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Heat Transfer Research

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ISSN Print: 1064-2285
ISSN Online: 2162-6561

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Heat Transfer Research

DOI: 10.1615/HeatTransRes.v38.i5.30
pages 407-415

Analytical Treatment of Fins with Temperature-Dependent Surface Heat Flux Using the Homotopy Perturbation Method and Comparison of Decomposition and Numerical Methods

Davood D. Ganji
Department of Mechanical Engineering, Babol University of Technology, Babol, Iran
http://sciencewatch.com/dr/ne/08decne
M. Mostofi
Department of Mechanical Engineering, Babol University of Technology, Mazandaran University, P.O.Box 484, Babol, Iran
Mojtaba Aghajani Delavar
Faculty of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran
A. Kazemi
Department of Mechanical Engineering, Babol University of Technology, Mazandaran University, P.O.Box 484, Babol, Iran

ABSTRACT

In this paper, the homotopy perturbation method (HPM) is used to solve nonlinear equations of a straight rectangular fin for all possible kinds of heat transfer. The local heat transfer coefficient varies as a power-law function of temperature. The results obtained by HPM have been compared and validated with those of the Adomian decomposition method (ADM) and numerical method. The comparison of HPM, ADM, and numerical methods shows that all of the three obtained solutions are in excellent agreement and illustrates the effectiveness of the method. The solution obtained by HPM gives an explicit expression of temperature distribution as a function of position along the fin. The obtained solution is in the form of an infinite power series that can be truncated to obtain numerical results.