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An optimal homotopy asymptotic approach applied to nonlinear MHD Jeffery-Hamel flow. (English) Zbl 1235.76110

Summary: A simple and effective procedure is employed to propose a new analytic approximate solution for nonlinear MHD Jeffery-Hamel flow. This technique called the Optimal Homotopy Asymptotic Method (OHAM) does not depend upon any small/large parameters and provides us with a convenient way to control the convergence of the solution. The examples given in this paper lead to the conclusion that the accuracy of the obtained results is growing along with increasing the number of constants in the auxiliary function, which are determined using a computer technique.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76W05 Magnetohydrodynamics and electrohydrodynamics
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[1] G. B. Jeffery, “The two-dimensional steady motion of a viscous fluid,” Philosophical Magazine, vol. 6, no. 20, pp. 455-465, 1915. · JFM 45.1088.01
[2] G. Hamel, “Spiralförmige bewegungen zäher flussigkeiten,” Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 25, pp. 34-60, 1916. · JFM 46.1255.01
[3] M. Esmaeilpour and D. D. Ganji, “Solution of the Jeffery-Hamel flow problem by optimal homotopy asymptotic method,” Computers & Mathematics with Applications, vol. 59, no. 11, pp. 3405-3411, 2010. · Zbl 1197.76043
[4] A. A. Joneidi, G. Domairy, and M. Babaelahi, “Three analytical method applied to Jeffery-Hamel flow,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 11, pp. 3423-3434, 2010.
[5] S. M. Moghimi, D. D. Ganji, H. Bararnia, M. Hosseini, and M. Jalaal, “Homotopy perturbation method for nonlinear MHD Jeffery-Hamel problem,” Computers & Mathematics with Applications, vol. 61, no. 8, pp. 2213-2216, 2011. · Zbl 1219.76038
[6] R. Sadri, Channel entrance flow, Ph.D. thesis, Department Mechanical Engineering, University of Western Ontario, 1997.
[7] I. J. Sobey and P. G. Drazin, “Bifurcations of two-dimensional channel flows,” Journal of Fluid Mechanics, vol. 171, pp. 263-287, 1986. · Zbl 0609.76050
[8] W. I. Axford, “The magnetohydrodynamic Jeffrey-Hamel problem for a weakly conducting fluid,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 14, pp. 335-351, 1961. · Zbl 0106.40801
[9] G. Domairry and A. Aziz, “Approximate analysis of MHD squeeze flow between two parallel disks with suction or injection by homotopy perturbation method,” Mathematical Problems in Engineering, vol. 2009, Article ID 603916, 19 pages, 2009. · Zbl 1245.76100
[10] V. Marinca, N. Heri\csanu, and I. Neme\cs, “Optimal homotopy asymptotic method with application to thin film flow,” Central European Journal of Physics, vol. 6, pp. 648-653, 2008.
[11] V. Marinca, N. Heri\csanu, C. Bota, and B. Marinca, “An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate,” Applied Mathematics Letters, vol. 22, no. 2, pp. 245-251, 2009. · Zbl 1163.76318
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