The proposed equations are theoretically interesting in themselves and they are also useful as benchmark results for validating numerical applications. They are also of great practical use in the formulation of three dimensional heat transfer problems in layered solid formations using integral transform methods and/or boundary elements.

The final expressions for heat conduction in an unbounded medium are validated first, since time solutions are known in analytical form. This requires the prior application of an inverse Fourier transform to our frequency domain results, using complex frequencies to avoid the aliasing phenomena. The results provided by the proposed expressions for half-space and slab are then compared with those computed using the image source technique, while the solutions obtained for the layered media are then verified with those calculated by the Boundary Element Method solution, which requires the discretization of the interfaces between layers with boundary elements. KW - Green's functions KW - transient heat conduction KW - frequency domain DO - 10.3970/cmes.2004.006.043