Effective boundary conditions of the heat equation on a body coated by functionally graded material
Huicong Li · Discrete and Continuous Dynamical Systems · 2015
We consider the linear heat equation on abounded domain, which has two components with a thin coatingsurrounding a body (of metallic nature), subject to the Dirichlet boundary condition.The coating is composed of two layers, the pure ceramic part and the mixed part.The mixed part is considered to be functionally graded material (FGM) that is meant to makea smooth transition from being metallic to being ceramic.The diffusion tensor is isotropic on the body,and allowed to be anisotropic on the coating; and the size of diffusion tensor may differ significantlyin these components. We findeffective boundary conditions (EBCs) that are approximatelysatisfied by the solution of the heat equation on theboundary of the body.A concrete example is considered to study the effect of FGM coating. We alsoprovide numerical simulations to verify our theoretical results.