A Comprehensive Review on Multi-Dimensional Heat Conduction of Multi-Layer and Composite Structures: Analytical Solutions

Heat conduction in multi-layer and composite materials is one of the fundamental heat transfer problems in many industrial applications. Due to different materials types, interface conditions, and various geometries of these laminates, the heat conduction mechanism is more complicated than that of one-layer isotropic media. Analytical solutions are the best ways to study and understand such problems in depth. In this study, different existing analytical solutions for heat conduction in multi-layer and composite materials are reviewed and classified in rectangular, cylindrical, spherical, and conical coordinates. Applied boundary conditions, internal heat source, and thermal contact resistance as the most critical parameters in the solution complexity investigated in the literature, are discussed and summarized in different tables. Various types of multi-layer structures such as isotropic, anisotropic, orthotropic, and reinforced laminates are included in this study. It is found that although more than half a century has passed since the beginning of the research on heat transfer in multi-layer composites, new researches that can help with a better understanding in this area are still being offered. The challenges and shortcomings in this area are also discussed to guide future researches.