Three-dimensional transient heat conduction in functionally graded materials

The Green’s function for three-dimensional transient heat conduction (diffusion equation) for function-ally graded materials (FGMs) is derived. The thermal conductivity and heat capacitance both vary exponentially in one coordinate. In the process of solving this diffusion problem numerically, a Laplace transform approach is used to eliminate the dependence on time. The fundamental solution in Laplace space is derived and the boundary integral equation formulation for the Laplace Transform Boundary Element Method (LTBEM) is obtained. The numerical implementation is performed using a Galerkin approximation, and the time-dependence is restored by numerical inversion of the Laplace transform using Stehfest’s algorithm. A number of test problems have been examined, and the results are in excellent agreement with available analytical solutions. 1.