This paper presents a two-dimensional axi-symmetrical model for the formulation of the problem of fusion of PCM around a vertical cylinder in the presence of natural convection. The basic equations of mass, momentum and energy were formulated in terms of the vorticity and the stream function. The numerical predictions were compared with available experimental results indicating good agreement. Additional results show the effects of the geometrical and operational parameters on the solid-liquid interface, stream function, energy stored and melt mass fraction. The model was extended to produce charts and correlations for the mean heat transfer rate, total solidification (or fusion) time in terms of the geometrical parameter, the modified Rayleigh number and the Stefan number. These charts and correlations are helpful in engineering design of PCM storage units.