Analytical solutions for three-dimensional steady and transient heat conduction problems of a double-layer plate with a local heat source

In this paper, analytical solutions for three-dimensional steady and transient heat conduction problems of a double-layer plate with a local heat source are presented, the double-layer structure includes a coating layer and FGM layer. The Poisson method and layer wise (LW) approach are applied to solve the three-dimensional steady heat conduction problem. Meanwhile, to solve the three-dimensional transient heat conduction problem of the double-layer plate, the method of separation of variables (SOV) and LW approach are together applied. The aim of this research is to understand the influences of selected coating material, local heat source and structural parameters on temperature distribution of the double-layer plate, and to guide engineers designing the double-layer structures in thermal environment.