Exploration of Variable Conductance Effects During Input and Extraction of Heat From Phase Change Thermal Storage

Previous efforts to model the effectiveness of heat input and extraction from a thermal storage unit have generally been based on the definition of a constant conductance of heat from the working fluid to the phase change storage material. In order to capture the effects of changing thermal resistance between the working fluid and melt front location, this paper presents a method using a resistor network analogy to account for thermal conductance as a function of melt fraction. This expression for thermal conductance is then implemented in an existing numerical framework. Results are validated by comparing calculations for a single unit cell using a quasi-steady Stefan problem approach, a finite difference scheme, and more general form solutions from literature. The variable approach is then compared with an average value for overall thermal conductivity, U, to characterize the performance of a thermal energy storage unit consisting of a series of these unit cells. Overall effectiveness in the thermal energy storage device is found to be within 0.6% agreement when comparing these methods, though local percent deviation can be as high as 113%. Depending on the needed accuracy and use case for such a numerical framework, suggestions are provided on whether an average value for U is sufficient for characterizing such a thermal energy storage device. Discussion is also provided on the flexibility of the computation schemes described by testing the sensitivity of the results via changes in dimension-less input parameters.