A modified mixture theory framework for the melting of pure PCM and PCM/metal foam composite

Abstract

Since it was proposed in 1960, the mixture theory has been widely utilized to decouple the interactions between constituents in both homogeneous and heterogeneous mixtures in a macroscopic scale. In this thesis, a modified mixture theory framework is developed to analyze the phase change problems of phase change materials (PCMs) and their composites. Mixture theory based mathematical models are established for one-dimensional pure PCMs and PCM/metal foam composites, and two-dimensional melting of pure PCMs. Volume change due to the density variation during the phase change of PCMs is considered. For the one-dimensional model, the local thermal non-equilibrium effect is considered, and the velocity correlated to the density change during paraffin melting is introduced. A new constituential heat flux term is presented to explain the heat supply from different constituents, and a new interpretation for internal energy supply term is introduced. The governing equations are numerically solved by using a finite difference method. Temperature field, mushy zone evolution, and velocity profile at the boundary are predicted. Experiments are conducted to validate the numerical analysis. It is shown that the numerical results obtained by the mixture theory model have a satisfying agreement with the real situation. For the two-dimensional model, we propose that the three regions can be modeled individually and then coupled using an enthalpy method. Like the one-dimensional mixture model, in the two-dimensional model we assume that the velocity field in the mushy zone is solely dependent on the density variation and the flow in the liquid region can not penetrate the boundary of the mushy zone. We also revise the energy equation to a more general form for different mixture structures. Both local thermal equilibrium and local thermal non-equilibrium situations are considered. The different mixture structures are considered by proposing an effective volumetric fraction for each constituent of the mixture. A new expression for the effective thermal conductivity is provided for mixtures with local thermal equilibrium model, while for the local thermal non-equilibrium situations, a new energy equation set is given together with our interpretations of heat flux terms and local thermal interaction terms. Moreover, it is shown that the expression of the effective thermal conductivity under the local thermal equilibrium conditions can be obtained by assuming the temperatures of the constituents are the same in the local thermal non-equilibrium model. By comparing the numerical results, it is shown that the mixture model can provide satisfying predictions for the real situations for different types of mixture structures and for both local thermal equilibrium and local thermal non-equilibrium. With this revised heat equation, the scope of the previously proposed mixture theory framework is extended. On one hand, it can be used to predict the heat transfer behavior of multi-constituent materials with different structures including soil, tissues, nanoparticle-embedded materials, etc.; on the other hand, it can also be used to develop optimized structures for heat transfer enhancement.