Identification of the effective heat capacity–temperature relationship and the phase change hysteresis in PCMs by means of an inverse heat transfer problem solved with metaheuristic methods

Abstract

Two metaheuristic optimisation methods were employed to solve an inverse heat transfer problem involving a phase change material (PCM). The aim was to identify the relationship ceff(T) between the effective heat capacity and temperature during melting and solidification of the PCM. Many researchers have reported a significant asymmetricity between the melting and solidification processes of PCMs. This phenomenon is usually referred to as the phase change hysteresis. To account for the phase change hysteresis, the relationship between the effective heat capacity and temperature was sought in the form of two independent ceff(T) curves; one for the melting process and the other for the solidification process. A numerical model of an air-PCM heat exchanger was employed for the development, testing, fine-tuning, and evaluation of the calculation procedure for the inverse heat transfer problem. The particle swarm optimisation method and the differential evolution method were employed for the inverse identification of the ceff(T) curves. The developed calculation procedure proved to be robust and accurate when applied to pre-simulated data where the exact solution was known to exist. When applied to the data from the experiments with the air-PCM heat exchanger, the calculation procedure confirmed its robustness (the solution was always found), but the accuracy of the results was somewhat lower. The discrepancy of between 2.9% and 15.7% was observed between the phase change enthalpies obtained by the Differential Scanning Calorimetry (DSC) and the phase change enthalpies obtained by the solution of the inverse problem. The temperatures of the phase change peaks, identified from the inverse problem, differed by between 0.34°C and 4.93°C from the temperatures obtained from the DSC analysis.