm">Archived</a> from the original on 2011-07-06<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-02-07</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Fog+And+Stratus+%E2%80%93+Meteorological+Physical+Background&rft.pub=Zentralanstalt+f%C3%BCr+Meteorologie+und+Geodynamik&rft.date=2007&rft_id=http%3A%2F%2Fwww.zamg.ac.at%2Fdocu%2FManual%2FSatManu%2Fmain.htm%3F%2Fdocu%2FManual%2FSatManu%2FCMs%2FFgStr%2Fbackgr.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFMooney2007" class="citation book cs1">Mooney, Chris C. (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=RRSzR4NQdGkC&pg=PA20"><i>Storm world: hurricanes, politics, and the battle over global warming</i></a>. Houghton Mifflin Harcourt. p. 20. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-15-101287-9" title="Special:BookSources/978-0-15-101287-9"><bdi>978-0-15-101287-9</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2009-08-31</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Storm+world%3A+hurricanes%2C+politics%2C+and+the+battle+over+global+warming&rft.pages=20&rft.pub=Houghton+Mifflin+Harcourt&rft.date=2007&rft.isbn=978-0-15-101287-9&rft.aulast=Mooney&rft.aufirst=Chris+C.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DRRSzR4NQdGkC%26pg%3DPA20&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-Extreme_Weather-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-Extreme_Weather_23-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFMogil2007" class="citation book cs1">Mogil, Michael H. (2007). <a rel="nofollow" class="external text" href="https://archive.org/details/extremeweatherun0000mogi/page/210"><i>Extreme Weather</i></a>. New York: Black Dog & Leventhal Publisher. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/extremeweatherun0000mogi/page/210">210–211</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-57912-743-5" title="Special:BookSources/978-1-57912-743-5"><bdi>978-1-57912-743-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Extreme+Weather&rft.place=New+York&rft.pages=210-211&rft.pub=Black+Dog+%26+Leventhal+Publisher&rft.date=2007&rft.isbn=978-1-57912-743-5&rft.aulast=Mogil&rft.aufirst=Michael+H.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fextremeweatherun0000mogi%2Fpage%2F210&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-tsbasics-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-tsbasics_24-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090825000832/http://www.nssl.noaa.gov/primer/tstorm/tst_basics.html">"A Severe Weather Primer: Questions and Answers about Thunderstorms"</a>. <a href="/wiki/National_Oceanic_and_Atmospheric_Administration" title="National Oceanic and Atmospheric Administration">National Oceanic and Atmospheric Administration</a>. National Severe Storms Laboratory. 2006-10-15. Archived from <a rel="nofollow" class="external text" href="http://www.nssl.noaa.gov/primer/tstorm/tst_basics.html">the original</a> on 2009-08-25<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-09-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+Severe+Weather+Primer%3A+Questions+and+Answers+about+Thunderstorms&rft.pub=National+Oceanic+and+Atmospheric+Administration&rft.date=2006-10-15&rft_id=http%3A%2F%2Fwww.nssl.noaa.gov%2Fprimer%2Ftstorm%2Ftst_basics.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20081211050708/http://amsglossary.allenpress.com/glossary/search?id=trade-winds1">"trade winds"</a>. <i>Glossary of Meteorology</i>. American Meteorological Society. 2009. Archived from <a rel="nofollow" class="external text" href="http://amsglossary.allenpress.com/glossary/search?id=trade-winds1">the original</a> on 2008-12-11<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-09-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Glossary+of+Meteorology&rft.atitle=trade+winds&rft.date=2009&rft_id=http%3A%2F%2Famsglossary.allenpress.com%2Fglossary%2Fsearch%3Fid%3Dtrade-winds1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text">Glossary of Meteorology (2009). <a rel="nofollow" class="external text" href="http://amsglossary.allenpress.com/glossary/search?id=westerlies1">Westerlies.</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100622073904/http://amsglossary.allenpress.com/glossary/search?id=westerlies1">Archived</a> 2010-06-22 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> <a href="/wiki/American_Meteorological_Society" title="American Meteorological Society">American Meteorological Society</a>. Retrieved on 2009-04-15.</span>
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<li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text">Matthias Tomczak and J. Stuart Godfrey (2001). <a rel="nofollow" class="external text" href="http://www.es.flinders.edu.au/~mattom/regoc/pdffiles/colour/double/04P-Ekman-left.pdf">Regional Oceanography: an Introduction.</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090914120630/http://www.es.flinders.edu.au/~mattom/regoc/pdffiles/colour/double/04P-Ekman-left.pdf">Archived</a> 2009-09-14 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> Matthias Tomczak, pp. 42. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/81-7035-306-8" title="Special:BookSources/81-7035-306-8">81-7035-306-8</a>. Retrieved on 2009-05-06.</span>
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<li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">Angela Colling (2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=tFJRLhSez_YC&pg=PA90">Ocean circulation.</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180302144439/https://books.google.com/books?id=tFJRLhSez_YC&pg=PA90">Archived</a> 2018-03-02 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> Butterworth-Heinemann, pp. 96. Retrieved on 2009-05-07.</span>
