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Thermal energy storages based on the phase change materials are considered as bright technologies because they have more advantages than other energy storage methods. In addition to the thermal parameters of phase change materials, the performance of the thermal energy storage system using latent heat depends on the heat exchanger properties. Here, several different parameters related to the use of fins in the thermal energy storage devices have been studied. Using enthalpy-porosity method, the process of phase-change material melting into a square cavity is evaluated. Cylindrical thermal chargers with a circular cross-section that transfer heat energy to the phase change material are installed inside the chamber. Longitudinal fins are placed on the heat charger surface to assist the heat charging process. By increasing the fins number to four compared with two fins, the melting process shows a significant increase for the position where the heat charger is located in the center and at the bottom of the cavity. Also for these conditions, higher temperature gradients and a thinner boundary layer are observed at the melting point. Also, the heat transfer rate increases and the melting process is accelerated.