A General Correlation for Melting in Rectangular Enclosures

Abstract

The problem of melting of ordinary (nonmetallic) and metallic solids in enclosures has received considerable research attention due to its importance, for example, in materials processing and latent heat energy storage. It is well known that natural convection in the melt, as well as heat condition in the solid, considerably influence the solid/liquid interface shape and motion. However, attempts to correlate the average heat transfer and melting rates have been relatively unsuccessful, except for a few special cases. Consequently, the objective of this study is to demonstrate that a more general melt fraction correlation can be obtained covering the entire time domain as well as the additional effect of heat conduction in the solid. The present analysis is based on the assumptions that (1) the melting proceeds through the three heat transfer regimes described above and (2) the liquid and solid Stefan numbers are small so that the heat transfer is quasi-steady (i.e., negligible thermal inertia of the liquid and solid). The latter assumption is supported by the fact that in virtually all previous numerical and experimental studies the Stefan numbers were less than about 0.3. For conciseness, this study concentrates on melting in rectangular enclosures. However, the methods presentedmore » can easily be applied to other geometries (e.g., cylinders, etc.). The melt fraction correlation derived in this study is validated using the example of melting of metals in vertical cavities.« less