Free convection in a shallow annular cavity filled with a porous medium

In this paper we use asymptotic analysis to examine free convection in a shallow annular cavity filled with a fluid-saturated porous medium. The sidewalls of the cavity are maintained at different temperatures and the upper and lower boundaries are insulating. Results are obtained in the limit as the aspect ratio A, defined as the ratio of the height of the annular cavity to its width, goes to zero. This problem was first studied by Pop, Rees, and Storesletten. (J. Porous Media, vol. 1, pp. 227-241, 1998) who considered the case when delta = O(1/A) where delta is the ratio of the inner cylinder radius to the height of the cavity. The results of Pop et al. are extended in this paper by considering convection in the limit as A --> 0 with delta = 0(1). The results indicate that curvature effects strongly influence the nature of convection in shallow annular cavities.