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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.
MSC:
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)
References:
[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)
[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)
[9]Schlichting, Hermann: Boundary-layer theory, (2000)