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<li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text">National Environmental Satellite, Data, and Information Service (2009). <a rel="nofollow" class="external text" href="http://www.science-house.org/nesdis/gulf/background.html">Investigating the Gulf Stream.</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100503013457/http://www.science-house.org/nesdis/gulf/background.html">Archived</a> 2010-05-03 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> <a href="/wiki/North_Carolina_State_University" title="North Carolina State University">North Carolina State University</a>. Retrieved on 2009-05-06.</span>
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<li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFRussel" class="citation web cs1">Russel, Randy. <a rel="nofollow" class="external text" href="http://www.windows.ucar.edu/tour/link=/earth/Water/thermohaline_ocean_circulation.html">"Thermohaline Ocean Circulation"</a>. University Corporation for Atmospheric Research. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090325062339/http://www.windows.ucar.edu/tour/link=/earth/Water/thermohaline_ocean_circulation.html">Archived</a> from the original on 2009-03-25<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-01-06</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Thermohaline+Ocean+Circulation&rft.pub=University+Corporation+for+Atmospheric+Research&rft.aulast=Russel&rft.aufirst=Randy&rft_id=http%3A%2F%2Fwww.windows.ucar.edu%2Ftour%2Flink%3D%2Fearth%2FWater%2Fthermohaline_ocean_circulation.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFBehl" class="citation web cs1">Behl, R. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080523170145/http://seis.natsci.csulb.edu/rbehl/NADW.htm">"Atlantic Ocean water masses"</a>. <a href="/wiki/California_State_University" title="California State University">California State University</a> Long Beach. Archived from <a rel="nofollow" class="external text" href="http://seis.natsci.csulb.edu/rbehl/NADW.htm">the original</a> on May 23, 2008<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-01-06</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Atlantic+Ocean+water+masses&rft.pub=California+State+University+Long+Beach&rft.aulast=Behl&rft.aufirst=R.&rft_id=http%3A%2F%2Fseis.natsci.csulb.edu%2Frbehl%2FNADW.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-University_of_Winnipeg-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-University_of_Winnipeg_33-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFKobesKunstatter2002" class="citation web cs1">Kobes, Randy; Kunstatter, Gabor (2002-12-16). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110114151750/http://theory.uwinnipeg.ca/mod_tech/node195.html">"Mantle Convection"</a>. Physics Department, University of Winnipeg. Archived from <a rel="nofollow" class="external text" href="http://theory.uwinnipeg.ca/mod_tech/node195.html">the original</a> on 2011-01-14<span class="reference-accessdate">. Retrieved <span class="nowrap">2010-01-03</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Mantle+Convection&rft.pub=Physics+Department%2C+University+of+Winnipeg&rft.date=2002-12-16&rft.aulast=Kobes&rft.aufirst=Randy&rft.au=Kunstatter%2C+Gabor&rft_id=http%3A%2F%2Ftheory.uwinnipeg.ca%2Fmod_tech%2Fnode195.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-Condie-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-Condie_34-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFCondie1997" class="citation book cs1">Condie, Kent C. (1997). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=HZrA6OQzsvgC&pg=PA5"><i>Plate tectonics and crustal evolution</i></a> (4th ed.). Butterworth-Heinemann. p. 5. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7506-3386-4" title="Special:BookSources/978-0-7506-3386-4"><bdi>978-0-7506-3386-4</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131029161501/http://books.google.com/books?id=HZrA6OQzsvgC&pg=PA5">Archived</a> from the original on 2013-10-29.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Plate+tectonics+and+crustal+evolution&rft.pages=5&rft.edition=4th&rft.pub=Butterworth-Heinemann&rft.date=1997&rft.isbn=978-0-7506-3386-4&rft.aulast=Condie&rft.aufirst=Kent+C.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DHZrA6OQzsvgC%26pg%3DPA5&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFBless1996" class="citation book cs1">Bless, Robert C. (1996). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=jC47sk3mfjcC&pg=PA310"><i>Discovering the Cosmos</i></a>. University Science Books. p. 310. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780935702675" title="Special:BookSources/9780935702675"><bdi>9780935702675</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Discovering+the+Cosmos&rft.pages=310&rft.pub=University+Science+Books&rft.date=1996&rft.isbn=9780935702675&rft.aulast=Bless&rft.aufirst=Robert+C.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DjC47sk3mfjcC%26pg%3DPA310&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-:0-36"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_36-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_36-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_36-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:0_36-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:0_36-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-:0_36-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFBanaszekJaluriaKowalewskiRebow1999" class="citation journal cs1">Banaszek, J.; Jaluria, Y.; Kowalewski, T. A.; Rebow, M. (1999-10-01). "Semi-Implicit Fem Analysis of Natural Convection in Freezing Water". <i>Numerical Heat Transfer, Part A: Applications</i>. <b>36</b> (5): 449–472. