Analysis of melting by natural convection in an enclosure

This paper reports theoretical solutions for the quasi-steady and time-dependent regimes of melting in the presence of natural convection in an enclosed phase-change material heated from the side. The first part consists of developing two boundary layer solutions for the flows near the heated wall and the solid-liquid interface, and then matching these solutions with a unique solution for the core of the liquid region. The second part of the paper outlines an analysis for the earlier, time-dependent regime, when the liquid counterflow through the slender gap convects heat in the vertical direction. This two-part analysis shows that the liquid superheat (Stefan number, Ste) has a sizeable effect on the flow and temperature fields. As Ste increases, the average melting rate decreases and the overall heat transfer rate into the enclosure increases.