Major and minor hysteresis loops in the enthalpy-temperature and phase fraction-temperature diagrams of solid/liquid phase change materials

A rate-independent hysteresis model originally proposed by Ivshin and Pence (1994) is extended to describe thermal hysteresis in enthalpy, specific heat capacity and phase fraction of solid/liquid phase transitions. It turns out that, even for smooth cyclic temperature variations, major and minor loops in the enthalpy-temperature diagram are not necessarily closed. Jump discontinuities may occur upon switches between heating and cooling. This issue is highly problematic: the model does not obey the law of conservation of energy. This problem particularly concerns the frequently found setting that solid and liquid heat capacities do not coincide and the phase transition enthalpy is assumed constant, i.e. independent of temperature. Two possible solutions are proposed. They follow the idea of Kirchhoff's Law and relate temperature variations of the phase transition enthalpy to the difference in specific heat capacities of the distinct phases. Conditions for path reversibility and for the existence of closed major and minor loops (limit cycles) are given. The models show good agreement with experimental data generated by differential scanning calorimetry (DSC) of three types of paraffin-based solid/liquid phase change materials (PCM). These materials are increasingly adopted for storing thermal energy in building applications and show thermal hysteresis for complete and partial melting/solidification cycles.