Three-dimensional Green’s functions for transient heat conduction problems in anisotropic bimaterial

Abstract

In this paper, three-dimensional Green’s functions for transient heat conduction problems in general anisotropic bimaterial are obtained based on two-dimensional Fourier transform and Laplace transform, and are separated as a sum of a full-space Green’s function and a complementary part. We can get the bimaterial Green's functions in the transformed domain by boundary conditions, and then in the physical domain by the inverse Fourier and Laplace transform. Although the present paper aims to develop Green's function in anisotropic bimaterial, the derived solutions can be reduced to simple cases, such as in isotropic or orthotropic materials, and in half-space or full-space. Moreover, this method can be extended to derivation of new Green’s functions in multi-layer materials. Numerical examples are presented to verify the validity and applicability of present solutions. When the source is constant and time extends to infinity, the present transient solution approaches the steady one. Besides, the anisotropic solution indicates high correlation with the properties of material.