Analysis of Convective Straight and Radial Fins with Temperature-Dependent Thermal Conductivity Using Variational Iteration Method with Comparison with Respect to Finite Element Analysis

Coşkun, Safa Bozkurt; Atay, Mehmet Tarik

doi:https://doi.org/10.1155/2007/42072

Mathematical Problems in Engineering

On this page

Abstract References Copyright Related Articles

Research Article | Open Access

Volume 2007 | Article ID 042072 | https://doi.org/10.1155/2007/42072

Analysis of Convective Straight and Radial Fins with Temperature-Dependent Thermal Conductivity Using Variational Iteration Method with Comparison with Respect to Finite Element Analysis

Safa Bozkurt Coşkun¹and Mehmet Tarik Atay²

Academic Editor: Josef Malek

Received13 Dec 2006

Revised11 Apr 2007

Accepted22 Sept 2007

Published31 Dec 2007

Abstract

In order to enhance heat transfer between primary surface and the environment, radiating extended surfaces are commonly utilized. Especially in the case of large temperature differences, variable thermal conductivity has a strong effect on performance of such a surface. In this paper, variational iteration method is used to analyze convective straight and radial fins with temperature-dependent thermal conductivity. In order to show the efficiency of variational iteration method (VIM), the results obtained from VIM analysis are compared with previously obtained results using Adomian decomposition method (ADM) and the results from finite element analysis. VIM produces analytical expressions for the solution of nonlinear differential equations. However, these expressions obtained from VIM must be tested with respect to the results obtained from a reliable numerical method or analytical solution. This work assures that VIM is a promising method for the analysis of convective straight and radial fin problems.