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1999NHTA...36..449B">1999NHTA...36..449B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F104077899274624">10.1080/104077899274624</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/issn/1040-7782">1040-7782</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:3740709">3740709</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Numerical+Heat+Transfer%2C+Part+A%3A+Applications&rft.atitle=Semi-Implicit+Fem+Analysis+of+Natural+Convection+in+Freezing+Water&rft.volume=36&rft.issue=5&rft.pages=449-472&rft.date=1999-10-01&rft_id=info%3Adoi%2F10.1080%2F104077899274624&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A3740709%23id-name%3DS2CID&rft.issn=1040-7782&rft_id=info%3Abibcode%2F1999NHTA...36..449B&rft.aulast=Banaszek&rft.aufirst=J.&rft.au=Jaluria%2C+Y.&rft.au=Kowalewski%2C+T.+A.&rft.au=Rebow%2C+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html">"Water - Density, Specific Weight and Thermal Expansion Coefficient"</a>. <i>www.engineeringtoolbox.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2018-12-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.engineeringtoolbox.com&rft.atitle=Water+-+Density%2C+Specific+Weight+and+Thermal+Expansion+Coefficient&rft_id=https%3A%2F%2Fwww.engineeringtoolbox.com%2Fwater-density-specific-weight-d_595.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-:1-38"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_38-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_38-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:1_38-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFDebenedettiStanley2003" class="citation news cs1">Debenedetti, Pablo G.; Stanley, H. Eugene (June 2003). <a rel="nofollow" class="external text" href="http://polymer.bu.edu/hes/articles/ds03.pdf">"Supercooled and Glassy Water"</a> <span class="cs1-format">(PDF)</span>. <i>Physics Today</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060301224729/http://polymer.bu.edu/hes/articles/ds03.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2006-03-01<span class="reference-accessdate">. Retrieved <span class="nowrap">1 December</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Today&rft.atitle=Supercooled+and+Glassy+Water&rft.date=2003-06&rft.aulast=Debenedetti&rft.aufirst=Pablo+G.&rft.au=Stanley%2C+H.+Eugene&rft_id=http%3A%2F%2Fpolymer.bu.edu%2Fhes%2Farticles%2Fds03.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFGiangiStellaKowalewski1999" class="citation journal cs1">Giangi, Marilena; Stella, Fulvio; Kowalewski, Tomasz A. (December 1999). "Phase change problems with free convection: fixed grid numerical simulation". <i>Computing and Visualization in Science</i>. <b>2</b> (2–3): 123–130. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.9300">10.1.1.31.9300</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs007910050034">10.1007/s007910050034</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/issn/1432-9360">1432-9360</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:3756976">3756976</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Computing+and+Visualization+in+Science&rft.atitle=Phase+change+problems+with+free+convection%3A+fixed+grid+numerical+simulation&rft.volume=2&rft.issue=2%E2%80%933&rft.pages=123-130&rft.date=1999-12&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.31.9300%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A3756976%23id-name%3DS2CID&rft.issn=1432-9360&rft_id=info%3Adoi%2F10.1007%2Fs007910050034&rft.aulast=Giangi&rft.aufirst=Marilena&rft.au=Stella%2C+Fulvio&rft.au=Kowalewski%2C+Tomasz+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFTongKoster1993" class="citation journal cs1">Tong, Wei; Koster, Jean N. (December 1993). "Natural convection of water in a rectangular cavity including density inversion". <i>International Journal of Heat and Fluid Flow</i>. <b>14</b> (4): 366–375. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0142-727x%2893%2990010-k">10.1016/0142-727x(93)90010-k</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/issn/0142-727X">0142-727X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Heat+and+Fluid+Flow&rft.atitle=Natural+convection+of+water+in+a+rectangular+cavity+including+density+inversion&rft.volume=14&rft.issue=4&rft.pages=366-375&rft.date=1993-12&rft_id=info%3Adoi%2F10.1016%2F0142-727x%2893%2990010-k&rft.issn=0142-727X&rft.aulast=Tong&rft.aufirst=Wei&rft.au=Koster%2C+Jean+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
</li>
<li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFEzanKalfa2016" class="citation journal cs1">Ezan, Mehmet Akif; Kalfa, Mustafa (October 2016). "Numerical investigation of transient natural convection heat transfer of freezing water in a square cavity". <i>International Journal of Heat and Fluid Flow</i>. <b>61</b>: 438–448. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.ijheatfluidflow.2016.06.004">10.1016/j.ijheatfluidflow.2016.06.004</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/issn/0142-727X">0142-727X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Heat+and+Fluid+Flow&rft.atitle=Numerical+investigation+of+transient+natural+convection+heat+transfer+of+freezing+water+in+a+square+cavity&rft.volume=61&rft.pages=438-448&rft.date=2016-10&rft_id=info%3Adoi%2F10.1016%2Fj.ijheatfluidflow.2016.06.004&rft.issn=0142-727X&rft.aulast=Ezan&rft.aufirst=Mehmet+Akif&rft.au=Kalfa%2C+Mustafa&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
