Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem
We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classific...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/671548 |
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| author | R. J. Moitsheki M. D. Mhlongo |
| author_facet | R. J. Moitsheki M. D. Mhlongo |
| author_sort | R. J. Moitsheki |
| collection | DOAJ |
| description | We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. The effects of thermogeometric fin parameter and the exponent on temperature are studied. Also, the fin efficiency is analyzed. |
| format | Article |
| id | doaj-art-168ee23266714e5c94919fcf984a06be |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-168ee23266714e5c94919fcf984a06be2025-02-03T06:44:34ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/671548671548Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin ProblemR. J. Moitsheki0M. D. Mhlongo1Center for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South AfricaDepartment of Mathematical Sciences, Mangosuthu University of Technology, P.O. Box 12363, Jacobs, Umlazi 4026, South AfricaWe consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. The effects of thermogeometric fin parameter and the exponent on temperature are studied. Also, the fin efficiency is analyzed.http://dx.doi.org/10.1155/2012/671548 |
| spellingShingle | R. J. Moitsheki M. D. Mhlongo Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem Journal of Applied Mathematics |
| title | Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem |
| title_full | Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem |
| title_fullStr | Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem |
| title_full_unstemmed | Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem |
| title_short | Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem |
| title_sort | classical lie point symmetry analysis of a steady nonlinear one dimensional fin problem |
| url | http://dx.doi.org/10.1155/2012/671548 |
| work_keys_str_mv | AT rjmoitsheki classicalliepointsymmetryanalysisofasteadynonlinearonedimensionalfinproblem AT mdmhlongo classicalliepointsymmetryanalysisofasteadynonlinearonedimensionalfinproblem |