Free convection between two horizontal concentric cylinders filled with a porous medium - a perturbed solution

A theoretical analysis of the steady free convection in a saturated porous medium confined between two horizontal concentric cylinders is made in this paper. It is assumed that the flow is driven by a constant vertical temperature gradient. Analytical solutions in terms of Bessel functions for the first-order perturbed flow and temperature field from the heat conduction steady state are determined. Four types of thermal convection with cellular structure are found, and the dependence of the critical Darcy-Rayleigh number on the thickness of the annular region is obtained for these flow types. Typical streamlines and isotherms corresponding to these critical modes are presented. It is worth mentioning that these results have a bearing on the design of thermal insulators.