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Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.5 P.648-653

http://doi.org/10.1631/jzus.A0720024


A numerical analysis to the non-linear fin problem


Author(s):  Rafael CORTELL

Affiliation(s):  Department of Applied Physics, Polytechnic University of Valencia, 46022 Valencia, Spain

Corresponding email(s):   rcortell@fis.upv.es

Key Words:  Fins, Ordinary differential equations (ODEs), Numerical solution, Heat transfer


Rafael CORTELL. A numerical analysis to the non-linear fin problem[J]. Journal of Zhejiang University Science A, 2008, 9(5): 648-653.

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DOI - 10.1631/jzus.A0720024


Abstract: 
In this paper a numerical analysis is carried out to obtain the temperature distribution within a single fin. It is assumed that the heat transfer coefficient depends on the temperature. The complete highly non-linear problem is solved numerically and the variations of both, dimensionless surface temperature and dimensionless surface temperature gradient as well as heat transfer characteristics with the governing non-dimensional parameters of the problem are graphed and tabulated.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Aziz, A., 1977. Perturbation solution for convective fin with internal heat generation and temperature-dependent thermal conductivity. Int. J. Heat Mass Transfer, 20(11):1253-1255.

[2] Chang, C.W., Chang, J.R., Liu, C.S., 2006. The Lie-group shooting method for boundary layer equations in fluid mechanics. J. Hydrodynamics Ser. B, 18(3):103-108.

[3] Chang, M.H., 2005. A decomposition solution for fins with temperature dependent surface heat flux. Int. J. Heat Mass Transfer, 48(9):1819-1824.

[4] Chiu, C.H., Chen, C.K., 1977. A decomposition method for solving the convective longitudinal fins with variable thermal conductivity. Int. J. Heat Mass Transfer, 45(10):2067-2075.

[5] Chowdhury, M.S.H., Hashim, I., 2007. Analytical solutions to heat transfer equations by homotopy-perturbation method revisited. Phys. Lett. A, in press.

[6] Chowdhury, M.S.H., Hashim, I., Abdulaziz, O., 2007. Comparison of homotopy-analysis method and homotopy-perturbation method for purely nonlinear fin-type problems. Communications in Nonlinear Science & Numerical Simulation, in press.

[7] Cortell, R., 1993. Application of the fourth-order Runge-Kutta method for the solution of high-order general initial value problems. Comput. & Struct., 49(5):897-900.

[8] Cortell, R., 1994. Similarity solutions for flow and heat transfer of a viscoelastic fluid over a stretching sheet. Int. J. Non-Linear Mech., 29(2):155-161.

[9] Cortell, R., 1995. Fourth Order Runge-Kutta Method in 1D for High Gradient Problems. In: Topping, B.H.V. (Ed.), Developments in Computational Engineering Mechanics. Civil-Comp. Press, New York, p.121-124.

[10] Cortell, R., 2005a. Flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/absorption and suction/blowing. Fluid Dyn. Research, 37(4):231-245.

[11] Cortell, R., 2005b. Numerical solutions of the classical Blasius flat-plate problem. Appl. Math. Comp., 170(1):706-710.

[12] Cortell, R., 2006a. A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet. Int. J. Non-Linear Mech., 41(1):78-85.

[13] Cortell, R., 2006b. MHD boundary-layer flow and heat transfer of a non-Newtonian power-law fluid past a moving plate with thermal radiation. Nuovo Cimento-B 121(9):951-964.

[14] Cortell, R., 2007a. Viscoelastic fluid flow and heat transfer over a stretching sheet under the effects of a non-uniform heat source, viscous dissipation and thermal radiation. Int. J. Heat Mass Transfer, 50(15-16):3152-3162.

[15] Cortell, R., 2007b. Effects of heat source/sink, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a stretching sheet. Comput. Math. Appl., 53(2):305-316.

[16] Domairry, G., Fazeli, M., 2007. Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature dependent thermal conductivity. Communications in Nonlinear Science & Numerical Simulation, in press.

[17] Fang, T., Guo, F., Lee, C.F., 2006. A note on the extended Blasius equation. Appl. Math. Lett., 19(7):613-617.

[18] Ganji, D.D., 2006. The application of He’s homotopy perturbation method to nonlinear equations arising in heat transfer. Phys. Lett. A, 355(4-5):337-341.

[19] Ganji, D.D., Hosseini, M.J., Shayegh, J., 2007. Some nonlinear heat transfer equations solved by three approximate methods. Int. Comm. Heat Mass Transfer, 34(8):1003-1016.

[20] Hutcheon, I.C., Spalding, D.B., 1958. Prismatic fin non-linear heat loss analysed by resistance network and iterative analogue computer. British Journal of Applied Physics, 9(5):185-190.

[21] Ishak, A., Nazar, R., Pop, I., 2007a. Boundary-layer flow of a micropolar fluid on a continuously moving or fixed permeable surface. Int. J. Heat Mass Transfer, 50(23-24):4743-4748.

[22] Ishak, A., Nazar, R., Pop, I., 2007b. Boundary layer on a moving wall with suction and injection. Chin. Phys. Lett., 24(8):2274-2276.

[23] Kim, S., Huang, C.H., 2006. A series solution of the fin problem with temperature-dependent thermal conductivity. J. Phys. D: Appl. Phys., 39(22):4894-4901.

[24] Kim, S., Huang, C.H., 2007. A series solution of the non-linear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. J. Phys. D: Appl. Phys., 40(9):2979-2987.

[25] Kim, S., Moon, J.H., Huang, C.H., 2007. An approximate solution of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. J. Phys. D: Appl. Phys., 40(14):4382-4389.

[26] Kiwan, S., 2007. Effect of radiative losses on the heat transfer from porous fins. Int. J. Thermal Sci., 46(10):1046-1055.

[27] Lesnic, D., Hegs, P.J., 2004. A decomposition method for power-law fin-type problems. Int. Comm. Heat Mass Transfer, 31(5):673-682.

[28] Liaw, S.P., Yeh, R.H., 1994. Fins with temperature dependent surface heat flux. I. Single heat transfer mode. Int. J. Heat Mass Transfer, 37(10):1509-1515.

[29] Miansari, Mo., Ganji, D.D., Miansari, Me, 2008. Application of He’s variational iteration method to nonlinear heat transfer equations. Phys. Lett. A, 372(6):779-785.

[30] Taigbenu, A.E., Onyejekwe, O.O., 1999. Green’s function-based integral approaches to nonlinear transient boundary value problems (II). Appl. Math. Modelling, 23(3):241-253.

[31] Tari, H, Ganji, D.D., Babazadeh H., 2007. The application of He’s variational iteration method to nonlinear equations arising in heat transfer. Phys. Lett. A, 363(3):213-217.

[32] Yang, I.C., Lee, H.L., Wei, E.J., Lee, J.F., Wu, T.S., 2005. Numerical analysis of two dimensional pin fins with non-constant base heat flux. Energy Conv. Management, 46(6):881-892.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

SERIR@URAER<lserir@uraer.dz>

2010-05-29 06:17:06

I need this paper for my Ph.D thesis

Lazhar SERIR@URAER<lserir@hotmail.com>

2010-05-29 06:13:00

I'm interesting about this paper for my PhD thesis

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