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General exact solution of the fin problem with the power law temperature‐dependent thermal conductivity
Author(s) -
Abdel Kader Abass H.,
Abdel Latif Mohamed S.,
Nour Hamed M.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3585
Subject(s) - fin , mathematics , heat transfer , thermal conductivity , ordinary differential equation , annular fin , constant (computer programming) , thermodynamics , nonlinear system , mathematical analysis , heat transfer coefficient , differential equation , materials science , physics , composite material , quantum mechanics , computer science , programming language
In this paper, the general exact implicit solution of the second‐order nonlinear ordinary differential equation governing heat transfer in rectangular fin is obtained using Lie point symmetry method. General relationship among the fin efficiency, the rate of heat transfer from the entire fin, the fin effectiveness, and the thermo‐geometric fin parameter is obtained for any value of the mode of heat transfer n and the constant β . Copyright © 2015 John Wiley & Sons, Ltd.