Nanoparticle-enhanced phase change materials (NEPCM) were proposed recently as alternatives to conventional phase change materials due to their enhanced thermophysical properties. In this study, the effect of the size of the nanoparticles on the morphology of the solid-liquid interface and evolving concentration field, during solidification had been reported. The numerical method that was used is based on the one-fluid-mixture model. The model takes into account the thermal as well as the solutal convection effects. A square cavity model was used in the simulation. The NEPCM that was composed of a suspension of copper nanoparticles in water was solidified from the bottom. The nanoparticles size used were 5 nm and 2 nm. The temperature difference between the hot and cold sides was 5 degrees centigrade and the loading of the nanoparticles that have been used in the simulation was 10% by mass. The results obtained from the model were compared with those existing in the literature, and the comparison was satisfactory. The solid-liquid interface for the case of NEPCM with 5 nm particle size was almost planar throughout the solidification process. However, for the case of the NEPCM with particle size of 2 nm, the solid-liquid interface evolved from a planar stable shape to an unstable dendritic shape, as the solidification process proceeded with time. This was attributed to the constitutional supercooling effect. It has been observed that the constitutional supercooling effect is more pronounced as the particle size decreases. Furthermore, the freezing time increases as the particle size decreases.