Heat transfer during melting and solidification is of importance in materials processing, purification of metals, welding, single crystal growth, and many other technologies. The influence of natural convection during melting and solidification has received considerable attention during the last two decades [1-4]. Natural convection during phase-change influences the process in two different ways. During melting, convection increases the overall transport rate and, hence, the growth rate of the new phase. On the other hand, during solidification, convection decreases the growth of the new phase and also affects the morphology of the solid-liquid interface. The nature of the resulting solid is largely determined by the transport process occurring in the vicinity of the solid-liquid interface. Experimental and numerical studies [1, 5, 6] have been carried out to investigate the different possible regimes during melting of pure metals inside a rectangular enclosure.