Holow 1-D cylinders with heat generation: a sufficiently general approach to solving problems with a time variable Dirichlet condition
DOI:
https://doi.org/10.35819/remat2021v7i1id4638Keywords:
Hollow Cylinder, Bessel Functions, Green’s Function Method, Approximated General SolutionAbstract
In this work, a sufficiently approximated general solution to transient heat conduction problems in 1-D cylindrical geometry, with heat generation and time variable Dirichlet conditions, was presented using the Green’s function method. An important integral involving Bessel functions, that is part of the solution, has been solved in detail here. The results obtained from the use of this solution, when applied in some particular cases of practical interest, were aligned with the solutions reported by the literature. We have adopted, in this sense, a methodology that consists of addressing a non-homogeneous problem solution with non-homogeneous boundary conditions in a non-homogeneous problem solution with homogeneous border conditions and two more stationary solutions related to the given Dirichlet conditions. As a result, the solution obtained has no problems of convergence at the boundaries of the cylindrical region with the temperature prescribed conditions.
Downloads
References
CARSLAW, H. S.; JAEGER, J. C. Conduction of heat in solids. 2. ed. Oxford: Clarendon Press, 2011.
CINELLI, G. An extension of the finite Hankel transform and applications. International Journal of Engineering Science, v. 3, n. 5, p. 539-559, out. 1965. DOI: https://doi.org/10.1016/0020-7225(65)90034-0.
CRANK, J. The mathematics of diffusion. 2. ed. Oxford: Clarendon Press, 2011.
DAVIS, H. F. Fourier Series and Orthogonal Functions. New York: Dover Publications, Inc., 1963.
FERNANDES, A. P. Funções de Green: soluções analíticas aplicadas em problemas inversos de condução de calor. Orientador: Gilmar Guimarães. 2009. 130 f. Dissertação (Mestrado em Engenharia Mecânica) - Faculdade de Engenharia Mecânica, Universidade Federal de Uberlândia, Uberlândia, 2009. Disponível em: https://repositorio.ufu.br/bitstream/123456789/14844/1/ana.pdf. Acesso em: 28 jun. 2021.
FOX, R. W.; PRITCHARD, P. J.; MCDONALD, A. T. Introdução à mecânica dos fluidos. Tradução e revisão técnica: Ricardo Koury e Luiz Machado. 7. ed. Rio de Janeiro: LTC, 2015.
HAHN, D. W.; ÖZISIK, M. N. Heat conduction. New Jersey: John Wiley & Sons, 2012.
MEYER, R. E. Introduction to Mathematical Fluid Dynamics. New York: John Wiley & Sons, 2007.
ÖZISIK, M. N. Heat conduction. New York: John Wiley & Sons, 1993.
PERROTTA, J. A. Curso de introdução à engenharia do núcleo de reatores. São Paulo: Instituto de Pesquisas Energéticas e Nucleares, jul. 1999. Disponível em: https://www.ipen.br/portal_por/conteudo/posgraduacao/arquivos/200906040956360-apperrotta.pdf. Acesso em: 5 jan. 2020.
RODRIGUES, R. R; MESQUITA, A. Z. Desenvolvimento de sistema para inspeção de elementos combustíveis de reatores nucleares de pesquisa Triga. Revista Tecnológica, Fortaleza, v. 38, n. 2, p. 1-13, 2017. DOI: https://doi.org/10.5020/23180730.2017.V38.2.7222.
ROMER, R. Você sabe o que são os cilindros que ficam no final dos cabos ligados ao seu PC? Canaltech, 8 mar. 2013. Disponível em: https://canaltech.com.br/produtos/Voce-sabe-o-que-sao-os-cilindros-que-ficam-no-final-dos-cabos-ligados-ao-seu-PC/. Acesso em: 10 jun. 2020.
SOTOMAYOR, J. Lições de equações diferenciais ordinárias. Projeto Euclides. Rio de Janeiro: IMPA, 1979.
Downloads
Published
Issue
Section
License
Copyright (c) 2021 REMAT: Revista Eletrônica da Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
REMAT retains the copyright of published articles, having the right to first publication of the work, mention of first publication in the journal in other published media and distribution of parts or of the work as a whole in order to promote the magazine.
This is an open access journal, which means that all content is available free of charge, at no cost to the user or his institution. Users are permitted to read, download, copy, distribute, print, search or link the full texts of the articles, or use them for any other legal purpose, without requesting prior permission from the magazine or the author. This statement is in accordance with the BOAI definition of open access.
How to Cite
https://orcid.org/0000-0002-0893-7426
