3-DIMENSIONAL NATURAL-CONVECTION IN A CONFINED FLUID OVERLYING A POROUS LAYER

This paper presents a numerical study of three-dimensional, laminar na tural convection in an enclosure containing a fluid layer overlying a porous layer saturated with the same fluid. The Brinkman-extended Darc y formulation is used to model fluid flow in the porous layer as this facilitates the imposition of a no-slip boundary condition at the flui d/porous layer interface. The enclosure is heated from one side wall a nd cooled from an opposite wall, while the remaining walls are adiabat ic. The mathematical analysis is carried out in terms of a vorticity- vector potential formulation that ensures the conservation of mass. Th e governing equations in non-dimensional dimensional form are transfor med into parabolic equations by means of a false transient method in o rder to facilitate a solution procedure by an alternating direction im plicit method. Accuracy of the numerical solutions with respect to uni formly and nonuniformly spaced grid points has been tested by performi ng extensive numerical experiments. As expected, it is found that the intensity of free convection is much more profound in the fluid layer. The numerical results indicate that penetration of the fluid into the porous region depends strongly upon the Darcy and Rayleigh numbers. T he effect of the ratio of thermal conductivities (porous to fluid regi ons) is to intensify the convection current in the fluid layer.