In this study, molten paraffin wax dispersed with CuO nanoparticles inside a square enclosure is investigated numerically using the enthalpy-porosity technique. A cosinusoidally varying temperature is imposed on a hot wall, while the facing cold wall is kept at a constant temperature. The other walls in the square enclosure are considered insulated. The temperatureand phase-dependent thermophysical properties are incorporated into the governing equations and numerical calculations. The effect of the volume fraction of nanoparticles (phi = 0 vol.%, 1 vol.%, and 3 vol.%) in conjunction with the orientation of the heated wall (heating from a side wall or heating from the bottom) on the melting process are examined. Computed numerical results demonstrated that the melting rate and the stored energy for the case of heating from below is considerably higher than in the case of heating from the side. With dispersion of nmloparticles in the paraffin wax, the melting rate and the stored energy are enlarged more significantly than in the case of heating from the side. A higher enlargement is attained for a nanoparticle volume fraction of phi = 7 vol.% as compared to that of phi = 3 vol.%.