Convection

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 type of flow, of motion of a liquid such as water or a gas such as air, in which the fluid motion is not generated by any external source (like a pump, fan, suction device, etc.) but by some parts of the 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, with gravity and possible changes in heat energy. The driving force for natural convection is gravity. For example if there is a layer of cold dense air on top of hotter less dense air, gravity pulls more strongly on the denser layer on top, so it falls while the hotter less dense air rises to take its place. This creates circulating flow: convection. As it relies on gravity, 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 forces). 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).

Note that 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 materials that are fluid at common temperatures expand when they are heated, becoming less dense. Correspondingly, they become denser when they are cooled. 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 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.[4] 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.[5]

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.

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,[6] and other bodies in the outer Solar System.[7]

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.

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.

Thermal circulation of air masses

Thermal convection in liquids can be demonstrated by placing a heat source (e.g. 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.[8][9]

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 (eg. 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).[10]

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 (eg. 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.[11]

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.[12]

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.

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.

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.[13] 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.[14][15] 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.[16][17]

Stages of a thunderstorm's life.

Warm air has a lower density than cool air, so warm air rises within cooler air,[18] similar to hot air balloons.[19] 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 condense.[20] 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,[21] continuing the cloud's ascension. If enough instability is present in the atmosphere, this process will continue long enough for 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 thunderstorms, regardless of type, go through three stages: the developing stage, the mature stage, and the dissipation stage.[22] 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.[23]

Ocean currents

Solar radiation affects the oceans: warm water from the Equator tends to circulate toward the poles, 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,[24] and the westerlies blow eastward at mid-latitudes.[25] This wind pattern applies a stress to the subtropical ocean surface with negative curl across the Northern Hemisphere,[26] and the reverse across the Southern Hemisphere. The resulting Sverdrup transport is equatorward.[27] 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.[28] 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.[29]

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.[30] 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 southgoing stream.[31]

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.[32] It is one of 3 driving forces that causes tectonic plates to move around the Earth's surface.[33]

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) 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, 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 ⁴⁰K, 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 potential energy, as a result of physical rearrangement of denser portions of the Earth's interior toward the center of the planet (i.e., a type of prolonged falling and settling).

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 towers operate on this principle; similarly the solar updraft tower is a proposed device to generate electricity based on the stack effect.

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 core region primarily by convection rather than radiation. This occurs at radii which are sufficiently opaque that convection is more efficient than radiation at transporting energy.[34]

Granules on the photosphere of the Sun are the visible tops of convection cells in the photosphere, caused by convection of 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.

Water is a fluid that does not obey the Boussinesq approximation.[35] This is because its density varies nonlinearly with temperature, which causes its thermal expansion coefficient to be inconsistent near freezing temperatures.[36][37] 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.[35] 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.[35][38][39][40] 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 super-cooling, where the water is cooled to below freezing temperatures but does not immediately begin to freeze.[37][41] 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.[35] This plume is caused by a delay in the nucleation of the ice.[35][37][41] Once ice begins to form, the flow returns to a similar pattern as before and the solidification propagates gradually until the flow is redeveloped.[35]

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 [42][43][44] and S8G[45][46][47] United States Naval reactors, 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.

The onset of natural convection is determined by the Rayleigh number (Re). This dimensionless number is given by

${\displaystyle {\textbf {Re}}={\frac {\Delta \rho gL^{3}}{D\mu }}}$

where

• ${\displaystyle \Delta \rho }$ is the difference in density between the two parcels of material that are mixing
• ${\displaystyle g}$ is the local gravitational acceleration
• ${\displaystyle L}$ is the characteristic length-scale of convection: the depth of the boiling pot, for example
• ${\displaystyle D}$ is the diffusivity of the characteristic that is causing the convection, and
• ${\displaystyle \mu }$ 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:

${\displaystyle \Delta \rho =\rho _{0}\beta \Delta T}$

where

• ${\displaystyle \rho _{0}}$ is the reference density, typically picked to be the average density of the medium,
• ${\displaystyle \beta }$ is the coefficient of thermal expansion, and
• ${\displaystyle \Delta T}$ is the temperature difference across the medium.

The general diffusivity, ${\displaystyle D}$, is redefined as a thermal diffusivity, ${\displaystyle \alpha }$.

${\displaystyle D=\alpha }$

Inserting these substitutions produces a Rayleigh number that can be used to predict thermal convection.[48]

${\displaystyle {\textbf {Re}}={\frac {\rho _{0}g\beta \Delta TL^{3}}{\alpha \mu }}}$

The tendency of a particular naturally convective system towards turbulence relies on the Grashof number (Gr).[49]

${\displaystyle Gr={\frac {g\beta \Delta TL^{3}}{\nu ^{2}}}}$

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 ${\displaystyle g\Delta \rho L^{2}/\mu }$, 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).

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:

${\displaystyle Gr={\frac {g\beta \Delta CL^{3}}{\nu ^{2}}}}$

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

${\displaystyle Nu=\left[Nu_{0}^{\frac {1}{2}}+Ra^{\frac {1}{6}}\left({\frac {f_{4}\left(Pr\right)}{300}}\right)^{\frac {1}{6}}\right]^{2}}$

The value of f₄(Pr) is calculated using the following formula

${\displaystyle f_{4}(Pr)=\left[1+\left({\frac {0.5}{Pr}}\right)^{\frac {9}{16}}\right]^{\frac {-16}{9}}}$

Nu is the Nusselt number and the values of Nu₀ and the characteristic length used to calculate Re are listed below (see also Discussion):

Geometry	Characteristic length	Nu0
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	${\displaystyle \pi D/2}$ (D = diameter of cylinder)	0.36${\displaystyle \pi }$

Warning: The values indicated for the Horizontal cylinder are wrong; see discussion.