Hi, I am trying to model natural convection in a closed domain using the boussinesq approximation with Fluent. I am wondering which value I must specify for the operating temperature. Since the buoyancy force is proportionnal to (T-Toper), I guess that the results I will get will depend strongly on the value that I specify.

Thanks in advance, Stéphane

Actually, under the assumptions of the Boussinesque approximation, Toper is used as value at which you compute the viscosity and density, both constant. And that's it, because the temperature equation is linear in T so you can subtract from it any constant value and it will be unaffected (try by yourself).

You can actually solve the temperature equation for (T-Toper) rather than T.

However, Toper comes from the boundary conditions. Because it is the value around which you linearize the density variation, it is usually selected as the middle value between Tmax and Tmin, whose values usually comes from the boundary and initial conditions on T. The requirement is that:

(T-Toper) << Toper

If your T equation has Neumann type b.c.s (rather than the Dirichlet type) maybe you will not be able to get a proper estimate on the temperature bounds for the time of your simulation and maybe the Boussinesque approximation could be wrong.

Two further remarks:

1) The momentum equations with the boussinesque approximation are actually equations for a perturbation from a state at which there is static equilibrium, that is:

GRAD(P0)= rho (Toper) * g

and so the actual pressure which is calculated is a perturbation from P0. This should better explain the fact that any value of Toper will be handled in the proper way because it will just give rise to a different background pressure gradient

2) Just for curiosity, when you use a vorticity-streamfunction approach no such reference value Toper emerges at all (just to calculate the reference values for viscosity and density) because Temperature derivatives are involved (also for the pressure calculation) so you can actually solve the problem without any reference to it. However, for the approximation to be valid, everything said before still holds.