Natural convection fluid flow and heat transfer has been studied numerically in the enclosed space between two concentrically positioned vertical cylinders having different finite heights. The cylinders were maintained at different uniform temperatures. The enclosed space was occupied by a system of two fluids, one situated atop the other in a layered manner. For the numerical work, consideration was given to three two-fluid systems: air-water, air-hexadecane, and hexadecane-water. Parametric variations were made of the position of the fluid-fluid interface and of the Rayleigh number. Another parameter was the retention or omission of the interfacial (surface) tension in the force balance at the fluid-fluid interface. The presentation of results included the patterns of fluid flow, velocity profiles, average Nusselt numbers, per-fluid heat transfer rates, and local heat flux distributions. Average Nusselt number definitions were constructed which virtually eliminated the dependence of the results on the location of the interface. Only the liquid-liquid system (hexadecane-water) was found to be sensitive to the interfacial tension.