Transient buoyancy-driven convection of water around 4°C in a porous cavity with internal heat generation

Abstract

The transient buoyancy-driven convection in a water saturated porous cavity with internal heat generation is studied numerically. The Brinkman-Forchheimer-extended Darcy model is employed to investigate the average heat transfer rate and to study the effects of density maximum, the Grashof number, porosity, the Darcy number, and the internal heat generation parameter on buoyancy-induced flow and heat transfer. The finite volume method with the power law scheme for convection terms is used to discretize the governing equations for momentum and energy, which are solved by the Gauss-Seidel and successive-over-relaxation methods. A systematic investigation on transient, steady fluid flow, and heat transfer phenomena under different physical conditions is carried out. The results obtained in the steady state regime are presented in the form of streamlines, isotherms, and midheight velocity profiles for various values of Grashof number, porosity, and Darcy number. It is found that the effect of density maximum is to slow down the buoyancy-driven convection and reduce the average heat transfer. The strength of convection and the heat transfer rate become weak due to more flow restriction in the porous medium for small porosity and high internal heat generation parameter. © 2008 American Institute of Physics.