A numerical study of the stability of thermohaline convection in a rectangular box containing a porous medium

The finite element method is used to study double diffusive convection in a rectangular box containing a porous medium. The porous medium is described by means of the Darcy-Brinkman model. The problem solved is the Benard problem in the box. It is found that the stability of the flow is dependent on a combination of thermal Rayleigh number, buoyancy ratio, and Lewis number. This combination for the onset of cellular motion can be written as Ra (1+ N.Le )=4π π 2 . This criterion holds for all combinations of Ra, N, and Le whether the thermal and solutal gradients are aiding or opposing each other. Numerical results are presented in the form of flow, temperature, and concentration fields and average Nusselt and Sherwood numbers.