</li>
<li id="cite_note-:2-42"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_42-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_42-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFMooreMolinero2011" class="citation journal cs1">Moore, Emily B.; Molinero, Valeria (November 2011). "Structural transformation in supercooled water controls the crystallization rate of ice". <i>Nature</i>. <b>479</b> (7374): 506–508. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1107.1622">1107.1622</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011Natur.479..506M">2011Natur.479..506M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnature10586">10.1038/nature10586</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/issn/0028-0836">0028-0836</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/22113691">22113691</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1784703">1784703</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Structural+transformation+in+supercooled+water+controls+the+crystallization+rate+of+ice&rft.volume=479&rft.issue=7374&rft.pages=506-508&rft.date=2011-11&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A1784703%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2011Natur.479..506M&rft_id=info%3Aarxiv%2F1107.1622&rft.issn=0028-0836&rft_id=info%3Adoi%2F10.1038%2Fnature10586&rft_id=info%3Apmid%2F22113691&rft.aulast=Moore&rft.aufirst=Emily+B.&rft.au=Molinero%2C+Valeria&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
</li>
<li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060127003651/http://www.chinfo.navy.mil/navpalib/cno/n87/history/tech-3.html">"Technical Innovations of the Submarine Force"</a>. Chief of Naval Operations Submarine Warfare Division. Archived from <a rel="nofollow" class="external text" href="http://www.chinfo.navy.mil/navpalib/cno/n87/history/tech-3.html">the original</a> on 2006-01-27<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-03-12</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Technical+Innovations+of+the+Submarine+Force&rft.pub=Chief+of+Naval+Operations+Submarine+Warfare+Division&rft_id=http%3A%2F%2Fwww.chinfo.navy.mil%2Fnavpalib%2Fcno%2Fn87%2Fhistory%2Ftech-3.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
</li>
<li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120204154809/http://ar.inel.gov/images/pdf/200506/2005061600214ALL.pdf">"Appendix C, Attachment to NR:IBO-05/023, Evaluation of Naval Reactors Facility Radioactive Waste Disposed of at the Radioactive Waste Management Complex"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://ar.inel.gov/images/pdf/200506/2005061600214ALL.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2012-02-04<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-03-12</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Appendix+C%2C+Attachment+to+NR%3AIBO-05%2F023%2C+Evaluation+of+Naval+Reactors+Facility+Radioactive+Waste+Disposed+of+at+the+Radioactive+Waste+Management+Complex&rft_id=http%3A%2F%2Far.inel.gov%2Fimages%2Fpdf%2F200506%2F2005061600214ALL.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
</li>
<li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFJonesRoderick2014" class="citation book cs1">Jones, Edward Monroe; Roderick, Shawn S. (4 November 2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=6F6QBQAAQBAJ"><i>Submarine Torpedo Tactics: An American History</i></a>. McFarland. p. 153. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7864-9646-4" title="Special:BookSources/978-0-7864-9646-4"><bdi>978-0-7864-9646-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Submarine+Torpedo+Tactics%3A+An+American+History&rft.pages=153&rft.pub=McFarland&rft.date=2014-11-04&rft.isbn=978-0-7864-9646-4&rft.aulast=Jones&rft.aufirst=Edward+Monroe&rft.au=Roderick%2C+Shawn+S.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D6F6QBQAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
</li>
<li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1 cs1-prop-script cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060714151444/http://ship.bsu.by/main.asp?id=100092"><bdi lang="ru">Энциклопедия кораблей /Ракетные ПЛ /Огайо</bdi></a> (in Russian). Archived from <a rel="nofollow" class="external text" href="http://ship.bsu.by/main.asp?id=100092">the original</a> on 2006-07-14<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-03-12</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=%D0%AD%D0%BD%D1%86%D0%B8%D0%BA%D0%BB%D0%BE%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F+%D0%BA%D0%BE%D1%80%D0%B0%D0%B1%D0%BB%D0%B5%D0%B9+%2F%D0%A0%D0%B0%D0%BA%D0%B5%D1%82%D0%BD%D1%8B%D0%B5+%D0%9F%D0%9B+%2F%D0%9E%D0%B3%D0%B0%D0%B9%D0%BE&rft_id=http%3A%2F%2Fship.bsu.by%2Fmain.asp%3Fid%3D100092&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060720075350/http://www.submarinesonstamps.co.il/openhist.php?ID=269">"The Ohio, US Navy's nuclear-powered ballistic missile submarine"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.submarinesonstamps.co.il/openhist.php?ID=269">the original</a> on 2006-07-20<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-03-12</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Ohio%2C+US+Navy%27s+nuclear-powered+ballistic+missile+submarine&rft_id=http%3A%2F%2Fwww.submarinesonstamps.co.il%2Fopenhist.php%3FID%3D269&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070223130956/http://tech.military.com/equipment/viewEquipment.do?eq_id=89213">"Members-only