Currently working on verifying my CHT with a richard bénard simulation (the solver is not as in a boussinesq approximation, but fully compressible) although the pressure variations are 0. This is because my solver later will need large temperature variations.
When verifying I am going for a Gr = 10^3, Ra = 7.1e-2
Using Pr = 0.71, beta = 0.01 (as I simulate ideal gas, from 100 to 99 K), Cp = 1000 (stabilization), P = 1e5, M = 8.314 g/mol, rho = 1 (solution of the paramters). dynamic viscosity = 0.001.
For the wanted Gr I find g = 0.1
This leads to alpha = 1.40845e-3
kappa_f = 1.40845
I use Kr = kappa_s/kappa_F = 10
kappa_s = 14.0845
I initialize the temperature field already with
T(t=0) = 100 -5/6 x
Then I run my simulation, I calculate the heatFlux on the CHT wall with. Finally finding a Nu = 1.5, although it should be 1.04