Temperature and Heat Flux Boundary Conditions
The heat equation accepts two basic types of boundary conditions: specified temperature and specified heat flux. The specified condition is of constraint type and prescribes the temperature on a boundary:
while the latter specifies the inward heat flux
where
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q is the conductive heat flux vector (SI unit: W/m2), q = −k∇T.
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n is the normal vector on the boundary.
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q0 is the inward heat flux (SI unit: W/m2), normal to the boundary.
The inward heat flux, q0, is often a sum of contributions from different heat transfer processes (for example, radiation and convection). The special case q0 = 0 is called thermal insulation.
A common type of heat flux boundary conditions is one for which q0 = h·(Text − T), where Text is the temperature far away from the modeled domain and the heat transfer coefficient, h, represents all the physics occurring between the boundary and “far away.” It can include almost anything, but the most common situation is that h represents the effect of an exterior fluid cooling or heating the surface of a solid, a phenomenon often referred to as convective cooling or heating.
The CFD Module and the Heat Transfer Module contain a set of correlations for convective heat flux and heating. See Heat Transfer and Fluid Flow Coupling.