Hi,

I am working on a conjugate heat transfer problem (conduction for solids and natural convection for fluids). The fluid is air. What is the typical way of modeling natural convection?

For example, one can treat air as compressible fluid, then, uses ideal gas law to couple density with temperature.

Or, one can treat air as incompressible fluid, and uses Boussinesq approximation.

Thanks!

phsieh2005

As a general rule based on mach number you can select between incompressible/compressible model, for mach<0.3 incompressible assumption is feasible (u can find more about this in a formal fluid dynamic text).

Hi, rt,

Thanks for the reply.

The problem I am solving is like heat transfer inside an refrigirator with cooling attached on the wall of the box. I will think that flow will be significantly lower than mach 0.3. In this case, is it better to using compressible flow approach or incompressible flow with Bossinesq approximation?

phsieh2005

>heat transfer inside an refrigirator with cooling attached

for your application incompressible modeling is sufficient

>is it better to using compressible flow approach or incompressible flow with Bossinesq approximation?

no (my opinion), but, note that, theoritically compressible approach is always feasible but is not always computationally tractable. So people usually prefar incompressible approach when it is sufficient and i reccomend it for u.

simple and better solution for u is looking in related literarue !

look for "Rayleigh-Benard convection". Benchmark solutions 2D/3D,laminar/turbulent, different Rayleigh numbers and boundary conditions etc available.

Hi, p,

Thanks a lot for the reply!

Most of the Rayleigh-Bernard convection I have seen used water. Is it Boussinesq approximation valid for gas (air, in this case)?

phsieh2005

there are papers which have compared/validated results of numerical simulation with (physical) experimental results - and that too with water. there are institutes where this set up is available for experimentation with air!

Thanks a lot p!

phsieh2005