Density maximum effect on buoyancy-driven convection of water in a porous cavity with variable side wall temperatures

The buoyancy-driven convection in a square cavity filled with water-saturated porous medium is studied numerically. While the right and left side wall temperatures vary linearly from θa to θo and θo to θb, respectively with height and θo is the mean of θa and θb, the top and bottom walls of the cavity are thermally insulated. The Brinkman–Forchheimer extended Darcy model is considered to study the effects of density maximum, Grashof numbers, porosity and Darcy numbers on the buoyancy-induced flow and heat transfer. The finite volume method is used to discretize the governing equations, which are solved by Gauss–Seidel and successive over relaxation methods. The temperature distribution and flow fields are presented in the form of streamlines, isotherms and mid-height velocity profiles. It is found that the effect of density maximum is to slow down the natural convection and reduce the average heat transfer. The strength of convection and heat transfer rate become weak due to more flow restriction in the porous medium for small porosity.