Convection in a Porous Layer with Solid Partitions

Abstract

In this chaper we address the problem of nonlinear stability for thermal convection in a system which consists of $N$ identical horizontal porous layers of the same thickness interleaved with $N-1$ identical layers of a rigid heat conducting solid each of the same thickness, where $N$ is an integer greater than or equal to 2. The temperatures of the upper surface of the top layer, at $z=H$, and lower surface of the bottom layer, at $z=0$, are fixed at constant values $T_U$ and $T_L$, respectively, with $T_L>T_U$. The key parameters governing the behaviour of the solution to the instability problem are the ratio of the depth of rigid solid to the depth of porous layer, $\delta$, and the ratio of the thermal conductivity of the solid to the thermal conductivity of the porous material, $d$, and the number of porous layers, $N$. The porous materials are allowed to be of Darcy type or Brinkman type and the permeability may be anisotropic.