feature, registration required"</a>. Archived from <a rel="nofollow" class="external text" href="http://tech.military.com/equipment/viewEquipment.do?eq_id=89213">the original</a> on 2007-02-23<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-03-12</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Members-only+feature%2C+registration+required&rft_id=http%3A%2F%2Ftech.military.com%2Fequipment%2FviewEquipment.do%3Feq_id%3D89213&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFDonald_L._TurcotteGerald_Schubert.2002" class="citation book cs1">Donald L. Turcotte; Gerald Schubert. (2002). <i>Geodynamics</i>. Cambridge: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-66624-4" title="Special:BookSources/978-0-521-66624-4"><bdi>978-0-521-66624-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geodynamics&rft.place=Cambridge&rft.pub=Cambridge+University+Press&rft.date=2002&rft.isbn=978-0-521-66624-4&rft.au=Donald+L.+Turcotte&rft.au=Gerald+Schubert.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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<li id="cite_note-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-50">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFKays,_WilliamCrawford,_MichaelWeigand,_Bernhard2004" class="citation book cs1">Kays, William; Crawford, Michael; Weigand, Bernhard (2004). <i>Convective Heat and Mass Transfer, 4E</i>. McGraw-Hill Professional. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0072990737" title="Special:BookSources/978-0072990737"><bdi>978-0072990737</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Convective+Heat+and+Mass+Transfer%2C+4E&rft.pub=McGraw-Hill+Professional&rft.date=2004&rft.isbn=978-0072990737&rft.au=Kays%2C+William&rft.au=Crawford%2C+Michael&rft.au=Weigand%2C+Bernhard&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
</li>
<li id="cite_note-unitop-51"><span class="mw-cite-backlink">^ <a href="#cite_ref-unitop_51-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-unitop_51-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFW._McCabe_J._Smith1956" class="citation book cs1">W. McCabe J. Smith (1956). <i>Unit Operations of Chemical Engineering</i>. McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-044825-4" title="Special:BookSources/978-0-07-044825-4"><bdi>978-0-07-044825-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Unit+Operations+of+Chemical+Engineering&rft.pub=McGraw-Hill&rft.date=1956&rft.isbn=978-0-07-044825-4&rft.au=W.+McCabe+J.+Smith&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
</li>
<li id="cite_note-bennett-52"><span class="mw-cite-backlink">^ <a href="#cite_ref-bennett_52-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-bennett_52-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-bennett_52-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-bennett_52-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-bennett_52-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFBennett1962" class="citation book cs1">Bennett (1962). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/momentumheatmass00benn"><i>Momentum, Heat and Mass Transfer</i></a></span>. McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-004667-2" title="Special:BookSources/978-0-07-004667-2"><bdi>978-0-07-004667-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Momentum%2C+Heat+and+Mass+Transfer&rft.pub=McGraw-Hill&rft.date=1962&rft.isbn=978-0-07-004667-2&rft.au=Bennett&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmomentumheatmass00benn&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConvection" class="Z3988"></span></span>
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</ol></div></div>
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<ul><li><a href="/wiki/Hydraulics" title="Hydraulics">Hydraulics</a></li>
<li><a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a></li></ul>
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<ul><li><a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">Computational fluid dynamics</a></li>
<li><a href="/wiki/Aerodynamics" title="Aerodynamics">Aerodynamics</a></li>
<li><a href="/wiki/Navier%E2%80%93Stokes_equations" title="Navier–Stokes equations">Navier–Stokes equations</a></li>
<li><a href="/wiki/Boundary_layer" title="Boundary layer">Boundary layer</a>
<ul><li><a href="/wiki/Entrance_length_(fluid_dynamics)" title="Entrance length (fluid dynamics)">Entrance length</a></li></ul></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Dimensionless_numbers_in_fluid_mechanics" title="Dimensionless numbers in fluid mechanics">Dimensionless numbers</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Archimedes_number" title="Archimedes number">Archimedes</a></li>
<li><a href="/wiki/Atwood_number" title="Atwood number">Atwood</a></li>
<li><a href="/wiki/Bagnold_number" title="Bagnold number">Bagnold</a></li>
<li><a href="/wiki/Bejan_number#Fluid_mechanics_and_heat_transfer" title="Bejan number">Bejan</a></li>
<li><a href="/wiki/Biot_number" title="Biot number">Biot</a></li>
<li><a href="/wiki/E%C3%B6tv%C3%B6s_number" title="Eötvös number">Bond</a></li>
<li><a href="/wiki/Brinkman_number" title="Brinkman number">Brinkman</a></li>
<li><a href="/wiki/Capillary_number" title="Capillary number">Capillary</a></li>
<li><a href="/wiki/Cauchy_number" title="Cauchy number">Cauchy</a></li>
<li><a href="/wiki/Chandrasekhar_number" title="Chandrasekhar number">Chandrasekhar</a></li>
<li><a href="/wiki/Damk%C3%B6hler_numbers" title="Damköhler numbers">Damköhler</a></li>
