Melting of ice in a rectangular enclosure heated from above was studied. Half of the upper surface was maintained at room temperature and the other half at a higher temperature to facilitate a 2-D phase change case. The ice cube was maintained at its melting point at the bottom. All the other side surfaces were insulated. The process was first modeled by ignoring the effect of natural convection in the liquid phase. However, the experimental investigation showed that the melt front progresses in a 1-D fashion due to strong effects of natural convection in the liquid phase. The model was then extended to include convective heat transfer in such a way that the liquid phase was assumed to be a mixed body subjected to natural convection from the top surface (at an averaged temperature) and the liquid-solid interface. The predictions of this convection model agreed well with the experimental results.