# Convection

This figure shows a calculation for thermal convection in the Earth's mantle. Colors closer to red are hot areas and colors closer to blue are in warm and cold areas. A hot, less-dense lower boundary layer sends plumes of hot material upwards, and likewise, cold material from the top moves downwards.

Convection is single or multiphase fluid flow that occurs 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.

Convective flow may be transient (such as when a multiphase mixture of oil and water separates) or steady state (see Convection cell). The convection may be due to gravitational, electromagnetic or fictitious body forces. Heat transfer by natural convection plays a role in the structure of Earth's atmosphere, its oceans, and its mantle. Discrete convective cells in the atmosphere can be identified by clouds, with stronger convection resulting in thunderstorms. Natural convection also plays a role in stellar physics. Convection is often categorised or described by the main effect causing the convective flow, e.g. Thermal convection.

Thermal image of a newly lit Ghillie kettle. The plume of hot air resulting from the convection current is visible.

Convection cannot take place in most solids because neither bulk current flows nor significant diffusion of matter can take place.

## Terminology

The word convection has different but related usages in different scientific or engineering contexts or applications. The broader sense is in fluid mechanics, where convection refers to the motion of fluid driven by density (or other property) difference.[1][2]

In thermodynamics "convection" often refers to 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.[3]

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, e.g. thermo-capilliary convection and Granular convection.

## Examples and applications

Convection occurs on a large scale in atmospheres, oceans, planetary mantles, and it provides the mechanism of heat transfer for a large fraction of the outermost interiors of our 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 holes, at speeds which may closely approach that of light.

### Demonstration experiments

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.[4][5]

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).[6]

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.[7]

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.[8]

### Convection cells

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.

#### Atmospheric circulation

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.

#### Weather

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.[9] 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.[10][11] 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.[12][13]

Stages of a thunderstorm's life.

Warm air has a lower density than cool air, so warm air rises within cooler air,[14] similar to hot air balloons.[15] 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.[16] 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,[17] 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.[18] 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.[19]

### Oceanic circulation

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,[20] and the westerlies blow eastward at mid-latitudes.[21] This wind pattern applies a stress to the subtropical ocean surface with negative curl across the Northern Hemisphere,[22] and the reverse across the Southern Hemisphere. The resulting Sverdrup transport is equatorward.[23] 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.[24] 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.[25]

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.[26] 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.[27]

### Mantle convection

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.[28] It is one of 3 driving forces that causes tectonic plates to move around the Earth's surface.[29]

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.

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

### Stellar physics

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 primarily by convection.

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.

## 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 forces acting within the fluid, such as gravity.

### Natural convection

This color schlieren image reveals thermal convection originating from heat conduction from a human hand (in silhouette) to the surrounding still atmosphere.

Natural convection, or free convection, occurs due to temperature differences which affect the density, and thus relative buoyancy, of the fluid. Heavier (denser) components will fall, while lighter (less dense) components rise, leading to bulk fluid movement. Natural convection can only occur, therefore, in a gravitational field. A common example of natural convection is the rise of smoke from a fire. It can be seen in a pot of boiling water in which the hot and less-dense water on the bottom layer moves upwards in plumes, and the cool and more dense water near the top of the pot likewise sinks.

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).

### 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.[30] 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.[31]

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

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,[32] and other bodies in the outer solar system.[33]

### 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.

## 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 ${\displaystyle {\rm {Gr/Re^{2}\gg 1}}}$, forced convection may be neglected, whereas if ${\displaystyle {\rm {Gr/Re^{2}\ll 1}}}$, natural convection may be neglected. If the ratio, known as the Richardson number, is approximately one, then both forced and natural convection need to be taken into account.

• Bénard cells
• Churchill–Bernstein equation
• Double diffusive convection
• Fluid dynamics
• Heat transfer
• Convective heat transfer
• Laser-heated pedestal growth
• Nusselt number
• Thermomagnetic convection
• Vortex tube
• Convective mixing

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