This paper presents the results of a numerical investigation on the thermal performance of a latent heat storage unit of cylindrical annular geometry and alternate fins including the effects of the geometrical and operational parameters. In the storage unit considered, the water as the phase change material is allocated in the shell while the working fluids flow in the inner tube and the outer shell. The mathematical model is based upon two dimensional formulation of the pure conduction based phase change around an externally and internally finned cylinders. The numerical solution is realized using the finite control volume method and the ADI scheme. The coupling of the phase change problem with the two working fluids, is obtained by energy balance on the respective fluid and phase changing elements, and consequently the fluid bulk temperature is determined in terms of the time and space. The numerical predictions are compared with available results due to other authors in an attempt to validate the present model. The solidified/melt mass fraction, the energy stored and the temperature profiles are analyzed in terms of the variation in the geometry, number of fins, the annular spacing, the Biot and Stefan numbers, and Reynolds numbers of the working fluids.