Low- and high-Rayleigh number convections induced by internal heat generation in a vertical porous cylinder are studied in different ways according to their flow structures. At low Rayleigh numbers, a first-order partial Galerkin scheme is proved to be effective. Convection at high Rayleigh numbers is characterized by a homogeneous upward flow in the central part of the cylinder and a very thin downward boundary layer on the cooling wall, with the effect of the curvature of the boundary being negligible. By introducing a characteristic length in the same form as the hydraulic radius, the results can be applied to any other enclosures with non-circular boundaries. Comparison of results for a cylinder with those for a rectangular enclosure strongly supports the idea.