Thermal conduction in bi-layer materials with an interfacial inclusion

We establish an analytical model for a thermal inclusion in bi-layer materials. The inclusion is considered as either an elliptic filler of finite thermal conductivity or a crack of ideal thermal insulation. Unlike most existing studies, this article focuses on bonded media of finite size in both their height and the length directions. The temperature field is formulated by a singular integral equation method. The effects of inclusion size and interfacial cracking on the effective thermal conductivity of the medium are studied. In addition, the crack tip thermal flux intensity factors are also given as they are not available in the open literature.