BUOYANT CONVECTION OF A POWER-LAW FLUID IN AN ENCLOSURE FILLED WITH HEAT-GENERATING POROUS MEDIA

Abstract

A numerical study is performed of the buoyant convection in a rectangular enclosure. A heat-generating porous medium, saturated with a non-Newtonian fluid, fills the enclosure. The non-Newtonian fluid is assumed to follow the power-law rheological model. The flow is described by the Darcy equation for a porous medium. The vertical side walls of the enclosure are cooled at constant temperature T 0, and the horizontal walls are thermally insulated. The modified internal Rayleigh number Ra I∗ is large to render a boundary-layer-type flow. Comprehensive numerical solutions are acquired for the governing equations. Details of flow and thermal characteristics are portrayed for ranges of RaI∗ and the power-law index n. The behavior of the Nusselt number, based on the maximum temperature θmax in the enclosure, is delineated. By combining the numerical results, a correlation for the average Nusselt number is proposed. The validity of the assumption of local thermal equilibrium in the present configuration is discussed.