Green's functions and boundary integral analysis for exponentially graded materials: Heat conduction

Free space Green's functions are derived for graded materials in which the thermal Conductivity varies exponentially, in one coordinate. Closed-form expressions are obtained for the steady-state diffusion equation, in two and three dimensions. The corresponding boundary, integral equation formulations for these problems are derived, and the three-dimensional case is solved numerically using a Galerkin approximation. The results of test calculations are in excellent agreement with exact solutions and finite element simulations.