New derivations of the fundamental solution for heat conduction problems in three-dimensional general anisotropic media |
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| Authors: | Rogério José Marczak Mitsunori Denda |
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| Affiliation: | 1. Mechanical Eng. Dept., Federal University of Rio Grande do Sul, Rua Sarmento Leite 425, Porto Alegre, RS 90050-170, Brazil;2. Mechanical & Aerospace Dept., Rutgers University, 98 Brett Road, Piscataway, NJ 08854-8058, USA;1. Department of Mathematics, UCT, Osmania University, Hyd, TS, India;2. Department of Mathematics, KakatiyaUniversity, Warangal, TS, India;1. ITeCons, University of Coimbra, Pólo II, Rua Pedro Hispano, 3030-289 Coimbra, Portugal;2. Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia;1. Department of Microbiology, Grant Government Medical College, Sir Jamshedjee Jeejeebhoy Group of Hospitals, Byculla, Mumbai, Maharashtra, India;1. Department of Microbiology (ST, AO), Christian Medical College and Hospital, Ludhiana, Punjab, India. |
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| Abstract: | This work presents two new methods to derive the fundamental solution for three-dimensional heat transfer problems in the general anisotropic media. Initially, the basic integral equations used in the definition of the general anisotropic fundamental solution are revisited. We show the relationship between three, two and one-dimensional integral definitions, either by purely algebraic manipulation as well as through Fourier and Radon transforms. Two of these forms are used to derive the fundamental solutions for the general anisotropic media. The first method gives the solution analytically for which the solution for the orthotropic case agrees with the well known result obtained by the domain mapping, while the fundamental solution for the general anisotropic media is new. The second method expresses the solution by a line integral over a semi-circle. The advantages and disadvantages of the two methods are discussed with numerical examples. |
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