Modelling the effect of binary phase composition on inward solidification of a particle

In the traditional inward solidification model of a sphere, the interface temperature of liquid–solid is considered as a constant freezing point, but majority of materials have a freezing temperature range and the freezing temperature descends with the change of liquid–solid two phase composition. By taking binary alloy for instance, a new liquid–solid interface model is proposed based on the solid fraction, because the solid fraction plays the bridge between the freezing temperature and the binary phase composition. The new model determines a corresponding relationship between the position of liquid–solid moving interface and the freezing temperature, and it is applied in the solidification analysis of a single encapsulated phase change material (PCM) particle. For different type of PCMs, two rules have been built. A linear rule is designed for the material with the narrow freezing temperature range; to materials with the wide freezing temperature range like Copper (Cu–Al), the solid fraction presents a complicated function relationship with the freezing temperature, so in the numerical calculation, the local linear rule is employed based on the transient interpolation of the solid fraction in the discrete points which represent the freezing temperature against solid fraction in DSC measurements or equilibrium phase diagrams.