Magnetic Field Effect on Natural Convection in a Porous Cavity Heating from below and Salting from Side

Abstract

The effect of magnetic field on double-diffusive natural convection in a square cavity filled with a fluid-saturated porous medium is studied numerically. The bottom wall is fully heated at a constant temperature, and the top wall is maintained at a constant cold temperature. The right wall is fully salted to a high concentration, while the left wall is fully salted at a lower concentration than the right one. A magnetic force is applied on the cavity along the gravity force direction. The Darcy model is used for the mathematical formulation of the fluid flow through porous media. The governing equations for heat and mass transfer are solved using the finite volume method. The governing parameters of the present study are Rayleigh number (Ra), Lewis number (Le), buoyancy ratio ( N), and Hartmann number (Ha). The numerical solutions were studied in the range of −10 ≤ N ≤ 10, 0 ≤ Ha ≤ 10, 50 ≤ Ra ≤ 500, and 10−4 ≤ Le ≤ 10. The results were discussed considering the effect of these parameters on the heat and mass transfer processes. The results were presented in terms of streamlines, isotherms, isoconcentration, average Nusselt number, and average Sherwood number for different values of the governing parameters. In general, it has been found that the increase of magnetic force has an effect to retard the strength of the flow inside the cavity and reduce the heat and mass transfer processes. For high Hartmann number, the flow is almost suppressed.