Inverse method for simultaneously estimating temperature-dependent solid- and liquid-phase thermal conductivities during phase transition

Abstract

As phase change material (PCM) undergoes the phase transformation under the working conditions such as thermal energy storage (TES), it is essential to simultaneously and accurately measure the temperature-dependent thermal conductivities (TCs) of solid and liquid phases. In this study, a novel inverse method is proposed to simultaneously estimate the temperature-dependent solid and liquid phase TCs of a PCM. Several theoretical issues such as the parameter sensitivity, discretization schemes, estimation algorithms are clarified. The Monte Carlo method is used to verify the three discretization schemes, and the results show that both the solid and liquid TCs have high sensitivity coefficients. Additionally, the estimation algorithm results are strongly related to the temperature measurement position, measurement time, boundary conditions, and discrete scheme of the mathematical model. The uncertainty analysis shows that the error caused by the position of the temperature sampling point accounts for approximately 50% of the total estimation error, which suggests that the time-discrete scheme is preferred for the application of the proposed method in real experiments. This study demonstrate that the proposed algorithms provide accurate and reliable estimates of temperature-dependent TC for solid and liquid phases.