×

zbMATH — the first resource for mathematics

Analysis of convective straight and radial fins with temperature-dependent thermal conductivity using variational iteration method with comparison with respect to finite element analysis. (English) Zbl 1347.80001
Summary: 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.

MSC:
80A20 Heat and mass transfer, heat flow (MSC2010)
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] J. G. Bartas and W. H. Sellers, “Radiation fin effectiveness,” Journal of Heat Transfer, Series C, vol. 82, pp. 73-75, 1960.
[2] J. E. Wilkins Jr., “Minimizing the mass of thin radiating fins,” Journal of Aerospace Science, vol. 27, p. 145, 1960.
[3] 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. · doi:10.1016/0017-9310(63)90027-9
[4] R. D. Cockfield, “Structural optimization of a space radiator,” Journal of Spacecraft Rockets, vol. 5, no. 10, p. 1240, 1968.
[5] H. Keil, “Optimization of a central-fin space radiator,” Journal of Spacecraft Rockets, vol. 5, no. 4, p. 463, 1968.
[6] 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.
[7] 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. · Zbl 1024.80501 · doi:10.1016/S0017-9310(02)00356-3
[8] R. J. Naumann, “Optimizing the design of space radiators,” International Journal of Thermophys, vol. 25, no. 6, pp. 1929-1941, 2004. · doi:10.1007/s10765-004-7747-0
[9] 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. · Zbl 1011.80011 · doi:10.1016/S0017-9310(01)00286-1
[10] 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. · doi:10.1115/1.1532012
[11] 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. · doi:10.1016/S0735-1933(04)00054-5
[12] C. Arslantürk, “Optimum design of space radiators with temperature-dependent thermal conductivity,” Applied Thermal Engineering, vol. 26, no. 11-12, pp. 1149-1157, 2006.
[13] 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.
[14] 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. · Zbl 1016.80005 · doi:10.1016/S0016-0032(97)00021-5
[15] P. Razelos and K. Imre, “The optimum dimensions of circular fins with variable thermal parameters,” Journal of Heat Transfer, vol. 102, p. 420, 1980.
[16] 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. · doi:10.1016/0017-9310(95)00296-0
[17] 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.
[18] 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. · Zbl 0922.35189 · doi:10.1006/jmaa.1998.6243
[19] D. Lesnic, “Convergence of adomian/s decomposition method: periodic temperatures,” Computers & Mathematics with Applications, vol. 44, no. 1-2, pp. 13-24, 2002. · Zbl 1125.65347 · doi:10.1016/S0898-1221(02)00127-X
[20] 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. · doi:10.1016/S0735-1933(04)00054-5
[21] 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. · Zbl 1011.80011 · doi:10.1016/S0017-9310(01)00286-1
[22] 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. · Zbl 1027.74018 · doi:10.1007/BF01182160
[23] G. Adomian, Solving Frontier Problems in Physics: The Decomposition Method, Kluwer Academic, Dordrecht, The Netherlands, 1988.
[24] 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. · Zbl 1342.34005 · doi:10.1016/S0020-7462(98)00048-1
[25] M. A. Abdou and A. A. Soliman, “New applications of variational iteration method,” Physica D, vol. 211, no. 1-2, pp. 1-8, 2005. · Zbl 1084.35539 · doi:10.1016/j.physd.2005.08.002
[26] 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. · Zbl 1378.76084 · doi:10.1016/j.physleta.2006.02.048
[27] 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. · Zbl 1110.65068 · doi:10.1016/j.amc.2006.05.138
[28] 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. · Zbl 1131.74018 · doi:10.1016/j.chaos.2005.11.028
[29] 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. · Zbl 1128.76019 · doi:10.1016/j.chaos.2005.11.050
[30] S. -Q. Wang and J.-H. He, “Variational iteration method for solving integrodifferential equations,” Physics Letter A, 2007.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.