Heat transfer coefficients were determined experimentally for natural convection in the enclosed space between two vertical cylinders maintained at different uniform temperatures. The cylinders were of different height as well as of different diameter. During the course of the experiments, the vertical positioning (i.e. elevation) of the inner cylinder and its eccentricity were varied parametrically. For each enclosure configuration, the inner cylinder Rayleigh number ranged between 1.5×103 and 105. The heat transfer medium was air. To supplement the experimental work, numerical results obtained from finite difference solutions are presented for the concentric case. Comparisons between the experimental and numerical results yielded agreement which, for the most part, was within 1%. In general, the average Nusselt number was nearly independent of both the elevation and eccentricity of the inner cylinder. This finding enabled the Nusselt number to be correlated as a function of the Rayleigh number and the cylinder-to-cylinder diameter ratio, without regard to elevation and eccentricity.