Effect of Darcy, fluid rayleigh and heat generation parameters on natural convection in a porous square enclosure: A Brinkman-extended Darcy model

Abstract

A Pressure-velocity solution for natural convection for fluid saturated heat generating porous medium in a square enclosure is analysed by finite element method. The numerical solutions obtained for wide range of fluid Rayleigh number, Raf, Darcy number, Da, and heat generating number, Qd. The justification for taking these non-dimensional parameters independently is to establish the effect of individual parameters on flow patterns. It has been observed that peak temperature occurs at the top central part and weaker velocity prevails near the vertical walls of the enclosure due to the heat generation parameter alone. On comparison, the modified Rayleigh number used by the earlier investigators[4,6], can not explain explicitly the effect of heat generation parameter on natural convection within an enclosure having differentially heated vertical walls. At higher Darcy number, the peak temperature and peak velocity are comparatively more, resulting in better enhancement of heat transfer rate.