Asymptotic analysis of natural convection through horizontal porous layer

Abstract

Two-dimensional cellular convection in a fluid saturated horizontal porous layer is studied using a simple asymptotic analysis. Based on the physical grounds, supported by experiments, the entire region of study is divided into no-slip regime governed by the Brinkinan equations and slip regime governed by the Darcy equations. Self-consistent solutions for velocity and temperature are obtained in a closed form using the technique of matched asymptotic expansion. The transition from the no-slip regime to the slip regime is followed exactly and the maximum value of velocity is obtained. It is shown that the point of maximum velocity gets close to the bounding walls as the permeability parameter decreases. This exhibits the boundary layer behaviour. It is: also shown that permeability has negligible effect on the temperature distribution. Close agreement between analytical and numerical results is observed.