Maximum density effects on natural convection in a porous cavity under thermal non-equilibrium conditions

The problem of natural convection flow in a cavity filled with a water near its maximum density saturated porous medium and subjected to thermal non-equilibrium condition is investigated numerically in the present article. The natural convection flow in the horizontally heated rectangular cavity is assumed to be two-dimensional. A parabolic relationship of the density-temperature is used in Darcy's model. The dimensionless governing equations were solved using the finite volume method, and the results are presented to show the effect of the governing parameters. The numerical results are presented in the form of variations of the average Nusselt number with the Rayleigh number with different values of the heat transfer coefficient parameter H, and the thermal conductivity parameter Kr. It is found that by increasing H and Kr the shape of the isotherms of the solid phase appear to be similar to those of the water due to the enhancement of the thermal communications between the two phases. The results for the average Nusselt number of the thermal equilibrium model, which is the maximum possible value, can be achieved for high values of H×Kr. The numerical results reveal the dependence of the total (solid + fluid) average Nusselt number on the aspect ratio, and the maximum values of the average Nusselt number are found for the cavities of aspect ratio A≈0.5.