An approximate analytical solution for the initial transient process of close-contact melting on an isothermal surface

Abstract

An approximate analytical solution for the initial transient process of close-contact melting occurring between a phase change material kept at its melting temperature and an isothermally heated flat surface is derived. The model is so developed that it can cover both rectangular and circular cross-sectional solid blocks. Normalization of simplified model equations in reference to the steady solution enables the solution to be expressed in a generalized form depending on the liquid-to-solid density ratio only. A selected result shows an excellent agreement with the previously reported numerical data, which justifies the present approach. The solution appears to be capable of describing all the fundamental characteristics of the transient process. In particular, dependence of the solid descending velocity oft the density ratio at the early stage of melting is successfully resolved. The effects of other parameters except the density ratio on the transient behaviors are efficiently represented via the steady solution implied in the normalized result. A simple approximate method for estimating the effect of convection on heat transfer across the liquid film is also proposed.