Numerical simulation of heat and mass transfer in composite fluid-porous layer with transverse magnetic field

Abstract

The aim of this paper is to simulate numerically the two-dimensional steady state double diffusive flow in a composite fluid- porous layer, submitted to a transverse magnetic field. Both the temperature and solute gradients are imposed horizontally, and the two-buoyancy effects can either augment or counteract each other. The Darcy equation, including Brinkman and Forchheimer terms to account for viscous and inertia effects, respectively is used for the momentum equation, and the SIMPLER algorithm, based on finite volume approach is used to solve the pressure-velocity coupling. An extensive series of numerical simulations is conducted in the range: Ra = 10⁵, 10^-8 ≤ Da ≤1, N = 1, Le = 10 and 0 ≤ Ha ≤ 10² This study is limited to Pr = 7 for the binary solution of (Na2Co3). This choice is motivated by the experimental work on phase change realized in laboratory. It is shown that the main effect of the porous layer is to reduce the heat and mass transfer when the permeability is reduced. Isotherms and streamlines are plotted for several values of Hartman (Ha), Darcy number (Da) and porous layer thickness (Xp) . The effect of the magnetic field is found to be rather significant on the flow pattern, heat and mass transfer.