An interface integral equation method for solving transient heat conduction in multi-medium materials with variable thermal properties

In this paper, a new single interface integral equation method is presented for solving transient heat conduction problems consisting of multi-medium materials with variable thermal properties. Firstly, adopting the fundamental solution for the Laplace equation, the boundary-domain integral equation for transient heat conduction in single medium is established. Then from the established integral equation, a new single interface integral equation is derived for transient heat conduction in general multi-medium functionally graded materials, by making use of the variation feature of the material properties. The derived formulation, which makes up for the lack of boundary integral equation in solving multi-medium problems, has the feature that only a single boundary integral equation is used to solve multi-medium transient heat conduction problems. Compared with conventional multi-domain boundary element method, the newly proposed method is more efficient in computational time, data preparing, and program coding. Based on the implicit backward differentiation scheme, an unconditionally stable and non-oscillatory time marching solution scheme is developed for solving the time-dependent system of differential equations. Numerical examples are given to verify the correctness of the presented method.