7.14 Thermal wall functions
Wall functions were introduced in Sec. 7.5 in order to improve the calculation of wall shear stress when cells are too large near a wall to resolve accurately. The same problem exists with heat ﬂux and an under-predicted . As before, the universal character of the boundary layer can be exploited, this time to improve the calculation of .
The temperature distribution is characterised by Eq. (7.51 ) for the viscous sub-layer, and the log law Eq. (7.52 ) for the inertial sub-layer. The transition for occurs at the intersection of the two equations, i.e. when
Using and Eq. (7.55 ) for , for air at with . For water under the same conditions, and the corresponding .
A wall function can be derived which adjusts the turbulent conductivity , in a similar manner to in the standard wall function in Sec. 7.5 . The model calculates for each patch face based on the near-wall cell .
No adjustment is made to when corresponds to the viscous sub-layer. When corresponds to the inertial sub-layer, is calculated as
The wall function is derived based on adjusting to improve the numerical calculation of by