Anisotropy effects on heat and fluid flow by unsteady natural convection and radiation in saturated porous media

This article deals with a numerical study of fluid flow and heat transfer by unsteady natural convection and thermal radiation in a vertical channel opened at both ends and filled with anisotropic, in both thermal conductivity and permeability, fluid-saturated porous medium. The bounding walls of the channel are gray and kept at a constant hot temperature. In the present study we suppose the validity of the Darcy law for motion and of the local thermal equilibrium assumption. The radiative transfer equation (RTE) is solved by the finite-volume method (FVM). The numerical results allow us to represent the time-space variations of the different state variables. The sensitivity of the fluid flow and the heat transfer to different controlling parameters, namely, the single scattering albedo omega, the temperature ratio R-c, the anisotropic thermal conductivity ratio R-k, and the anisotropic permeability ratio R-k, are addressed. Numerical results indicate that the controlling parameters of the problem, namely, omega, R, R-c, and R-k, have significant effects on the flow and thermal field behavior and also on the transient process of heating or cooling of the medium. Effects of such parameters on time variations of the volumetric flow rate q(v), and the convected heat flux Q at the channel's outlet are also studied.