The effect of thermal stratification on natural convection in a vertical porous insulation layer

Abstract We consider the two-dimensional free convection flow in a rectangular porous container where the impermeable bounding walls are held at a temperature which is a linearly decreasing function of height. Attention is focused on the case where the local temperature drop across the container is zero. Two cases are considered, namely, containers of finite aspect ratio and those of asymptotically large aspect ratio. For both cases it is found that modes bifurcate in pairs as the linear stability equations admit an infinite set of double eigenvalues. The weakly nonlinear evolution of the primary pair of eigenmodes is analysed, and it is found that the resulting steady-state flow is nonunique as the realized steady flow is dependent on the precise form of the initial disturbance. For asymptotically tall boxes the weakly nonlinear evolution of the pair of modes is governed by coupled pair of Burger-like equations. These are analyzed both numerically and using asymptotic methods. No evidence of persistently unsteady flow is found. Copyright © 1996 Elsevier Science Ltd.