Thermophysical characterization of three paraffin waxes (RT27, RT21 and RT35HC) is carried out in this study using DSC, TGA and transient plane source technics. Then, a numerical study of their melting in a rectangular enclosure is examined. The enthalpy-porosity approach is used to formulate this problem in order to understand the heat transfer mechanism during the melting process. The analysis of the solid-liquid interface shape, the temperature field shows that the conduction is the dominant heat transfer mode in the beginning of the melting process. It is followed by a transition regime and the natural convection becomes the dominant heat transfer mode. The effects of the Rayleigh number and the aspect ratio of the enclosure on the melting phenomenon are studied and it is found that the intensity of the natural convection increases as the Rayleigh number is higher and the aspect ratio is smaller. In the second part of the numerical study, a comparison of the performance of paraffins waxes during the melting process is conducted. Results reveals that from a kinetically RT21 is the most performant but in term of heat storage capacity, it was inferred that RT35HC is the most efficient PCM.