Natural convection flow in a fluid-saturated porous medium enclosed by non-isothermal walls with heat generation

Abstract

Unsteady laminar natural convection flow has been considered in a rectangular enclosure formed by non-isothermal walls, filled with a fluid-saturated porous medium and with internal heat generation. The top horizontal wall and right vertical wall of the enclosure are cold, the bottom wall is heated at a constant temperature and the left vertical wall is considered to be non-isothermal. The equations are non-dimensionalized and solved numerically by an upwind finite difference method together with a successive over-relaxation (SOR) technique. The effects of heat generation and the porosity of the medium on the streamlines and isotherms are presented, as well as on the rate of heat transfer from the walls of the enclosure. The fluid has Prandtl number Pr=0.7 while the value of the Rayleigh number is 10 5.