Large mismatch for wall temperature with turbulent Prandtl model and y+ > 1

[bigfooted]

when
TURBULENT_CONDUCTIVITY_MODEL= CONSTANT_PRANDTL_TURB
the temperature imposed at the wall is wrong and can be off by hundreds of degrees.
The case below has an inlet velocity of 40 m/s using INC_RANS and SST. The wall temperature is set to 1200K.
For a large part, the wall temperature is close to 400K.
The inlet fluid temperature is 300K. All fluid properties are constant.
This case is completely converged with residuals of -15

[bigfooted]

This is due to coarse wall meshes and treatment of temperature boundary condition as a flux. The computation of the heat flux using Fourier's law is inaccurate in turbulent flows when the mesh is coarse and no wall model is used. The only solution is to use a very fine near-wall mesh to properly resolve the turbulent boundary layer, or to have wall functions to compute a heat flux.

y+ = 5 leads to a discrepancy of 1% and then it quickly goes south from there.

[pcarruscag]

Have a look at my comment in @Cristopher-Morales PR for the strong BC, I think @NAnand-TUD also mentioned this issue in an dev meeting.