Diffusion Term

Interior Faces

The heat flux vector is given by:

(105)

where is the effective thermal conductivity given by:

(106)

with being the turbulent Prandtl number. The diffusive flux at an interior face is then discretized as described in Finite Volume Discretization as follows:

(107)

Boundary Faces

For inviscid flows, the heat flux is zero.

For viscous flows, the heat flux is required. This is specified directly in the case of adiabatic or specified heat flux walls. It can also inferred as a convective heat transfer condition, such that

(108)

where is a convective heat transfer coefficient and is a reference temperature.

For laminar flow in which the wall temperature is specified, the heat flux is obtained as follows:

(109)

For turbulent flow in which the wall temperature is specified, thermal wall laws are employed as follows:

(110)

where is defined in terms of the appropriate thermal wall law.