The initial focus of turbulence modelling is to capture the eﬀect of mixing on momentum diﬀusion since it inﬂuences the overall ﬂow solution. But other properties are also transported by the turbulent eddying motions, in particular heat.
The eﬀects of turbulence on heat transfer can be described using the following equation for internal energy , obtained by substituting the material derivative in Eq. (2.57 ) and ignoring :
Similarly, can be modelled using a turbulent thermal conductivity due to turbulent mixing, by analogy with Fourier’s law Eq. (2.54 ) for conduction due to molecular interaction
Turbulent heat transfer can be incorporated into turbulence models based on eddy-viscosity and Reynolds-averaging, with additional thermal wall functions.
First, the calculation of by Eq. (7.47) requires from the turbulence model. A common approach to calculate is from based on an estimate of turbulent Prandtl number
The calculation of heat transfer through boundary walls is an important aspect of a many CFD simulations. Near walls, the distribution of tends to mimic .
Consequently, the challenges of calculating wall heat ﬂux are similar to wall shear stress . Cells close to the wall must be very thin to resolve the viscous sub-layer in (when ).
Otherwise, wall functions can be used to adjust to compensate for the under-prediction of as described in Sec. 7.14 .