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Some Exact Solutions of Nonlinear Fin Problem for Steady Heat Transfer in Longitudinal Fin with Different Profiles

Author

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  • M. D. Mhlongo
  • R. J. Moitsheki

Abstract

One‐dimensional steady‐state heat transfer in fins of different profiles is studied. The problem considered satisfies the Dirichlet boundary conditions at one end and the Neumann boundary conditions at the other. The thermal conductivity and heat coefficients are assumed to be temperature dependent, which makes the resulting differential equation highly nonlinear. Classical Lie point symmetry methods are employed, and some reductions are performed. Some invariant solutions are constructed. The effects of thermogeometric fin parameter, the exponent on temperature, and the fin efficiency are studied.

Suggested Citation

  • M. D. Mhlongo & R. J. Moitsheki, 2014. "Some Exact Solutions of Nonlinear Fin Problem for Steady Heat Transfer in Longitudinal Fin with Different Profiles," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlamp:v:2014:y:2014:i:1:n:947160
    DOI: 10.1155/2014/947160
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    References listed on IDEAS

    as
    1. R. J. Moitsheki & M. D. Mhlongo, 2012. "Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, January.
    2. R. J. Moitsheki & M. D. Mhlongo, 2012. "Classical Lie Point Symmetry Analysis of a Steady Nonlinear One‐Dimensional Fin Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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