This paper presents an analysis of the charge and discharge processes in a latent thermal energy storage cell. An individual cell is analyzed to study how its behavior affects the performance of a thermal energy storage system. The analysis considers the exchange of thermal energy between a thermal energy storage cell and a source or sink of thermal energy. Two cases are considered, (i) a process in which the phase change material melts and freezes when a constant and uniform temperature is imposed at the lower surface of the cell, and (ii) a process in which the phase change material melts and freezes when a fluid with a constant inlet temperature flows under the cell. The effect of the aspect ratio of the energy storage cell is analyzed in detail as a possible method to enhance heat transfer and improve performance of the thermal energy storage system. The results include, for different aspect ratios of the storage cell, the evolution of the solid-liquid interface, the rates of melting and solidification, the rate of energy storage and the total amount of energy storage.