Effects of anisotropy on convection in porous media subject to nonuniform thermal average gradient

Abstract

The objective of the present study is to investigate analytically the effect of anisotropy on the onset of natural convection heat transfer in a fluid saturated porous horizontal cavity subjected to nonuniform thermal gradients, taking into account the hydrodynamic anisotropy of the porous matrix and the rigid/rigid and stress-free/stress-free horizontal boundaries. We have obtained the exact solutions for the flow and heat transfer variables, valid for the onset of convection related to vanishingly small wave number and depending on the Darcy-Rayleigh number, the Darcy number, the anisotropic permeability ratio and the inclination of the principal axis. Furthermore the critical Rayleigh number for the onset of convection is computed and the cases when the Darcy number approaches 00 or 0 are discussed. The results of this paper are the generalization of the results obtained by Degan and Vasseu