This paper investigates the behavior of a Thermal Energy Storage (TES) system with Phase Change Material (PCM) under static and periodic boundary conditions. A commercial Computational Fluid Dynamics software is used to study the behavior of the system. A validation of the numerical model is done by comparing the numerical results with the measured melting fraction as function of time, determined from measurement of the temperature fields. A numerical analysis is then done with two different periods of the temperature of the heat source around one imposed temperature. The study presents results on the evolution of the liquid fraction, of the mean temperature of the medium and of the energy stored/retrieved by the heat source. Results show that the system is not efficient for all periods. For small time periods, energy storing is slower but the system is more efficient in retrieving it. For long time periods, the mean temperature is higher in the medium and the solidification front is far from the heat source, which means that heat removal is more complicated by counting only on the conduction phenomenon.