References

J. G. Bartas and W. H. Sellers, “Radiation fin effectiveness,” Journal of Heat Transfer, Series C, vol. 82, pp. 73–75, 1960.
View at: Google Scholar
J. E. Wilkins Jr., “Minimizing the mass of thin radiating fins,” Journal of Aerospace Science, vol. 27, p. 145, 1960.
View at: Google Scholar
B. V. Karlekar and B. T. Chao, “Mass minimization of radiating trapezoidal fins with negligible base cylinder interaction,” International Journal of Heat and Mass Transfer, vol. 6, no. 1, pp. 33–48, 1963.
View at: Publisher Site | Google Scholar
R. D. Cockfield, “Structural optimization of a space radiator,” Journal of Spacecraft Rockets, vol. 5, no. 10, p. 1240, 1968.
View at: Google Scholar
H. Keil, “Optimization of a central-fin space radiator,” Journal of Spacecraft Rockets, vol. 5, no. 4, p. 463, 1968.
View at: Google Scholar
B. T. F. Chung and B. X. Zhang, “Optimization of radiating fin array including mutual irradiations between radiator elements,” ASME Journal of Heat Transfer, vol. 113, p. 814, 1991.
View at: Google Scholar
C. K. Krishnaprakas and K. B. Narayana, “Heat transfer analysis of mutually irradiating fins,” International Journal of Heat and Mass Transfer, vol. 46, p. 761, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH
R. J. Naumann, “Optimizing the design of space radiators,” International Journal of Thermophys, vol. 25, no. 6, pp. 1929–1941, 2004.
View at: Publisher Site | Google Scholar
C. H. Chiu and C. K. Chen, “A decomposition method for solving the convective longitudinal fins with variable thermal conductivity,” International Journal of Heat and Mass Transfer, vol. 45, no. 10, pp. 2067–2075, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH
C. H. Chiu and C. K. Chen, “Applications of adomian's decomposition procedure to the analysis of convective-radiative fins,” Journal of Heat Transfer, vol. 125, no. 2, pp. 312–316, 2003.
View at: Publisher Site | Google Scholar
D. Lesnic and P. J. Heggs, “A decomposition method for power-law fin-type problems,” International Communications in Heat and Mass Transfer, vol. 31, no. 5, pp. 673–682, 2004.
View at: Publisher Site | Google Scholar
C. Arslantürk, “Optimum design of space radiators with temperature-dependent thermal conductivity,” Applied Thermal Engineering, vol. 26, no. 11-12, pp. 1149–1157, 2006.
View at: Google Scholar
A. Aziz and S. M. E. Hug, “Perturbation solution for convecting fin with variable thermal conductivity,” Journal of Heat Transfer, vol. 97, p. 300, 1975.
View at: Google Scholar
L. T. Yu and C. K. Chen, “Optimization of circular fins with variable thermal parameters,” Journal of the Franklin Institute, vol. 336, no. 1, pp. 77–95, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH
P. Razelos and K. Imre, “The optimum dimensions of circular fins with variable thermal parameters,” Journal of Heat Transfer, vol. 102, p. 420, 1980.
View at: Google Scholar
K. Laor and H. Kalman, “Performance and optimum dimensions of different cooling fins with a temperature-dependent heat transfer coefficient,” International Journal of Heat and Mass Transfer, vol. 39, no. 9, pp. 1993–2003, 1996.
View at: Publisher Site | Google Scholar
C. Arslantürk, “A decomposition method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity,” International Communications in Heat and Mass Transfer, vol. 32, no. 6, pp. 831–841, 2005.
View at: Google Scholar
D. Lesnic and L. Elliott, “The decomposition approach to inverse heat conduction,” Journal of Mathematical Analysis and Applications, vol. 232, no. 1, pp. 82–98, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
D. Lesnic, “Convergence of adomian's decomposition method: periodic temperatures,” Computers & Mathematics with Applications, vol. 44, no. 1-2, pp. 13–24, 2002.
View at: Publisher Site | Google Scholar | MathSciNet
D. Lesnic and P. J. Heggs, “A decomposition method for power-law fin-type problems,” International Communications in Heat and Mass Transfer, vol. 31, no. 5, pp. 673–682, 2004.
View at: Publisher Site | Google Scholar
C. H. Chiu and C. K. Chen, “A decomposition method for solving the convective longitudinal fins with variable thermal conductivity,” International Journal of Heat and Mass Transfer, vol. 45, no. 10, pp. 2067–2075, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH
C. H. Chiu and C. K. Chen, “Application of the decomposition method to thermal stresses in isotropic circular fins with temperature-dependent thermal conductivity,” Acta Mechanica, vol. 157, no. 1–4, pp. 147–158, 2002.
View at: Google Scholar
G. Adomian, Solving Frontier Problems in Physics: The Decomposition Method, Kluwer Academic, Dordrecht, The Netherlands, 1988.
View at: Google Scholar
J. H. He, “Variational iteration method—a kind of non-linear analytical technique: some examples,” International Journal of Nonlinear Mechanics, vol. 34, no. 4, pp. 699–708, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH
M. A. Abdou and A. A. Soliman, “New applications of variational iteration method,” Physica D, vol. 211, no. 1-2, pp. 1–8, 2005.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
S. Momani and Z. Odibat, “Analytical approach to linear fractional partial differential equations arising in fluid mechanics,” Physics Letter A., vol. 355, no. 4-5, pp. 271–279, 2006.
View at: Publisher Site | Google Scholar
S. Momani, S. Abuasad, and Z. Odibat, “Variational iteration method for solving nonlinear boundary value problems,” Applied Mathematics and Computation, vol. 183, no. 2, pp. 1351–1358, 2006.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
N. H. Sweilam and M. M. Khader, “Variational iteration method for one dimensional nonlinear thermoelasticity,” Chaos, Solitons and Fractals, vol. 32, no. 1, pp. 145–149, 2007.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
E. M. Abulwafa, M. A. Abdou, and A. A. Mahmoud, “Nonlinear fluid flows in pipe-like domain problem using variational-iteration method,” Chaos, Solitons and Fractals, vol. 32, no. 4, pp. 1384–1397, 2007.
View at: Publisher Site | Google Scholar | MathSciNet
S. -Q. Wang and J.-H. He, “Variational iteration method for solving integrodifferential equations,” Physics Letter A, 2007.
View at: Google Scholar

Copyright

Copyright © 2007 Safa Bozkurt Coşkun and Mehmet Tarik Atay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation Order printed copies

Views

541

Downloads

1328

Citations