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Laminar natural and mixed convection around a heated cylinder placed within confining walls is investigated numerically. The numerical scheme involves the use of a cylindrical network of nodes in the vicinity of the cylinder with a Cartesian mesh covering the remainder of the flow domain. Results are obtained for the streamlines, isotherms, and heat transfer coefficients. Effects of varying the ratio of width across the walls to cylinder diameter are also investigated. The results obtained are of direct use, for instance, in the design of certain thermal energy storage devices and ocean thermal energy conversion units under investigation.