Onset of convection in a porous medium with internal heat generationand downward flow

Abstract

The criteria for the onset of natural convection in a fluid-saturated porous medium with a distributed heat source from absorbed solar radiation and an externally imposed downward flow of the fluid are determined. The Brinkmanextended Darcy formulation is used in the equations of motion. Linear stability analysis is performed on the continuity, momentum, and energy equations and the resulting linearized equations are solved using a Galerkin method. The stability criteria so obtained are given in terms of the internal and external Rayleigh numbers, porous medium permeability and extinction coefficient, and Peclet number of the imposed downward flow. The predicted stability criteria in the limiting cases of no downward flow and no heat generation are in agreement with those obtained by others. These results can be applied to the evaluation of a possible improved solar pond design, an end that motivated this study.