A methodology for selecting phase transition models in solid/liquid phase change materials

Phase change materials play a critical role in latent heat thermal energy storage and thermal management systems due to their ability to absorb and release large amounts of heat during quasi-isothermal phase transitions. Accurate modelling of their thermophysical properties is essential for the optimal design and performance assessment of such systems. This study presents a systematic methodology for identifying the most reliable mathematical model to describe phase transition in a given material. First, a comprehensive review of modelling approaches was conducted. In addition, a classification of the existing models is proposed based on their underlying mathematical characteristics. Then, a benchmarking process is presented, which comprises three steps, a visual comparison of the experimental data and model outputs, numerical performance evaluation through the normalised root-mean-square error, and statistical assessment via the Taylor diagram. The performance of these models was evaluated by comparing their numerical estimations of enthalpy and apparent heat capacity against experimental data obtained for sodium nitrate. The selection of this particular PCM was associated with the ongoing research of the authors on high-temperature PCM-based TES systems. Experimental data were acquired using a differential scanning calorimeter within the temperature range of 285-330 °C, with a heating rate of 1 K/min, and employing isothermal periods of 10 minutes. The results revealed significant differences in model accuracy, offering valuable insights for selecting appropriate models for specific material. Utilising the concept of normalised root mean squared error, the Gumbel model demonstrated superior adjustment for apparent heat capacity, whereas the triangular model exhibited a more accurate fit for the enthalpy function of sodium nitrate, with errors of 26% and 17%, respectively. Based on the Taylor diagram, the Gumbel model was selected to represent the phase transition of sodium nitrate due to its high accuracy, evidenced by an error margin of less than 25%, and its strong correlation coefficient exceeding 0.95. This study not only enhances the understanding of modelling thermal properties in phase transition but also guides future research and development in this field. The proposed selection procedure can be effectively replicated to model the phase transition of various phase change materials commonly utilised in industrial applications, because its fundamentals are based on the mathematical principles of phase transition. Consequently, it can be applied to other materials, regardless of their melting temperature.