Exact, analytic temperature distributions of pin fins with constant thermal conductivity and power-law type heat transfer coefficient

Elyas Shivanian,

Elyas Shivanian

orcid.org/0000-0001-9383-6779

Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818 Iran

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Antonio Campo,

Antonio Campo

Department of Mechanical Engineering, The University of Vermont Burlington, VT, 05405 USA

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Elyas Shivanian,

Elyas Shivanian

orcid.org/0000-0001-9383-6779

Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818 Iran

Search for more papers by this author

Antonio Campo,

Antonio Campo

Department of Mechanical Engineering, The University of Vermont Burlington, VT, 05405 USA

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First published: 17 May 2017

https://doi.org/10.1002/htj.21289

Citations: 3

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Abstract

In this Technical Note, the problem of determining the temperature distribution in a pin fin with power-law heat transfer coefficients is addressed. It is demonstrated that the governing fin equation, a nonlinear second-order differential equation, is exactly solvable for the entire range of the exponent n in the power-law heat transfer coefficients. The exact, closed-form analytical solutions in implicit form are convenient for physical interpretation and optimization for maximum heat transfer. Furthermore, it is proved that the exact solutions have three different structures: (1) dual in the range of $urn:x-wiley:10992871:media:htj21289:htj21289-math-0001$ , (2) unique or dual in the range of $urn:x-wiley:10992871:media:htj21289:htj21289-math-0002$ , and (3) unique in the range of $urn:x-wiley:10992871:media:htj21289:htj21289-math-0003$ . Additionally, exact analytical expressions for the fin efficiency and the fin effectiveness are provided, both as a function of the dimensionless fin parameter for the gamma of n under study.

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Volume47, Issue1

January 2018

Pages 42-53

Exact, analytic temperature distributions of pin fins with constant thermal conductivity and power-law type heat transfer coefficient

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Exact, analytic temperature distributions of pin fins with constant thermal conductivity and power-law type heat transfer coefficient

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