NATURAL CONVECTION HEAT TRANSFER IN INCLINED TALL CAVITIES BOUNDED BY POROUS LAYERS

Thermally driven flow in a tall inclined cavity bounded by porous layers is studied analytically and numerically. A constant heat flux is applied for heating and cooling of two opposing walls of the cavity, while the other two are insulated. The Beavers—Joseph slip condition on velocity is applied at the interface between the fluid and porous layers. An analytical solution is obtained by assuming parallel flow in the core region of the cavity and a numerical solution by solving the complete governing equations. The flow and heat transfer variables are obtained in terms of the Rayleigh number, Ra, slip condition parameter N and angle of inclination of the cavity Φ. The critical Rayleigh numbers for the onset of convection in a layer heated from below are predicted for various hydrodynamic boundary conditions. The results for a fluid layer bounded by solid walls (N → ∞) and by free surfaces (N → 0) emerge from the present analysis as limiting cases.