Heatfunction Formulation of Thermal Convection in Rectangular Enclosures Filled with Porous Media

Numerical investigations were conducted to study the effects of Rayleigh, Ra, Prandtl, Pr, Darcy, Da, numbers, and the temperature difference ratio, J, on the fluid flow, isotherms, heat transfer, and distributions in a square cavity filled with porous medium. The range of parameters used is 5 × 102 ≤ Ra ≤ 106, 10−3 ≤ Pr ≤ 103, 10−3 ≤ Da ≤ 103, and 0 ≤ J ≤ 2. The flow governing equations including the Brinkman-extended Darcy equations of motion, energy, and heatfunction equations were thereby solved using the finite-difference method. The results show that all the problem governing parameters have strong effect on the convection vigour, isotherms, and heatfunction fields and profiles. An increase in the value of the Darcy number above unity has no more influence on the heatfunction profiles.