The effect of conducting boundaries on weakly nonlinear Darcy–Bénard convection

Abstract

We consider convection in a uniform fluid-saturated porous layer which is bounded by conducting plates and heated from below. The primary aim is to determine the identity of the postcritical convection planform as a function of the thicknesses and conductivities of the bounding plates relative to that of the porous layer. This work complements and extends an early paper by Riahi (J Fluid Mech 129:153–171, 1983) who considered a situation where the porous layer is bounded by infinitely thick conducting media.We present regions in parameter space wherein convection in the form of rolls is unstable and within which cells with square planform form the preferred pattern.