Effects of Throughflow and Internal Heat Generation on Convective Instabilities in an Anisotropic Porous Layer

Abstract

CConvective instabilities caused by a nonuniform temperature gradient due to vertical throughflow and internal heat generation were investigated in an anisotropic porous layer. The boundaries are taken to be either impermeable or porous and are perfect conductors of heat. The Forchheimer-extended Darcy model is used to describe the flow in the porous medium. The resulting eigenvalue problem is solved numerically by the Galerkin method with a modified external Rayleigh number as the eigenvalue. Both anisotropic parameters (i.e., effective thermal diffusivity, η, and permeability, ξ) appear through their ratio η/ξ only. We found that an increase in η/ξ increases the stability of the system. Furthermore, we observed that in the absence of internal heat generation, throughflow stabilizes when the boundaries are symmetric and destabilizes when they are asymmetric. However, if an internal heat source exists, throughflow destabilizes the system irrespective of the boundary types considered. A more precise control of the buoyancy-driven instability may be achieved by tuning the anisotropy parameters and internal heat source strength. Copyright © 2002 by Begell House, Inc.