<li><a href="/wiki/Darcy_number" title="Darcy number">Darcy</a></li>
<li><a href="/wiki/Dean_number" title="Dean number">Dean</a></li>
<li><a href="/wiki/Deborah_number" title="Deborah number">Deborah</a></li>
<li><a href="/wiki/Dukhin_number" title="Dukhin number">Dukhin</a></li>
<li><a href="/wiki/Eckert_number" title="Eckert number">Eckert</a></li>
<li><a href="/wiki/Ekman_number" title="Ekman number">Ekman</a></li>
<li><a href="/wiki/E%C3%B6tv%C3%B6s_number" title="Eötvös number">Eötvös</a></li>
<li><a href="/wiki/Euler_number_(physics)" title="Euler number (physics)">Euler</a></li>
<li><a href="/wiki/Froude_number" title="Froude number">Froude</a></li>
<li><a href="/wiki/Galilei_number" title="Galilei number">Galilei</a></li>
<li><a href="/wiki/Graetz_number" title="Graetz number">Graetz</a></li>
<li><a href="/wiki/Grashof_number" title="Grashof number">Grashof</a></li>
<li><a href="/wiki/G%C3%B6rtler_vortices" title="Görtler vortices">Görtler</a></li>
<li><a href="/wiki/Hagen_number" title="Hagen number">Hagen</a></li>
<li><a href="/wiki/Iribarren_number" title="Iribarren number">Iribarren</a></li>
<li><a href="/wiki/Kapitza_number" title="Kapitza number">Kapitza</a></li>
<li><a href="/wiki/Keulegan%E2%80%93Carpenter_number" title="Keulegan–Carpenter number">Keulegan–Carpenter</a></li>
<li><a href="/wiki/Knudsen_number" title="Knudsen number">Knudsen</a></li>
<li><a href="/wiki/Laplace_number" title="Laplace number">Laplace</a></li>
<li><a href="/wiki/Lewis_number" title="Lewis number">Lewis</a></li>
<li><a href="/wiki/Mach_number" title="Mach number">Mach</a></li>
<li><a href="/wiki/Marangoni_number" title="Marangoni number"> Marangoni</a></li>
<li><a href="/wiki/Morton_number" title="Morton number">Morton</a></li>
<li><a href="/wiki/Nusselt_number" title="Nusselt number">Nusselt</a></li>
<li><a href="/wiki/Ohnesorge_number" title="Ohnesorge number">Ohnesorge</a></li>
<li><a href="/wiki/P%C3%A9clet_number" title="Péclet number">Péclet</a></li>
<li><a href="/wiki/Prandtl_number" title="Prandtl number">Prandtl</a>
<ul><li><a href="/wiki/Magnetic_Prandtl_number" title="Magnetic Prandtl number">magnetic</a></li>
<li><a href="/wiki/Turbulent_Prandtl_number" title="Turbulent Prandtl number">turbulent</a></li></ul></li>
<li><a href="/wiki/Rayleigh_number" title="Rayleigh number">Rayleigh</a></li>
<li><a href="/wiki/Reynolds_number" title="Reynolds number">Reynolds</a>
<ul><li><a href="/wiki/Magnetic_Reynolds_number" title="Magnetic Reynolds number">magnetic</a></li></ul></li>
<li><a href="/wiki/Richardson_number" title="Richardson number">Richardson</a></li>
<li><a href="/wiki/Roshko_number" title="Roshko number">Roshko</a></li>
<li><a href="/wiki/Rossby_number" title="Rossby number">Rossby</a></li>
<li><a href="/wiki/Rouse_number" title="Rouse number">Rouse</a></li>
<li><a href="/wiki/Schmidt_number" title="Schmidt number">Schmidt</a></li>
<li><a href="/wiki/Scruton_number" title="Scruton number">Scruton</a></li>
<li><a href="/wiki/Sherwood_number" title="Sherwood number">Sherwood</a></li>
<li><a href="/wiki/Shields_parameter" title="Shields parameter">Shields</a></li>
<li><a href="/wiki/Stanton_number" title="Stanton number">Stanton</a></li>
<li><a href="/wiki/Stokes_number" title="Stokes number">Stokes</a></li>
<li><a href="/wiki/Strouhal_number" title="Strouhal number">Strouhal</a></li>
<li><a href="/wiki/Stuart_number" title="Stuart number">Stuart</a></li>
<li><a href="/wiki/Laplace_number" title="Laplace number">Suratman</a></li>
<li><a href="/wiki/Taylor_number" title="Taylor number">Taylor</a></li>
<li><a href="/wiki/Ursell_number" title="Ursell number">Ursell</a></li>
<li><a href="/wiki/Weber_number" title="Weber number">Weber</a></li>
<li><a href="/wiki/Weissenberg_number" title="Weissenberg number">Weissenberg</a></li>
<li><a href="/wiki/Womersley_number" title="Womersley number">Womersley</a></li></ul>
</div></td></tr></tbody></table></div>
<div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1061467846"></div><div role="navigation" class="navbox" aria-labelledby="Meteorological_data_and_variables" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="background-color: skyblue"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1063604349"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Meteorological_variables" title="Template:Meteorological variables"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Meteorological_variables" title="Template talk:Meteorological variables"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Meteorological_variables" title="Special:EditPage/Template:Meteorological variables"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Meteorological_data_and_variables" style="font-size:114%;margin:0 4em">Meteorological data and variables</div></th></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Adiabatic_process" title="Adiabatic process">Adiabatic processes</a></li>
<li><a href="/wiki/Advection" title="Advection">Advection</a></li>
<li><a href="/wiki/Buoyancy" title="Buoyancy">Buoyancy</a></li>
<li><a href="/wiki/Lapse_rate" title="Lapse rate">Lapse rate</a></li>
<li><a href="/wiki/Lightning" title="Lightning">Lightning</a></li>
<li><a href="/wiki/Solar_radiation" class="mw-redirect" title="Solar radiation">Surface solar radiation</a></li>
<li><a href="/wiki/Surface_weather_analysis" title="Surface weather analysis">Surface weather analysis</a></li>
<li><a href="/wiki/Visibility" title="Visibility">Visibility</a></li>
<li><a href="/wiki/Vorticity" title="Vorticity">Vorticity</a></li>
<li><a href="/wiki/Wind" title="Wind">Wind</a></li>
