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Homotopy perturbation method for nonlinear MHD Jeffery-Hamel problem. (English) Zbl 1219.76038
Summary: The article solves the Jeffery-Hamel flow using the homotopy perturbation method, an explicit analytical solution is obtained, and the effect of external magnetic field is studied.

76M25Other numerical methods (fluid mechanics)
76W05Magnetohydrodynamics and electrohydrodynamics
65N99Numerical methods for BVP of PDE
35Q35PDEs in connection with fluid mechanics
76D05Navier-Stokes equations (fluid dynamics)
Full Text: DOI
[1] Jeffery, G. B.: The two-dimensional steady motion of a viscous fluid, Phil. mag. 6, 455-465 (1915) · Zbl 45.1088.01
[2] Hamel, G.: Spiralförmige bewgungen zäher flüssigkeiten, Jahresber. deutsch. Math. -verein. 25, 34-60 (1916) · Zbl 46.1255.01
[3] Rosenhead, L.: The steady two-dimensional radial flow of viscous fluid between two inclined plane walls, Proc. R. Soc. A 175, 436-467 (1940) · Zbl 0025.37501 · doi:10.1098/rspa.1940.0068
[4] Batchelor, K.: An introduction to fluid dynamics, (1967) · Zbl 0152.44402
[5] Reza M. Sadri, Channel entrance flow, Ph.D. Thesis, Department of Mechanical Engineering, The University of Western Ontario, 1997.
[6] Axford, W. I.: The magnetohydrodynamic Jeffrey--Hamel problem for a weakly conducting fluid, Q. J. Mech. appl. Math. 14, 335-351 (1961) · Zbl 0106.40801 · doi:10.1093/qjmam/14.3.335
[7] He, J. H.: Homotopy perturbation technique, J. comput. Methods appl. Mech. engrg. 17, No. 8, 257-262 (1999) · Zbl 0956.70017
[8] Ganji, D. D.: The application of he’s homotopy perturbation method to nonlinear equations arising in heat transfer, Phys. lett. A 355, 337-341 (2006) · Zbl 1255.80026
[9] Schlichting, Hermann: Boundary-layer theory, (2000) · Zbl 0940.76003