Approximate semi-analytical technique based on eigenfunction expansion for phase change heat transfer in a cylindrical body contained within a thick multilayered annular wall

Abstract

Phase change heat transfer occurs commonly in thermal management and energy storage problems. Most literature in this direction assumes direct contact between the phase change material (PCM) and the heat source/sink. However, in practical problems, the PCM is often enclosed within a non-melting wall. This work presents an approximate eigenfunction expansion-based analysis of inwards phase change propagation in a cylindrical PCM encapsulated in a multilayer annular wall. The model accounts for imperfect thermal contact between layers. The transient temperature distribution is determined by solving a transient multilayer thermal conduction problem. Evolution of the phase change front is determined by inserting the temperature distribution into the interfacial energy conservation equation. Results are shown to agree with past work for special cases of the general problem considered here. Good agreement with both experimental and numerical data from past work, and with finite-element numerical simulations is demonstrated. The role of key non-dimensional parameters on phase change characteristics, including total time to melt/freeze is quantified. Ranges of non-dimensional numbers in which the approximate method offers good accuracy are determined. This work extends the state-of-the-art of phase change modeling, with potential applications in energy storage, nuclear engineering, oil/gas transport, and in mass transport problems.