Prediction of Natural Convection Heat Transfer in Layered Porous Cavities by Homogeneous Anisotropic Model

Steady-state heat transfer by natural convection in a layered porous cavity is examined by using homogeneous anisotropic model. The geometry considered is a two-dimensional square enclosure comprising of three or four porous layers with non-uniform thickness and distinct permeability. The cavity is subjected to differential heating from the vertical walls. The results, which include the flow patterns and temperature profiles as well as the heat transfer coefficients, are presented for a wide range of permeability ratio, sublayer thickness ratio, and Rayleigh number. Particularly, the heat transfer results obtained are compared with those reported from a rigorous numerical model for layered porous media. In addition, the results are compared with the lumped system model that was proposed recently. It has been found that homogeneous anisotropic model predicts the heat transfer coefficient reasonably well within the conductive flow regime. However, beyond this regime, the model fails to represent the layered case for the effective permeabilities and sublayer thickness ratios considered. On the other hand, it is observed that the lumped system model offers better agreement to the heat transfer coefficient of the actual layered porous system over a wider range of parameters and which also significantly reduces computational efforts.