Theoretical modeling of solid-liquid phase change in a phase change material protected by a multilayer Cartesian wall

Abstract

Theoretical modeling of solid-liquid phase change processes is of much interest in energy storage and thermal management. While most theoretical phase change models assume that the phase change material (PCM) is in direct contact with the thermal source/sink, in most practical scenarios, the two are separated by a thick wall, which, in some cases, may comprise multiple heterogeneous layers. Accounting for thermal conduction through the multi-layer wall is important to ensure accuracy of the predicted phase change characteristics. This paper presents theoretical analysis of phase change in a system comprising a PCM and a multi-layer Cartesian wall using the eigenfunction expansion method and analysis of multi-layer thermal conduction. Thermal contact resistance between wall layers, and between the wall and PCM are accounted for. The predicted phase change front propagation is shown to agree well with past work for special case of a homogeneous wall, as well as with numerical simulations. Two distinct timescales in the solution, related to diffusion through the wall and phase change propagation in the PCM are identified. The impact of the imposed temperature, wall thermal diffusivity and thickness are presented in non-dimensional forms. Practical problems related to design of a PCM wall for energy storage are solved, showing two very different characteristics of stainless steel and polypropylene walls, as well as the impact of wall thickness on phase change propagation. The results presented here improve the fundamental understanding of phase change heat transfer processes, and are particularly relevant for relatively thick, thermally insulating walls over relatively short time periods, for which a resistance approximation for the wall is not accurate.