Natural convection in a vertical porous slot heated from below and with horizontal concentration gradients

Abstract

Double-diffusive natural convection in a slender vertical porous enclosure is studied both analytically and numerically. The buoyancy forces that induce the fluid motion result from the imposition of both a vertical temperature gradient and a horizontal solutal gradient. The first part of the study contains an analytical solution valid for stratified flows in enclosures with relatively high aspect ratios. The second part of the study contains a numerical study of the full governing equations that validate the analytical model. Comparison between the numerical and analytical solutions covers the thermal Rayleigh number range −6×10 2⩽ R T ⩽10 4, the buoyancy range 0⩽ N⩽10 3 and the Lewis number range 10 −2⩽ Le⩽10 2. In the absence of a horizontal solutal gradient ( N=0), the solution takes the form of standard Bénard bifurcation. The asymmetry resulting from the imposition of a small ( N⪡1) horizontal solutal gradient is investigated. The existence of multiple solutions, for a given range of the governing parameters, is demonstrated.