Simplified numerical model for melting of ice with natural convection

Ice in a rectangular enclosure is melted by heating from the top, while maintained at its melting point at the bottom. The other surfaces are insulated. In the enclosure near the hot region, liquid phase starts forming as temperatures reach values higher than the melting point of ice. This phenomenon is first modeled by ignoring the effect of natural convection in the liquid phase. The resulting equations of conservation of energy are solved in each phase. The motion of melting front is governed by an energy balance at the interface. This conduction model is verified by applying it on a system for which an analytical solution is available. The model is then extended to include convective heat transfer in such a way that the liquid phase is assumed to be a mixed body subjected to natural convection from the top surface and the liquid-solid interface. The flux at the interface is obtained by finding a heat transfer coefficient for natural convection with a cold plate facing upward. Comparison of the results of the numerical work with experiments performed on water/ice system shows a strong effect of natural convection on melting of ice. The model involving natural convection in the liquid phase agrees well with the experimental work.