On the derivation of unsteady closed-form analytical solution for the solidification of pure and eutectic materials with boundary conditions of the third kind

Abstract

Abstract Solidification and fusion are important processes applied in several fields of science and technology. Recently, far beyond the realms of materials science and metallurgy, many applications have risen in latent heat thermal energy storage and melting and growth of ice plates. Due to the relative difficulty in obtaining numerical solutions for moving boundary problems for a wide range of space and time scales. In this work, four closed-form solutions for the transient solidification of pure and eutectic materials are proposed for one- and three-dimensional semi-infinite slabs considering convective boundary conditions and melting superheating. The analytical results are plotted against the numerical simulation results.