Technical Brief

Optimal Perturbation Iteration Method for Solving Nonlinear Heat Transfer Equations

[+] Author and Article Information
Sinan Deniz

Department of Mathematics,
Faculty of Art and Sciences,
Manisa Celal Bayar University,
Manisa 45140, Turkey
e-mail: sinan.deniz@cbu.edu.tr

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 16, 2016; final manuscript received February 21, 2017; published online April 4, 2017. Assoc. Editor: George S. Dulikravich.

J. Heat Transfer 139(7), 074503 (Apr 04, 2017) (4 pages) Paper No: HT-16-1277; doi: 10.1115/1.4036085 History: Received May 16, 2016; Revised February 21, 2017

In this paper, the new optimal perturbation iteration method (OPIM) is introduced and applied for solving nonlinear differential equations arising in heat transfer. The effectiveness of the proposed method will be tested by considering two specific applications: the temperature distribution equation in a thick rectangular fin radiation to free space and cooling of a lumped system with variable specific heat. Comparing different methods shows that the results obtained by optimal perturbation iteration method are very good agreement with the numerical solutions and perform better than the most existing analytic methods.

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Grahic Jump Location
Fig. 1

Comparison between the results obtained by OPIM (•, ▲) and the numerical results (–) for example 1: (a) OPIA-1 (•) and OPIA-2 (▲) solutions for ε = 1 and (b) OPIA-1 (•) and OPIA-2 (▲) solutions for ε = 2

Grahic Jump Location
Fig. 2

Absolute error of OPIM by third-order approximation and comparison between the results obtained by OPIM and the numerical results (–) for example 2: (a) second (•) and third-order (▲) approximate solutions for ε = 1 and (b) absolute error for ε = 1



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