Effect of anisotropy on the development of convective boundary layer flow in porous media

Abstract

The effects of anisotropy on the development of thermal boundary layer flow in a rectangular porous cavity is studied. The side walls of the cavity are respectively heated and cooled isothermally. Top and bottom walls are insulated. The porous medium is anisotropic both in permeability and thermal conductivity with its principal axes oriented in a direction that is oblique to the gravity vector. Scale analysis is applied to predict the orders of magnitude involved in the boundary layer regime. In the large Rayleigh number limit, the governing boundary layer equations are solved in closed form, using an intergral approach. A finite difference method is used to obtain numerical solutions of the full governing equations. The effects of the anisotropy in permeability and thermal conductivity on the development of free convective boundary layer flow are found to be significant.