General exact solution of the fin problem with the power law temperature-dependent thermal conductivity

被引：10

作者：

Kader, Abass H. Abdel ^{[1
]}

Latif, Mohamed S. Abdel ^{[1
]}

Nour, Hamed M. ^{[1
]}

机构：

[1] Mansoura Univ, Fac Engn, Math & Engn Phys Dept, Mansoura 35516, Egypt

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2016年 / 39卷 / 06期

关键词：

fin efficiency; heat transfer; exact solution; thermal conductivity; lie point symmetry;

D O I：

10.1002/mma.3585

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 . Copyright (c) 2015 John Wiley & Sons, Ltd.

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页码：1513 / 1521

页数：9

相关论文

共 11 条

[1]

[Anonymous], 2010, Handbook of Mathematical Functions

[2] 2-DIMENSIONAL PERFORMANCE OF CONVECTING-RADIATING FINS OF DIFFERENT PROFILE SHAPES [J].

AZIZ, A ;

NGUYEN, H .

WARME UND STOFFUBERTRAGUNG-THERMO AND FLUID DYNAMICS, 1993, 28 (08) :481-487

[3]

Baumann G., 2000, Symmetry analysis of differential equations with Mathematica

[4]

Cengel YA, 2014, Heat and mass transfer: fundamentals & applications

[5] A decomposition solution for fins with temperature dependent surface heat flux [J].

Chang, MH .

INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2005, 48 (09) :1819-1824

[6]

Hydon P.E., 2000, Symmetry methods for differential equations. A beginner's guide

[7] A series solution of the non-linear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient [J].

Kim, Sin ;

Huang, Cheng-Hung .

JOURNAL OF PHYSICS D-APPLIED PHYSICS, 2007, 40 (09) :2979-2987

[8] Transient response of longitudinal rectangular fins to step change in base temperature and in base heat flow conditions [J].

Mhlongo, M. D. ;

Moitsheki, R. J. ;

Makinde, O. D. .

INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2013, 57 (01) :117-125

[9] Some exact solutions of the fin problem with a power law temperature-dependent thermal conductivity [J].

Moitsheki, R. J. ;

Hayat, T. ;

Malik, M. Y. .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (05) :3287-3294

[10] Approximate solution of the nonlinear heat transfer equation of a fin with the power-law temperature-dependent thermal conductivity and heat transfer coefficient [J].

Mosayebidorcheh, Sobhan ;

Ganji, D. D. ;

Farzinpoor, Asoud .

PROPULSION AND POWER RESEARCH, 2014, 3 (01) :41-47