Abstract The main objective of this study is to investigate the enhancement of energy storage rate of a thermal energy storage unit filled with a phase change material (PCM) by inserting a fin array system into the storage device. Heat is transferred to the unit through the container walls, to which aluminum fins are attached. The PCM, a commercial paraffin wax, is stored between the fins. A mathematical model, based on finite volume method for a 2-Dimensional domain, is developed for solving the melting problem. Transient simulation has been performed on non uniform grids for different fin and PCM layer thicknesses while the ratio of PCM layer to fin thickness is held constant, for different container wall temperatures. A detailed parametric investigation is performed for the phase change process for different fin spacing and PCM layers and for different temperature differences between PCM and container walls. Computational results show that the phase change time and consequently heat absorption and release rate depends on thermal and geometrical parameters of the module, including different wall temperature and fin parameters such as spacing, thickness and height.