Natural convection in porous media bounded by concentric spheres and horizontal cylinders

Abstract

The present paper reports the results of an analytical investigation of natural convection in porous media completely enclosed by concentric spheres and horizontal cylinders. The steady, two-dimensional problem has been solved by the method of finite differences and the method of regular perturbations. The variations of the overall heat transfer with the modified Rayleigh number, the non-dimensional external heat-transfer coefficient, and the radius ratio have been assessed. Results indicate that a maximum value of the heat transfer occurs for the spherical and cylindrical geometries dependent solely upon the radius ratio for each geometry. The flow field has been examined and compared for the two geometries. An interesting feature is manifested by the occurrence of a relatively stagnant and stable cold region at the bottom of the enclosure if the inner bounding surface is considered to be heated, thus shifting the center of the gross circulation from the horizontal. Additionally, a possible qualitative analogy between the nature of the free convection when the enclosure is filled with a porous medium and when the enclosure is filled solely with a Newtonian fluid is scrutinized. Finally, some algebraic correlations of the data are set forth for the convenience of practical applications.