Numerical Solution of Transient Heat Conduction Problems with Solid-Liquid Phase Change Hysteresis

Abstract

This work presents a numerical method for accurately addressing transient heat conduction problems in phase change materials (PCMs) exhibiting enthalpy hysteresis. Hysteresis causes the melting and solidification processes to follow different enthalpy curves, making it difficult to predict the thermal behavior of the material. The finite element method (FEM) is used under a mixed enthalpy-temperature formulation, which facilitates numerical resolution and allows for realistic modeling of the liquid fraction evolution during phase change. The static hysteresis model is implemented in the FEM formulation, providing a mathematically sound physical basis for quantifying phase change hysteresis. The results obtained in this communication indicate that the proposed numerical scheme is reliable and robust, enabling the solution of the pronounced nonlinearities inherent in the static hysteresis model, making it a valuable tool for the design and optimization of thermal energy storage (TES) systems.