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Transient heat transfer in longitudinal fins of various profiles with temperature-dependent thermal conductivity and heat transfer coefficient

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Abstract

Transient heat transfer through a longitudinal fin of various profiles is studied. The thermal conductivity and heat transfer coefficients are assumed to be temperature dependent. The resulting partial differential equation is highly nonlinear. Classical Lie point symmetry methods are employed and some reductions are performed. Since the governing boundary value problem is not invariant under any Lie point symmetry, we solve the original partial differential equation numerically. The effects of realistic fin parameters such as the thermogeometric fin parameter and the exponent of the heat transfer coefficient on the temperature distribution are studied.

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Authors and Affiliations

  1. Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits, 2050, South Africa

    RASEELO J MOITSHEKI & CHARIS HARLEY

Authors
  1. RASEELO J MOITSHEKI
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  2. CHARIS HARLEY
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Correspondence to RASEELO J MOITSHEKI.

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MOITSHEKI, R.J., HARLEY, C. Transient heat transfer in longitudinal fins of various profiles with temperature-dependent thermal conductivity and heat transfer coefficient. Pramana - J Phys 77, 519–532 (2011). https://doi.org/10.1007/s12043-011-0172-6

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  • DOI: https://doi.org/10.1007/s12043-011-0172-6

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