On natural convection in vertical porous enclosures due to opposing fluxes of heat and mass prescribed at the vertical walls

Abstract

A two-dimensional mathematical model based on Darcy's law with Boussinesq approximation has been used to study double-diffusive natural convection in a rectangular fluid-saturated vertical porous enclosure subject to opposing and horizontal gradients of heat and solute. Results are presented for 50 ⩽ R c ⩽ 250 , 0.01 ⩽ N ⩽ 10, 10 ⩽ Le ⩽ 40 and 1 ⩽ A ⩽ 10, where R c , N, Le and A correspond to the solutal Rayleigh-Darcy number, inverse of buoyancy ratio, Lewis number and enclosure aspect ratio, respectively. The numerical integration of the full problem reveals that for sufficiently large R c , Le and A, there is a domain of N in which one obtains oscillating convection. Outside this domain, the solution approaches steady-state convection, for which analytical solutions are developed and presented. The agreement between the analytical and the numerical solutions is shown to be satisfactory.