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Solution of the MHD Falkner-Skan flow by homotopy analysis method. (English) Zbl 1221.76133
Summary: An analysis is performed to find the series solution of the boundary layer Falkner-Skan equation for wedge. The boundary layer similarity equation takes into account a special form of the chosen magnetic field. The results are obtained by solving the nonlinear differential system by homotopy analysis method (HAM). Numerical solution for the skin friction coefficient is also tabulated and compared with HAM.

76M25Other numerical methods (fluid mechanics)
76W05Magnetohydrodynamics and electrohydrodynamics
76D10Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids)
Full Text: DOI
[1] Schlichting, H.: Boundary layer theory, (1979) · Zbl 0434.76027
[2] Alizadeh, E.; Farhadi, M.; Sedighi, K.; Kebria, H. R. E.; Ghafourian, A.: Solution of the Falkner-Skan equation for wedge by Adomian decomposition method, Commun nonlinear sci numer simulat 14, 724733 (2009) · Zbl 1221.76136 · doi:10.1016/j.cnsns.2007.11.002
[3] Sutton, G. W.; Sherman, A.: Engineering magnetohydrodynamics, (1965)
[4] Liao, S. J.; Campo, A.: Analytic solutions of the temperature distribution in Blasius viscous flow problems, J fluid mech 453, 411-425 (2002) · Zbl 1007.76014 · doi:10.1017/S0022112001007169
[5] Liao, S. J.: Beyond perturbation: introduction to the homotopy analysis method, (2003)
[6] Liao, S. J.; Tan, Y.: A general approach to obtain series solutions of nonlinear differential equations, Stud appl math 119, 254-297 (2007)
[7] Liao, S. J.: Notes on the homotopy analysis method: some definitions and theorems, Commun nonlinear sci numer simulat 14, 983-997 (2009) · Zbl 1221.65126 · doi:10.1016/j.cnsns.2008.04.013
[8] Abbasbandy, S.; Zakaria, F. Samadian: Soliton solutions for the fifth-order KdV equation with the homotopy analysis method, Nonlinear dynam 51, 83-87 (2008) · Zbl 1170.76317 · doi:10.1007/s11071-006-9193-y
[9] Abbasbandy, S.: Homotopy analysis method for generalized benjamin -- bona -- Mahony equation, Z angew math phys (ZAMP) 59, 51-62 (2008) · Zbl 1139.35325 · doi:10.1007/s00033-007-6115-x
[10] Abbasbandy, S.; Parkes, E. J.: Solitary smooth hump solutions of the Camassa -- Holm equation by means of the homotopy analysis method, Chaos, solitons & fractals 36, 581-591 (2008) · Zbl 1139.76013 · doi:10.1016/j.chaos.2007.10.034
[11] Hayat, T.; Javed, T.; Sajid, M.: Analytic solution for rotating flow and heat transfer analysis of a third-grade fluid, Acta mech 191, 219-229 (2007) · Zbl 1117.76069 · doi:10.1007/s00707-007-0451-y
[12] Hayat, T.; Khan, M.; Sajid, M.; Asghar, S.: Rotating flow of a third grade fluid in a porous space with Hall current, Nonlinear dynam 49, 83-91 (2007) · Zbl 1181.76149 · doi:10.1007/s11071-006-9105-1
[13] Hayat, T.; Sajid, M.: On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder, Phys lett A 361, 316-322 (2007) · Zbl 1170.76307 · doi:10.1016/j.physleta.2006.09.060
[14] Hayat, T.; Sajid, M.: Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet, Int J heat mass transfer 50, 75-84 (2007) · Zbl 1104.80006 · doi:10.1016/j.ijheatmasstransfer.2006.06.045
[15] Hayat, T.; Abbas, Z.; Sajid, M.; Asghar, S.: The influence of thermal radiation on MHD flow of a second grade fluid, Int J heat mass transfer 50, 931-941 (2007) · Zbl 1124.80325 · doi:10.1016/j.ijheatmasstransfer.2006.08.014
[16] Hayat, T.; Sajid, M.: Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid, Int J eng sci 45, 393-401 (2007) · Zbl 1213.76137 · doi:10.1016/j.ijengsci.2007.04.009
[17] Xu, H.; Liao, S. J.: Dual solutions of boundary layer flow over an upstream moving plate, Commun nonlinear sci numer simulat 13, 350-358 (2008) · Zbl 1131.35066 · doi:10.1016/j.cnsns.2006.04.008
[18] Asaithambi, N. S.: A numerical method for the solution of the Falkner-Skan equation, Appl math comput 81, 259-264 (1997) · Zbl 0873.76049 · doi:10.1016/S0096-3003(95)00325-8
[19] Na, T. Y.: Computational methods in engineering boundary value problems, (1979) · Zbl 0456.76002
[20] Asaithambi, A.: A second-order finite-difference method for the Falkner-Skan equation, Appl math comput 156, 779-786 (2004) · Zbl 1108.76048 · doi:10.1016/j.amc.2003.06.020
[21] Asaithambi, A.: Solution of the Falkner-Skan equation by recursive evaluation of Taylor coefficients, J comput appl math 176, 203-214 (2005) · Zbl 1063.65065 · doi:10.1016/j.cam.2004.07.013
[22] Chiam, T. C.: Hydromagnetic flow over a surface stretching with a power-law velocity, Int J eng sci 33, 429-435 (1995) · Zbl 0899.76375 · doi:10.1016/0020-7225(94)00066-S