Green's function for steady-state heat conduction in a bimaterial composite solid

Abstract

The derivation of a Green's function for steady-state heat conduction in anisotropic bimaterials is presented. The Green's function is obtained through a Fourier representation to obtain both free-space, singular parts and region-dependent, regular parts. To obtain the region-dependent parts of the Green's function, the homogeneous solution is written using the virtual force method. Full details of the necessary inversion integrals are provided. The Green's function is shown to degenerate to the usual logarithmic potential for steady-state heat conduction in isotropic solids. The normal derivatives necessary for implementation of the Green's function in boundary integral equations are provided, and an example calculation of the Green's function in a quartz-copper material system is presented.