Natural Convection in an Anisotropic Porous Medium Heated from the Side. Effects of Amisotropic Properties of Porous Matrix.

Abstract

Natural convection heat transfer in a square cavity filled with a saturated anisotropic porous medium has been investigated analytically. One vertical wall is kept at a constant temperature which is higher than that of the other. Top and bottom walls are insulated. All boundaries are assumed to be nonpenetrable for the fluid. The temperature and stream function are expanded about Ra, the Rayleigh number of the system. The series solutions are then substituted in the governing equations. Equating terms of equal power of Ra, a number of sets of the homogeneous or nonhomogeneous linear systems are generated. The linear systems are solved by Fourier series. Anisotropy of both permeability and thermal conductivity is considered in the process of solving these linear systems. The degrees of anisotropy of fluid permeability Kx/Ky and of thermal conductivity kx/ky are varied from 0.1 to 100 and from 0.01 to 100, respectively. The effect of both anisotropy of permeability and thermal conductivity on the overall heat transfer is found to be equally significant. It is also found that the anisotropy of a porous medium produces similar effects on flow and temperature patterns as does the geometric aspect ratio of the rectangular cavity.