# Convection

Papers are blown upward by air currents produced by heat from a radiator.

In the most general terms, convection refers to the movement of molecules within fluids (that is, liquids, gases, and rheids). It is one of the major modes of heat transfer and mass transfer. In fluids, convective heat and mass transfer take place through both diffusion (the random, Brownian motion of individual particles of the fluid) and advection (in which matter or heat is transported by the larger-scale motion of currents in the fluid). In the context of heat and mass transfer, the term "convection" is used to refer to the sum of advective and diffusive transfer.[1] A common use of the term convection leaves out the word "heat" but nevertheless refers to heat convection.

The scientific study of convection not only helps clarify the principles of heat and mass transfer in fluids but also shows how these principles can be utilized for heating and cooling applications.

## Scale and rate of convection

Convection may happen in fluids at all scales larger than a few atoms. Convection currents occur on large scales in the Earth's atmosphere, oceans, and planetary mantle. Current 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 that may approach the speed of light.

## Two types of heat convection

Heat convection can be of two major types. In one case, heat may be carried passively by fluid motion, which would occur even without the heating process (a heat transfer process termed loosely as "forced convection"). In the other case, heating itself may cause the fluid to move (via expansion and buoyancy forces), while simultaneously causing heat to be transported by this motion (a process loosely known as natural convection or "free convection"). In the latter case, the problem of heat transport (and related transport of other substances in the fluid due to it) is generally more complicated. Both forced and natural types of heat convection may occur together.

## Natural convective heat transfer

As noted above, when heat is carried by the circulation of fluids due to buoyancy from density changes induced by heating itself, then the process is known as "free" or "natural" convective heat transfer.

Familiar examples are the upward flow of air due to a fire or hot object and the circulation of water in a pot that is heated from below.

For a visual experience of natural convection, a glass full of hot water with red food dye may be placed in a fish tank with cold, clear water. The convection currents of the red liquid will be seen to rise and fall, then eventually settle, illustrating the process as heat gradients are dissipated.

## Forced convection

Natural heat convection (also called free convection) is distinguished from various types of forced heat convection, which refer to heat advection by a fluid which is not due to the natural forces of buoyancy induced by heating. In forced heat convection, transfer of heat is due to movement in the fluid resulting from many other forces, such as a fan or pump. A convection oven thus works by forced convection, as a fan that rapidly circulates hot air forces heat into food faster than would naturally happen due to simple heating without the fan. Aerodynamic heating is a form of forced convection. Common fluid heat-radiator systems, and also heating and cooling of parts of the body by blood circulation, are other familiar examples of forced convection.

In zero-g environments, there can be no buoyancy forces, and thus no natural (free) convection is possible. In that case, flames may smother in their own waste gases. However, flames may be maintained with any type of forced convection (breeze); or (in high oxygen environments, in "still" gas environments) entirely from the minimal forced convection that occurs as heat-induced expansion (not buoyancy) of gases allows for ventilation of the flame, as waste gases move outward and cool, and fresh, high-oxygen gas moves in to take up the low pressure zones created when flame-exhaust water condenses.[2]

## Gravitational convection

Buoyancy-induced convection not due to heat is known as gravitational convection. Gravitational heat convection is the same as free convection. However, differential buoyancy forces that cause convection in gravity fields may result from sources of density variations in fluids other than those produced by heat, such as variable composition. An example of gravitational convection is the diffusion of a source of dry salt downward into wet soil, assisted by the principle that, once the salt becomes wet, saline water is heavier than freshwater.[3]

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. 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.

## Oceanic convection

Solar radiation also affects the oceans. Warm water from the Equator tends to circulate toward the poles, while cold polar water heads towards the Equator. Oceanic convection is also frequently driven by density differences due to varying salinity, known as thermohaline convection, and is of crucial importance in the global thermohaline circulation. In this case it is quite possible for relatively warm, saline water to sink, and colder, fresher water to rise, reversing the normal transport of heat.

## Mantle convection

Convection within Earth's mantle is the driving force for plate tectonics. There are actually two convection currents occurring within the Earth. The outer core experiences convective turnover of fluid metals (primarily iron and nickel) which are responsible for the Earth's magnetic field. The movement of metals forms electrical currents, which in turn generate magnetic fields.

As heat from the inner and outer core heat the lower portion of the mantle, a second set of convective currents form. This mantle convection is extremely slow, as the mantle is a thick semi-solid with the consistency of a very thick paste. This slow convection can take millions of years to complete one cycle.

Neutrino flux measurements from the Earth's core (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 by rearrangement of denser portions to the center of the earth.

## Vibration convection in gravity fields

Vibration-induced convection occurs in powders and granulated materials in containers subject to vibration, in a gravity field. When the container accelerates upward, the bottom of the container pushes the entire contents upward. In contrast, when the container accelerates downward, the sides of the container push the adjacent material downward by friction, but the material more remote from the sides is less affected. The net result is a slow circulation of particles downward at the sides, and upward in the middle.

If the container contains particles of different sizes, the downward-moving region at the sides is often narrower than the larger particles. Thus, larger particles tend to become sorted to the top of such a mixture.

## Pattern formation

A fluid under Rayleigh-Bénard convection: The left picture represents the thermal field and the right picture its two-dimensional Fourier transform.[4]

Convection, especially Rayleigh-Bénard convection, where the convecting fluid is contained by two rigid horizontal plates, is a convenient example of a pattern forming system.

When heat is fed into the system from one direction (usually below), in small increments, it merely diffuses (conducts) from below upward, without causing fluid flow. If the heat flow rate is increased above a critical value of the Rayleigh number, the system undergoes a 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 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 change breaks the symmetry of the system, and generally changes the pattern of up- and down-moving fluid from stripes to hexagons, as seen in the diagram on the 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 spirals, may begin to appear.

## Notes

1. Frank P. Incropera and David P. DeWitt, Fundamentals of Heat and Mass Transfer, 3rd edition (New York: Wiley, 1990, ISBN 0471612464).
2. The Straight Dope, If you lit a match in zero gravity, would it smother in its own smoke? (Or, Does a candle burn in zero-g?) Retrieved August 24, 2008.
3. P.A.C. Raats, [http://soil.scijournals.org/cgi/content/abstract/33/4/483 Steady Gravitational Convection Induced by a Line Source of Salt in a Soil,] Soil Sci. Soc. Am. J. 33:483-487. Retrieved August 24, 2008.
4. A. Guarino and V. Vidal, Hexagonal pattern instabilities in rotating Rayleigh-Bénard convection of a non-Boussinesq fluid. Physical Review E 69:066311. Retrieved August 24, 2008.

## References

• Bejan, Adrian. Convection Heat Transfer. Hoboken, NJ: Wiley, 2004. ISBN 0470900377
• Incropera, Frank P., et al. Fundamentals of Heat and Mass Transfer, 6th edition. Hoboken, NJ: John Wiley, 2007. ISBN 978-0470055540
• Munson, Bruce Roy, Donald F. Young, and T. H. Okiishi. Fundamentals of Fluid Mechanics, 5th edition. Hoboken, NJ: J. Wiley & Sons, 2006. ISBN 978-0471675822
• Pitts, Donald R., and Leighton E. Sissom. Schaum's Outlines: Heat Transfer, 2nd edition. Schaum's Outline Series. New York: McGraw-Hill, 1998. ISBN 0070502072