Development of a generalized heat conduction model for metal-structure-enhanced solid-solid phase change materials using mixture theory

Abstract

This study introduces a novel theoretical heat transfer model for metal-structure-enhanced SSPCMs based on mixture theory. The model separately describes the heat transfer processes in both the SSPCM and the metal structure, thereby accounting for the local thermal non-equilibrium effects between them. A local thermal interaction coefficient is introduced to accurately represent thermal interactions within the composite, eliminating the need for empirical relationships. Unlike existing models, this approach defines an effective volume fraction to describe the continuous portions of each constituent that are parallel to the heat flow. The model is validated by analyzing three common types of metal structures used to enhance heat transfer in PCMs: triangular prism pins, plate fins, and honeycomb configurations. The mathematical model is numerically solved using the finite difference method. By comparing the numerical results with simulation outcomes from commercial software based on actual composite models, it is demonstrated that the proposed model accurately predicts heat transfer behaviors for all three structures. The model significantly simplifies the heat conduction problems of binary mixtures with repetitive structures and is less computationally demanding than solving coupled heat conduction problems directly based on the detailed models. Additionally, it is shown that as the mixing level of the composite increases, the temperature deviation between the metal and the SSPCM decreases, eventually converging to results from well-established local thermal equilibrium models, which further confirms the model's accuracy. This model provides a rapid and effective approach for predicting heat conduction behaviors for binary mixtures, which is critical for designing innovative metal structures in SSPCMs. It also holds potential for application in analyzing heat transfer in other heterogeneous mixtures across various fields.