Analytical modeling of phase change in a composite wall comprising two distinct phase change materials in series

Abstract

Most of the past literature on solid-liquid phase change heat transfer modeling focuses on a single phase change material (PCM), whereas, a sandwich of two or more PCMs arranged in series may be of interest in several applications. The modeling of heat transfer and phase change in such a system is complicated by the presence of multiple phase change fronts propagating at the same time. This work presents a theoretical analysis of the problem of melting of a two-PCM stack being heated from one end. Depending on whether the lower-melting PCM is located next to or away from the heat source, two distinct cases are considered. The propagation of the phase change fronts in each case is divided into several stages, each of which is characterized by a distinct phase change and/or sensible heating processes. The transient temperature field in each stage is determined in the form of infinite series solutions, and the propagation of phase change front over time is then determined using energy conservation at the phase change interface. In this manner, explicit expressions are derived for the time taken for each layer to completely melt. Results are shown to be in good agreement with finite-element simulations, and with the exact Stefan solution under special conditions. Key non-dimensional parameters that influence the nature of the two-PCM phase change process are identified, and their impact on phase change performance is analyzed. Quantitative predictions are presented for the conditions under which both PCMs finish melting at the same time, which is a favorable outcome for efficient energy storage.