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 Ra*(I) and the power-law index n. The behavior of the Nusselt number, based on the maximum temperature theta(max) 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.