Among many thermal storage methods, solid-liquids thermal energy storage has gained attentions due to its simple operating principle and considerable storage power because of latent heat. Most of studies on the phase change thermal storage have been done for a cavity under constant wall heating or cooling process. However, in many applications (such as solar energy), a periodical temperature or heat flux exists. In this study, melting and freezing of a Phase Change Material (PCM) placed in a square cavity with a sinusoidal periodic wall temperature is numerically analysed to find the distribution of melting fraction with changing of governing parameters which are dimensionless frequency, Rayleigh and Stefan numbers. The melting fraction ratio and temperature distribution in the cavity are found by solving the governing equations which are continuity, momentum and energy equations. The equations are solved by using finite volume method for the implemented periodic wall temperature. A chart involving Stefan number and dimensionless frequency is plotted to split the phase change in the cavity into three groups named as completed, overheated-subcooled and uncompleted processes. It is found that Rayleigh number does not have any effect on the type of the aforementioned processes. By using the suggested chart, a thermal designer can find out the completeness of the phase change process in the cavity without a computational study.