Journal of Applied Mathematics

Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem

R. J. Moitsheki and M. D. Mhlongo

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 671548, 13 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495019

Digital Object Identifier
doi:10.1155/2012/671548

Mathematical Reviews number (MathSciNet)
MR2872355

Zentralblatt MATH identifier
1234.35277

Citation

Moitsheki, R. J.; Mhlongo, M. D. Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem. J. Appl. Math. 2012 (2012), Article ID 671548, 13 pages. doi:10.1155/2012/671548. https://projecteuclid.org/euclid.jam/1355495019


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