<li><a href="/wiki/Wind_shear" title="Wind shear">Wind shear</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="/wiki/Condensation" title="Condensation">Condensation</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Cloud" title="Cloud">Cloud</a></li>
<li><a href="/wiki/Cloud_condensation_nuclei" title="Cloud condensation nuclei">Cloud condensation nuclei (CCN)</a></li>
<li><a href="/wiki/Fog" title="Fog">Fog</a></li>
<li><a href="/wiki/Convective_condensation_level" title="Convective condensation level">Convective condensation level (CCL)</a></li>
<li><a href="/wiki/Lifted_condensation_level" title="Lifted condensation level">Lifted condensation level (LCL)</a></li>
<li><a href="/wiki/Precipitable_water" title="Precipitable water">Precipitable water</a></li>
<li><a href="/wiki/Precipitation" title="Precipitation">Precipitation</a></li>
<li><a href="/wiki/Water_vapor" title="Water vapor">Water vapor</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="/wiki/Atmospheric_convection" title="Atmospheric convection">Convection</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Convective_available_potential_energy" title="Convective available potential energy">Convective available potential energy (CAPE)</a></li>
<li><a href="/wiki/Convective_inhibition" title="Convective inhibition">Convective inhibition (CIN)</a></li>
<li><a href="/wiki/Convective_instability" title="Convective instability">Convective instability</a></li>
<li><a href="/wiki/Convective_momentum_transport" title="Convective momentum transport">Convective momentum transport</a></li>
<li><a href="/wiki/Conditional_symmetric_instability" title="Conditional symmetric instability">Conditional symmetric instability</a></li>
<li><a href="/wiki/Convective_temperature" title="Convective temperature">Convective temperature (<i>T</i><sub>c</sub>)</a></li>
<li><a href="/wiki/Equilibrium_level" title="Equilibrium level">Equilibrium level (EL)</a></li>
<li><a href="/wiki/Free_convective_layer" title="Free convective layer">Free convective layer (FCL)</a></li>
<li><a href="/wiki/Hydrodynamical_helicity#Meteorology" title="Hydrodynamical helicity">Helicity</a></li>
<li><a href="/wiki/K-index_(meteorology)" title="K-index (meteorology)">K Index</a></li>
<li><a href="/wiki/Level_of_free_convection" title="Level of free convection">Level of free convection (LFC)</a></li>
<li><a href="/wiki/Lifted_index" title="Lifted index">Lifted index (LI)</a></li>
<li><a href="/wiki/Maximum_parcel_level" title="Maximum parcel level">Maximum parcel level (MPL)</a></li>
<li><a href="/wiki/Bulk_Richardson_number" title="Bulk Richardson number">Bulk Richardson number (BRN)</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="/wiki/Temperature" title="Temperature">Temperature</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Dew_point" title="Dew point">Dew point (<i>T</i><sub>d</sub>)</a></li>
<li><a href="/wiki/Dew_point_depression" title="Dew point depression">Dew point depression</a></li>
<li><a href="/wiki/Dry-bulb_temperature" title="Dry-bulb temperature">Dry-bulb temperature</a></li>
<li><a href="/wiki/Equivalent_temperature" title="Equivalent temperature">Equivalent temperature (<i>T</i><sub>e</sub>)</a></li>
<li><a href="/wiki/Forest_fire_weather_index" title="Forest fire weather index">Forest fire weather index</a></li>
<li><a href="/wiki/Haines_Index" title="Haines Index">Haines Index</a></li>
<li><a href="/wiki/Heat_index" title="Heat index">Heat index</a></li>
<li><a href="/wiki/Humidex" title="Humidex">Humidex</a></li>
<li><a href="/wiki/Humidity" title="Humidity">Humidity</a></li>
<li><a href="/wiki/Relative_humidity" class="mw-redirect" title="Relative humidity">Relative humidity (RH)</a></li>
<li><a href="/wiki/Mixing_ratio" title="Mixing ratio">Mixing ratio</a></li>
<li><a href="/wiki/Potential_temperature" title="Potential temperature">Potential temperature (<i>θ</i>)</a></li>
<li><a href="/wiki/Equivalent_potential_temperature" title="Equivalent potential temperature">Equivalent potential temperature (<i>θ</i><sub>e</sub>)</a></li>
<li><a href="/wiki/Sea_surface_temperature" title="Sea surface temperature">Sea surface temperature (SST)</a></li>
<li><a href="/wiki/Temperature_anomaly" title="Temperature anomaly">Temperature anomaly</a></li>
<li><a href="/wiki/Thermodynamic_temperature" title="Thermodynamic temperature">Thermodynamic temperature</a></li>
<li><a href="/wiki/Vapor_pressure" title="Vapor pressure">Vapor pressure</a></li>
<li><a href="/wiki/Virtual_temperature" title="Virtual temperature">Virtual temperature</a></li>
<li><a href="/wiki/Wet-bulb_temperature" title="Wet-bulb temperature">Wet-bulb temperature</a></li>
<li><a href="/wiki/Wet-bulb_globe_temperature" title="Wet-bulb globe temperature">Wet-bulb globe temperature</a></li>
<li><a href="/wiki/Wet-bulb_potential_temperature" title="Wet-bulb potential temperature">Wet-bulb potential temperature</a></li>
<li><a href="/wiki/Wind_chill" title="Wind chill">Wind chill</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="/wiki/Pressure" title="Pressure">Pressure</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Atmospheric_pressure" title="Atmospheric pressure">Atmospheric pressure</a></li>
<li><a href="/wiki/Baroclinity" title="Baroclinity">Baroclinity</a></li>
<li><a href="/wiki/Barotropic" class="mw-redirect" title="Barotropic">Barotropicity</a></li>
<li><a href="/wiki/Pressure_gradient" title="Pressure gradient">Pressure gradient</a></li>
