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2016 Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions
Inês Simões, António Tadeu, Nuno Simões
J. Appl. Math. 2016(SI1): 1-22 (2016). DOI: 10.1155/2016/6439710

Abstract

This paper presents a set of fully analytical solutions, together with explicit expressions, in the time and frequency domain for the heat conduction response of homogeneous unbounded and of bounded rectangular spaces (three-, two-, and one-dimensional spaces) subjected to point, line, and plane heat diffusion sources. Particular attention is given to the case of spatially sinusoidal, harmonic line sources. In the literature this problem is often referred to as the two-and-a-half-dimensional fundamental solution or 2.5D Green’s functions. These equations are very useful for formulating three-dimensional thermodynamic problems by means of integral transforms methods and/or boundary elements. The image source technique is used to build up different geometries such as half-spaces, corners, rectangular pipes, and parallelepiped boxes. The final expressions are verified here by applying the equations to problems for which the solution is known analytically in the time domain.

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Inês Simões. António Tadeu. Nuno Simões. "Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions." J. Appl. Math. 2016 (SI1) 1 - 22, 2016. https://doi.org/10.1155/2016/6439710

Information

Published: 2016
First available in Project Euclid: 13 April 2016

zbMATH: 07037290
MathSciNet: MR3465045
Digital Object Identifier: 10.1155/2016/6439710

Rights: Copyright © 2016 Hindawi

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Vol.2016 • No. SI1 • 2016
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