Analytical solutions to the unsteady close-contact melting on a flat plate (Q1578829)

This paper presents approximate analytical solutions describing the transient process of gravity-induced close-contact melting between a rectangular parallelepipedal solid and a flat plate on which either constant temperature or constant heat flux is imposed. Both the relative motion of the solid block tangential to the heating plate and the solid-liquid density difference is incorporated into this model. For ease of the analyses, it is assumed that the phase change material is kept at its melting temperature, and that the heating plate is flat and horizontal. Under these assumptions, the author obtains analytical solutions of the model equations which agree very well with available numerical data. Of particular interest is that the normalized liquid film thickness is independent of all characteristic parameters, which serves as a theoretical basis to define the unsteady period uniquely. The solution is also capable of resolving the distinctive behaviour of solid-descending velocity for non-unity density ratios during the early stage of melting. It is worth mentioning that the solution presented in this paper is applicable to simultaneous variations in height and cross-section of the solid.