<li><a href="/wiki/Pressure-gradient_force" title="Pressure-gradient force">Pressure-gradient force (PGF)</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="/wiki/Velocity" title="Velocity">Velocity</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Maximum_potential_intensity" title="Maximum potential intensity">Maximum potential intensity</a></li></ul>
</div></td></tr></tbody></table></div>
<style data-mw-deduplicate="TemplateStyles:r1130092004">.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;justify-content:center;align-items:baseline}.mw-parser-output .portal-bar-bordered{padding:0 2em;background-color:#fdfdfd;border:1px solid #a2a9b1;clear:both;margin:1em auto 0}.mw-parser-output .portal-bar-related{font-size:100%;justify-content:flex-start}.mw-parser-output .portal-bar-unbordered{padding:0 1.7em;margin-left:0}.mw-parser-output .portal-bar-header{margin:0 1em 0 0.5em;flex:0 0 auto;min-height:24px}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;flex:0 1 auto;padding:0.15em 0;column-gap:1em;align-items:baseline;margin:0;list-style:none}.mw-parser-output .portal-bar-content-related{margin:0;list-style:none}.mw-parser-output .portal-bar-item{display:inline-block;margin:0.15em 0.2em;min-height:24px;line-height:24px}@media screen and (max-width:768px){.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;flex-flow:column wrap;align-items:baseline}.mw-parser-output .portal-bar-header{text-align:center;flex:0;padding-left:0.5em;margin:0 auto}.mw-parser-output .portal-bar-related{font-size:100%;align-items:flex-start}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;align-items:center;flex:0;column-gap:1em;border-top:1px solid #a2a9b1;margin:0 auto;list-style:none}.mw-parser-output .portal-bar-content-related{border-top:none;margin:0;list-style:none}}.mw-parser-output .navbox+link+.portal-bar,.mw-parser-output .navbox+style+.portal-bar,.mw-parser-output .navbox+link+.portal-bar-bordered,.mw-parser-output .navbox+style+.portal-bar-bordered,.mw-parser-output .sister-bar+link+.portal-bar,.mw-parser-output .sister-bar+style+.portal-bar,.mw-parser-output .portal-bar+.navbox-styles+.navbox,.mw-parser-output .portal-bar+.navbox-styles+.sister-bar{margin-top:-1px}</style><div class="portal-bar noprint metadata noviewer portal-bar-bordered" role="navigation" aria-label="Portals"><span class="portal-bar-header"><a href="/wiki/Wikipedia:Contents/Portals" title="Wikipedia:Contents/Portals">Portals</a>:</span><ul class="portal-bar-content"><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="/media/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/17px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="17" height="19" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/26px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, /media/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/34px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </span><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="/media/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/19px-Crab_Nebula.jpg" decoding="async" width="19" height="19" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/29px-Crab_Nebula.jpg 1.5x, /media/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/38px-Crab_Nebula.jpg 2x" data-file-width="3864" data-file-height="3864" /></span></span> </span><a href="/wiki/Portal:Astronomy" title="Portal:Astronomy">Astronomy</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="/media/wikipedia/commons/thumb/8/83/Solar_system.jpg/15px-Solar_system.jpg" decoding="async" width="15" height="19" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/8/83/Solar_system.jpg/23px-Solar_system.jpg 1.5x, /media/wikipedia/commons/thumb/8/83/Solar_system.jpg/30px-Solar_system.jpg 2x" data-file-width="4500" data-file-height="5600" /></span></span> </span><a href="/wiki/Portal:Solar_System" title="Portal:Solar System">Solar System</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><a href="/wiki/File:Cumulus_clouds_in_fair_weather.jpeg" class="mw-file-description"><img alt="icon" src="/media/wikipedia/commons/thumb/b/b5/Cumulus_clouds_in_fair_weather.jpeg/21px-Cumulus_clouds_in_fair_weather.jpeg" decoding="async" width="21" height="16" class="mw-file-element" srcset="/media/wikipedia/commons/thumb/b/b5/Cumulus_clouds_in_fair_weather.jpeg/32px-Cumulus_clouds_in_fair_weather.jpeg 1.5x, /media/wikipedia/commons/thumb/b/b5/Cumulus_clouds_in_fair_weather.jpeg/42px-Cumulus_clouds_in_fair_weather.jpeg 2x" data-file-width="800" data-file-height="600" /></a></span> </span><a href="/wiki/Portal:Weather" title="Portal:Weather">Weather</a></li></ul></div>
<div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1061467846"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style></div><div role="navigation" class="navbox authority-control" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="/wiki/Q160329#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="/media/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="/media/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, /media/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4117572-4">Germany</a></span></li>
<li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007553273705171">Israel</a></span></li>
<li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Heat--Convection"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85059761">United States</a></span></span></li>
<li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00572556">Japan</a></span></li></ul>
</div></td></tr></tbody></table></div></div>' |
Whether or not the change was made through a Tor exit node (tor_exit_node) | false |
Unix timestamp of change (timestamp) | '1717502691' |
