the procedure

geometry

meshing

defined the material

boundary condition

solving

results

thanks dear Abbas for replying my question.

indeed i should precise what i mean by procedure, i mean what physics i should choose i used non isothermal flow (laminar flow and heat transfer in fluid) and non isothermal study it works but it dont converge when i put piecewise function of the density

in free convection or natural convection, you can applying Boussinesq approximation

thanks dear Abbas yes i put my fluid as weakly compressible and i added gravity and volume force to model but i dont checked boussinessq approximation i will try that and see if it works

Dear Messouad,

Numerical study of Natural convection has been used as a benchmark since 1982 to compare different numerical methods

One must start by fixing the physical problem (fluid, operational conditions, geometry, etc;;) then go to the mathematical model :the hypothesis, the equations of the transport phenomena( here the Navier-stokes equation plus the energy equation with Boussinesq assumption) , the boundary condition and the initial condition in the case of transient regime. You can use the dimensional analysis.. This is the main step to achieve.

Then , you have to choose your numerical method: finite difference, finite volume,

finite element, spectral method,etc...after that go to the software: it depends on if you want to use a commercial software or you will write your home software.

If you use a commercial or an open program read attentively its user guide.

In all cases, I advise you to transform your equations into a matrix system which will be solved by the numerical method. You complete your approach by meshing your space(in the case of comsol specify the number of control volume) and specify the time step and the number of steps. My main advise is to start with

in compressible fluid. Note that we consider air as incompressible with Prandtl number=0.713 , this can allow you to compare your results to those of other authors.

I'm not very familiar with comsol, so I can't help you more.

Pr. Mohamed Safi

thanks dear professor for the valuable information, indeed that was an old question since then I obtained some results by applying a tutorial, the physics is non isothermal flow coubling heat transfer in fluid and laminar or better creeping flow, by considering the liquid as weakly compressible and by applying gravity and volume force in which density depends on salinity the convection in stratified medium is almost abscent, the velocities are horizontal and in the order of micrometer per second

Any other favor?

thanks dear professor always hearing from you, god bless you and saha chribtek.