Heat and mass transfer by natural convection in a porous medium

Abstract This paper reports a fundamental study of the phenomenon of natural convection heat and mass transfer near a vertical surface embedded in a fluid-saturated porous medium. The buoyancy effect is due to the variation of temperature and concentration across the boundary layer. The study contains two parts. In the first part, scale analysis shows that the natural convection phenomenon conforms to one of four possible regimes, depending on the values of buoyancy ratio N and Lewis number Le . The scales of the heat and mass transfer rates are determined for each regime. In the second part of the study, the boundary-layer problem is solved via similarity formulation in the buoyancy ratio range − 5 ⩽ N ⩽ 4 and Lewis number range 1 ⩽ Le ⩽ 100. The similarity solutions confirm the validity of the order-of-magnitude limiting results revealed by scale analysis.