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On the similarity solutions for a steady MHD equation. (English) Zbl 1221.76222
Summary: We investigate the similarity solutions for the steady laminar incompressible boundary layer equations governing the magnetohydrodynamic (MHD) flow near the forward stagnation point of two-dimensional and axisymmetric bodies. This leads to the study of a boundary value problem involving a third order autonomous ordinary differential equation. Our main results are the existence, uniqueness and non-existence for concave or convex solutions.

MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
34B40 Boundary value problems on infinite intervals for ordinary differential equations
76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
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[1] Wu, Y.K., Magnetohydrodynamic boundary layer control with suction or injection, J appl phys, 44, 2166-2171, (1973)
[2] Takhar, H.S.; Raptis, A.A.; Perdikis, A.A., MHD asymmetric flow past a semi-infinite moving plate, Acta mech, 65, 278-290, (1987)
[3] Vajravelu, K.; Rollins, D., Hydromagnetic flow in a oscillating channel, J math phys sci, 31, 11-24, (1997) · Zbl 1059.76549
[4] Muhapatra, T.R.; Gupta, A.S., Magnetohydrodynamic stagnation-point flow towards a stretching sheet, Acta mech, 152, 191-196, (2001) · Zbl 0992.76099
[5] Chakrabarti, A.; Gupta, A.S., Hydromagnetic flow and heat transfer over a stretching sheet, Q appl maths, 37, 73-78, (1979) · Zbl 0402.76012
[6] Kumari, M.; Nath, G., Conjugate MHD flow past a flat plate, Acta mech, 106, 215-220, (1994) · Zbl 0847.76096
[7] Pop, I.; Na, T.-Y., A note of MHD flow over a stretching permeable surface, Mech res commun, 25, 263-269, (1998) · Zbl 0979.76097
[8] Takhar, H.S.; Ali, M.A.; Gupta, A.S., Stability of magnetohydrodynamic flow over a stretching sheet, (), 465-471
[9] Falkner, V.M.; Skan, S.W., Solutions of the boundary layer equations, Phil mag, 12, 865-896, (1931) · Zbl 0003.17401
[10] Coppel, W.A., On a differential equation of boundary layer theory, Phil trans roy soc London ser A, 253, 101-136, (1960) · Zbl 0093.19105
[11] Aly, E.H.; Elliott, L.; Ingham, D.B., Mixed convection boundary-layer flow over a vertical surface embedded in a porous medium, Eur J mech B fluids, 22, 529-543, (2003) · Zbl 1033.76055
[12] Brighi, B.; Hoernel, J.-D., On the concave and convex solution of mixed convection boundary layer approximation in a porous medium, Appl math lett, 19, 69-74, (2006) · Zbl 1125.34005
[13] Kumari, M.; Takhar, H.S.; Nath, G., Mixed convection flow over a vertical wedge embedded in a highly porous medium, Heat mass transfer, 37, 139-146, (2000)
[14] Blasius, H., Grenzchichten in flussigkeiten mit kleiner reibung, Z math phys, 56, 1-37, (1908) · JFM 39.0803.02
[15] Belhachmi, Z.; Brighi, B.; Taous, K., On the concave solutions of the Blasius equation, Acta math univ Comenian, 69, 2, 199-214, (2000) · Zbl 0972.34015
[16] Brighi B, Fruchard A, Sari T. On the Blasius problem, Preprint. · Zbl 1158.34016
[17] Utz, W.R., Existence of solutions of a generalized Blasius equation, J math anal appl, 66, 55-59, (1978) · Zbl 0393.34013
[18] Brighi B, Hoernel J-D. On a general similarity boundary layer equation. Submitted for publication. · Zbl 1164.34006
[19] Lawrence, P.S.; Rao, B.N., Effect of pressure gradient on MHD boundary layer over a flat plate, Acta mech, 113, 1-7, (1995) · Zbl 0859.76083
[20] Shercliff, J.A., A textbook of magnetohydrodynamics, (1965), Pergamon Press
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