Natural Convection Study with Internal Heat Generation on Heat Transfer and Fluid Flow Within a Differentially Heated Square Cavity Filled with Different Working Fluids and Porous Media

Abstract

To study the intricate natural convection in square cavity filled with porous medium with an electrically conductive fluid in the presence of internal heat source, a numerical methodology based on the finite volume method and a full multigrid acceleration is utilized in this paper. The Darcy–Brinkman is adopted to model the fluid flow and energy transport equations in order to predict the heat transfer process in the porous medium. Numerical solutions are generated for representative combinations of the controlling Grashof number (103 ≤ Gr ≤ 106), the Prandtl number (0.015 ≤ Pr ≤ 0.054), and the Darcy number (10−5 ≤ Da ≤ 10−2). Typical sets of streamlines, isotherms, and average Nusselt number profiles are presented to analyze the flow patterns set up by the competition between homogenous and porous medium. It is revealed that average Nusselt number values are strongly affected by the increase of Prandtl number and the presence of homogeneous medium overestimates the rate of heat transfer better than the presence of a porous medium. Correlations of heat transfer rates in porous medium cases are established in the current investigation.