In the current paper, the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient is revisited. In this problem, it has been assumed that the heat transfer coefficient is expressed in a power-law form and the thermal conductivity is a linear function of temperature. It is shown that its governing nonlinear differential equation is exactly solvable. A full discussion and exact analytical solution in the implicit form are given for further physical interpretation and it is proved that three possible cases may occur: there is no solution to the problem, the solution is unique, and the solutions are dual depending on the values of the parameters of the model. Furthermore, we give exact analytical expressions of fin efficiency as a function of thermogeometric fin parameter.
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November 2016
This article was originally published in
Journal of Heat Transfer
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Exact Closed-Form Solution of the Nonlinear Fin Problem With Temperature-Dependent Thermal Conductivity and Heat Transfer Coefficient
Mahdi Anbarloei,
Mahdi Anbarloei
Department of Mathematics,
Imam Khomeini International University,
Qazvin 34149-16818, Iran
e-mail: m.anbarloei@sci.ikiu.ac.ir
Imam Khomeini International University,
Qazvin 34149-16818, Iran
e-mail: m.anbarloei@sci.ikiu.ac.ir
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Elyas Shivanian
Elyas Shivanian
Department of Mathematics,
Imam Khomeini International University,
Qazvin 34149-16818, Iran
e-mail: shivanian@sci.ikiu.ac.ir
Imam Khomeini International University,
Qazvin 34149-16818, Iran
e-mail: shivanian@sci.ikiu.ac.ir
Search for other works by this author on:
Mahdi Anbarloei
Department of Mathematics,
Imam Khomeini International University,
Qazvin 34149-16818, Iran
e-mail: m.anbarloei@sci.ikiu.ac.ir
Imam Khomeini International University,
Qazvin 34149-16818, Iran
e-mail: m.anbarloei@sci.ikiu.ac.ir
Elyas Shivanian
Department of Mathematics,
Imam Khomeini International University,
Qazvin 34149-16818, Iran
e-mail: shivanian@sci.ikiu.ac.ir
Imam Khomeini International University,
Qazvin 34149-16818, Iran
e-mail: shivanian@sci.ikiu.ac.ir
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 12, 2015; final manuscript received May 26, 2016; published online June 28, 2016. Assoc. Editor: Alan McGaughey.
J. Heat Transfer. Nov 2016, 138(11): 114501 (6 pages)
Published Online: June 28, 2016
Article history
Received:
November 12, 2015
Revised:
May 26, 2016
Citation
Anbarloei, M., and Shivanian, E. (June 28, 2016). "Exact Closed-Form Solution of the Nonlinear Fin Problem With Temperature-Dependent Thermal Conductivity and Heat Transfer Coefficient." ASME. J. Heat Transfer. November 2016; 138(11): 114501. https://doi.org/10.1115/1.4033809
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