On steady natural convection in a vertical porous slab with permeable boundaries

Abstract

In this paper, we consider the steady-state base flow for natural convection in a vertical porous slab with permeable boundaries. Although recent work proposed a one-dimensional solution for this flow, we make a strong case for this flow to be two-dimensional; this centres on an oversight in the use of the Oberbeck–Boussinesq approximation in the earlier work. Two-dimensional numerical solutions for this flow are then obtained using a pressure–temperature formulation, and the results are backed up using asymptotic analysis. The relevance of these findings to other recent work on the stability of convection in porous slabs with permeable boundaries is also briefly discussed.