Numerical investigation of buoyancy balance effect on thermosolutal convection in a horizontal annular porous cavity

Abstract.

The effect of cooperating and opposite buoyancy forces on the flow structure and the heat and mass transfer rates is numerically investigated in a horizontal annular space of radius ratio R = 2, filled with a porous medium saturated by a binary fluid. Uniform and constant temperatures and concentrations are imposed along the active walls. The steady-state solutions have been obtained using the discretization of the governing equations with the Centered Finite Difference method based on the ADI scheme. The influence of the dimensionless thermosolutal parameters, namely Darcy-Rayleigh numbe, Ra, Lewis number, Le, and buoyancy ratio, N , is investigated. The study is focused on the effect of Ra and Le on the steady-state solution under the cooperating (N = 2) and opposite (N = -2) buoyancy forces cases. The increase in Rayleigh number in the opposite case results in a full development of the convection and gives rise to multicellular flow structures. The critical Rayleigh number values corresponding to the onset of this flow pattern are determined for a large range of Lewis number values by using two initial conditions types. On the other hand, the unicellular flow dominates the cooperating case whatever the Darcy-Rayleigh and Lewis numbers values. The heat and solutal transfer behaviors are also considered.

Graphical abstract