Open Access

ARTICLE

2.5D Green's Functions in the Frequency Domain for Heat Conduction Problems in Unbounded, Half-space, Slab and Layered Media

António Tadeu¹, Julieta António and Nuno Simões

1 Department of Civil Engineering, Faculty of Sciences and Technology, University of Coimbra, Portugal

Computer Modeling in Engineering & Sciences 2004, 6(1), 43-58. https://doi.org/10.3970/cmes.2004.006.043

Abstract

This Analytical Green's functions for the steady-state response of homogeneous three-dimensional unbounded, half-space, slab and layered solid media subjected to a spatially sinusoidal harmonic heat line source are presented. In the literature, this problem is frequently referred to as the two-and-a-half dimensional fundamental solution or 2.5D Green's functions.
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.

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