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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2006, 11(1), 25-30; https://doi.org/10.3390/mca11010025

A Similarity Solution of Fin Equation with Variable Thermal Conductivity and Heat Transfer Coefficient

1
Department of Mechanical Engineering, Celal Bayar University, 45140 Muradiye, Manisa, Turkey
2
Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
*
Author to whom correspondence should be addressed.
Published: 1 April 2006
PDF [135 KB, uploaded 30 March 2016]

Abstract

A nonlinear fin equation in which thermal conductivity is an arbitrary function of temperature and, heat transfer coefficient is an arbitrary function of spatial variable is considered. Scaling transformation is applied to the equations to determine the specific forms of these functions for which the equation admits such type of transformation. It is found that for arbitrary heat conduction function, scaling transformation exists for an inverse square heat transfer coefficient. Selecting also the conductivity as an exponential function, the partial differential equation is transferred to an ordinary differential equation via similarity transformations. The resulting equation is solved numerically and temperature distribution is determined for various heat conductivity parameters.
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Pakdemirli, M.; Şahin, A.Z. A Similarity Solution of Fin Equation with Variable Thermal Conductivity and Heat Transfer Coefficient. Math. Comput. Appl. 2006, 11, 25-30.

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