Development of a general heat conduction model for two-phase heterogeneous solid mixture based on mixture theory

Heat conduction in heterogeneous solid mixtures is a crucial problem across various engineering domains. There are two types of assumptions to build the heat conduction model for such mixtures, local thermal equilibrium (LTE) and local thermal non-equilibrium (LTNE). However, a general model works for both LTE and LTNE models for different mixture structures is still to be developed. In this research, we propose a flexible heat conduction model for two-phase solid mixtures under both LTE and local thermal non-equilibrium (LTNE) conditions. The model innovates by introducing an effective volume fraction that aligns with the heat flow direction, eschewing the need for empirical quantities. Our research demonstrates that the LTE model can be directly derived from the LTNE model when constituential temperatures are equal, ensuring methodological consistency. Four mixture structures are numerically analyzed using the finite difference method, validating the model's predictive accuracy and computational efficiency. It is shown that this general heat conduction model offers an effective approach to analyzing heat transfer behavior in different types of two-phase solid mixtures, and it can be extended to multi-phase problems.