Natural convection in horizontal space bounded by two concentric cylinders with different end temperatures

The gravity-induced flow in a long horizontal space of annular cross-section insulated laterally and with the two ends maintained at different temperatures was studied analytically. The velocity and temperature distribution in the central portion of the space was derived based on a perturbation analysis in the Rayleigh number. The Nusselt number for axial heat transfer was shown to depend on the Rayleigh number, the two geometric aspect ratios ri ro and L ro (inner radius/outer radius and length/outer radius) plus the conducting properties of the two cylindrical walls. The analysis was performed for the case where the horizontal space is filled with incompressible fluid and the case where the space is filled with a porous material saturated with an incompressible fluid. The limit r i → r o was used finally to derive expressions for the flow and temperature fields between two vertical planes subjected to a net temperature difference in the horizontal direction parallel to the planes.