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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 671548, 13 pages
http://dx.doi.org/10.1155/2012/671548
Research Article

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

1Center for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa
2Department of Mathematical Sciences, Mangosuthu University of Technology, P.O. Box 12363, Jacobs, Umlazi 4026, South Africa

Received 23 August 2011; Accepted 12 October 2011

Academic Editor: Jacek Rokicki

Copyright © 2012 R. J. Moitsheki and M. D. Mhlongo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. D. Kraus, A. Aziz, and J. Welte, Extended Surface Heat Transfer, John Wiley & Sons, New York, NY, USA, 2001.
  2. F. Khani, M. A. Raji, and H. H. Nejad, “Analytical solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 8, pp. 3327–3338, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. F. Khani, M. A. Raji, and S. Hamedi-Nezhad, “A series solution of the fin problem with a temperature-dependent thermal conductivity,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 7, pp. 3007–3017, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. S. Kim and C. H. Huang, “A series solution of the non-linear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient,” Journal of Physics D, vol. 40, no. 9, pp. 2979–2987, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. R. J. Moitsheki, T. Hayat, and M. Y. Malik, “Some exact solutions of the fin problem with a power law temperature-dependent thermal conductivity,” Nonlinear Analysis, vol. 11, no. 5, pp. 3287–3294, 2010. View at Publisher · View at Google Scholar
  6. A. H. Bokhari, A. H. Kara, and F. D. Zaman, “A note on a symmetry analysis and exact solutions of a nonlinear fin equation,” Applied Mathematics Letters, vol. 19, no. 12, pp. 1356–1360, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. M. Pakdemirli and A. Z. Sahin, “Group classification of fin equation with variable thermal properties,” International Journal of Engineering Science, vol. 42, no. 17-18, pp. 1875–1889, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. M. Pakdemirli and A. Z. Sahin, “Similarity analysis of a nonlinear fin equation,” Applied Mathematics Letters, vol. 19, no. 4, pp. 378–384, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. O. O. Vaneeva, A. G. Johnpillai, R. O. Popovych, and C. Sophocleous, “Group analysis of nonlinear fin equations,” Applied Mathematics Letters, vol. 21, no. 3, pp. 248–253, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. R. O. Popovych, C. Sophocleous, and O. O. Vaneeva, “Exact solutions of a remarkable fin equation,” Applied Mathematics Letters, vol. 21, no. 3, pp. 209–214, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. R. J. Moitsheki, “Steady heat transfer through a radial fin with rectangular and hyperbolic profiles,” Nonlinear Analysis, vol. 12, no. 2, pp. 867–874, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. S. Kim, J.-H. Moon, and C.-H. Huang, “An approximate solution of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient,” Journal of Physics D, vol. 40, no. 14, pp. 4382–4389, 2007. View at Publisher · View at Google Scholar
  13. P. J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, NY, USA, 1986.
  14. G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer, New York, NY, USA, 1989.
  15. H. Stephani, Differential Equations: Their Solution Using Symmetries, Cambridge University Press, Cambridge, UK, 1989.
  16. N. H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differential Equations, John Wiley & Sons, New York, NY, USA, 1999.
  17. G. W. Bluman and S. C. Anco, Symmetry and Integration Methods for Differential Equations, Springer, New York, NY, USA, 2002.
  18. G. W. Bluman, A. F. Cheviakov, and S. C. Anco, Applications of Symmetry Methods to Partial Differential Equations, Springer, New York, NY, USA, 2010.
  19. A. C. Hearn, “Reduce user’s manual version 3.4,” Rand Publication CP78, The Rand Cooporation, Santa Monica, Calif, USA, 1985. View at Google Scholar
  20. N. H. Ibragimov, M. Torrisi, and A. Valenti, “Preliminary group classification of equations vtt=f(x,vx)vxx+g(x,vx),” Journal of Mathematical Physics, vol. 32, no. 11, pp. 2988–2995, 1991. View at Publisher · View at Google Scholar
  21. F. M. Mahomed, “Symmetry group classification of ordinary differential equations: survey of some results,” Mathematical Methods in the Applied Sciences, vol. 30, no. 16, pp. 1995–2012, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. R. H. Yeh and S. P. Liaw, “An exact solution for thermal characteristics of fins with power-law heat transfer coefficient,” International Communications in Heat and Mass Transfer, vol. 17, no. 3, pp. 317–330, 1990. View at Publisher · View at Google Scholar
  23. R. J. Moitsheki and C. Harley, “Transient heat transfer in longitudinal fins of various profiles with temperature-dependent thermal conductivity and heat transfer coefficient,” Pramana, vol. 77, no. 3, pp. 519–532, 2011. View at Publisher · View at Google Scholar