Analytical Solutions for Anisotropic Heat Conduction Problems in a Trimaterial With Heat Sources

In this work, the analytical solution of a fundamental problem of heat conduction in anisotropic medium is derived. The steady-state temperature field in an anisotropic trimaterial subject to an arbitrary heat source is analyzed. “Trimaterial” denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces. The method of analytical continuation is applied across the two parallel interfaces in order to derive the trimaterial solution in a series form from the corresponding homogeneous solution. A variety of problems, e.g., bimaterial, a finite thin film on a semi-infinite substrate, and a finite strip, can be analyzed as special cases of the present study. The numerical results of the temperature distributions for some practical examples are provided in graphic form and discussed in details.