As convection is dependent on the bulk movement of a fluid it can only occur in liquids, gases and multiphase mixtures.
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 all weather systems. Convection is also seen in the rising plume of hot air from fire, oceanic currents, and sea-wind formation (where upward convection is also modified by Coriolus 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.
The parameter is the volume expansivity (K-1), g is acceleration due to gravity, T is the temperature difference between the hot surface and the bulk fluid (K), L is the characteristic length (this depends on the object) and ν is the viscosity.
For liquids, values of are tabulated. Additionally can be calculated from:
For an ideal gas, this number may be simply found:
Therefore, for an ideal gas is simply:
Thus, the Grashof number can be thought of as the ratio of the upwards buoyancy of the heated fluid to the internal friction slowing it down. In very sticky, viscous fluids, fluid movement is restricted, along with natural convection. In the extreme case of infinite viscosity, the fluid could not move and all heat transfer would be through conductive heat transfer.
A similar equation can be written 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.
The relative magnitudes of the Grashof and Reynolds number determine which form of convection dominates, if forced convection may be neglected, whereas if natural convection may be neglected. If the ratio is approximately one both forced and natural convection need to be taken into account.
Natural convection is highly dependent on the geometry of the hot surface, various correlations exist in order to determine the heat transfer coefficent. The Rayleigh number () is frequently used, where:
A general correlation that applies for a variety of geometries is
The value of f4(Pr) is calculated using the following formula
Nu is the Nusselt number and the values of Nu0 and the characteristic length used to calculate Ra are listed below:
|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||(D = Diameter of cylinder)||0.36|
Forced convection is a mechanism, or type of heat transport in which fluid motion is generated by an external source (like a pump, fan, suction device, etc.). Forced convection is often encountered by engineers designing or analyzing heat exchangers, pipe flow, and flow over a plate at a different temperature than the stream (the case of a shuttle wing during re-entry, for example). However, in any forced convection situation, some amount of natural convection is always present. When the natural convection is not negligible, such flows are typically referred to as mixed convection.
When analysing potentially mixed convection, a parameter called the Archimedes number (Ar) parametizes the relative strength of free and forced convection. The Archimedes number is the ratio of Grashof number and the square of Reynolds number, which represents the ratio of buoyancy force and inertia force, and which stands in for the contribution of natural convection. When Ar >> 1, natural convection dominates and when Ar << 1, forced convection dominates.
When natural convection isn't a significant factor, mathematical analysis with forced convection theories typically yields accurate results. The parameter of importance in forced convection is the Peclet number, which is the ratio of advection (movement by currents) and diffusion (movement from high to low concentrations) of heat.
When the Peclet number is much greater than unity (1), advection dominates diffusion. Similarly, much smaller ratios indicate a higher rate of diffusion relative to advection.