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Similarity solutions of a MHD boundary-layer flow past a continuous moving surface. (English) Zbl 1213.76234
Summary: This note deals with a theoretical and numerical analysis of multiple similarity solutions of the two-dimensional MHD boundary-layer flow over a permeable surface, with a power law stretching velocity, in the presence of a magnetic field $B$ applied normally to the surface. We have taken the free stream velocity to vary as $x^m$, where $x$ is the coordinate along the plate measured from the leading edge and $m$ is a constant. The magnetic field $B$ is assumed to be proportional to $x^{\frac{m-1}{2}}$. The problem depends on the power law exponent and the magnetic parameter $M$ or the Stewart number. It is shown, under certain circumstance, that the problem has an infinite number of solutions.

MSC:
76W05Magnetohydrodynamics and electrohydrodynamics
76D10Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids)
76M55Dimensional analysis and similarity (fluid mechanics)
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References:
[1] Abramowitz, M.; Stegun, I. A.: Handbook of mathematical functions. National bureau of standards (1964) · Zbl 0171.38503
[2] 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
[3] Devi, S. P. Anjali; Kandasamy, R.: Thermal stratification effects on non linear MHD laminar boundary-layer flow over a wedge with suction or injection. Int. commun. Heat mass transfer 30, 717-725 (2003) · Zbl 1112.76499
[4] Devi, S. P. Anjali; Thiyagarajan, M.: Steady nonlinear hydromagnetic flow and heat transfer over a stretching surface of variable temperature. Heat mass transfer 42, 671-677 (2006)
[5] Banks, W. H. H.: Similarity solutions of the boundary layer equations for a stretching wall. J. mécan. Théo. appl. 2, 375-392 (1983) · Zbl 0538.76039
[6] Banks, W. H. H.; Zaturska, M. B.: Eigensolutions in boundary-layer flow adjacent to a stretching wall. IMA J. Appl. math. 36, 375-392 (1986) · Zbl 0619.76011
[7] Belhachmi, Z.; Brighi, B.; Taous, K.: On a family of differential equation for boundary layer approximations in porous media. Eur. J. Appl. math. 12, 513-528 (2001) · Zbl 0991.76084
[8] Boyd, J. P.: Chebyshev and Fourier spectral methods. (2000)
[9] Brezis, H.; Peletier, L. A.; Terman, D.: A very singular solution of the heat equation with absorption. Arch. ration. Mech. anal. 95, 185-209 (1986) · Zbl 0627.35046
[10] B. Brighi, M. Benlahsen, M. Guedda, S. Peponas, Mixed convection on a wedge embedded in a porous medium, in preparation.
[11] Brighi, B.; Hoernel, J-D.: On the concave and convex solutions of mixed convection boundary layer approximation in a porous medium. Appl. math. Lett. 19, 69-74 (2006) · Zbl 1125.34005
[12] Canuto, C.; Hussaini, M. Y.; Quarterini, A.; Zang, T. A.: Spectral methods in fluid dynamics. (1988) · Zbl 0658.76001
[13] Chakrabarti, A.; Gupta, A. S.: Hydromagnetic flow and heat transfer over a stretching sheet. Quart. appl. Math. 37, 73-78 (1979) · Zbl 0402.76012
[14] Chaturvedi, N.: On MHD flow past an infinite porous plate with variable suction. Energ. convers. Manage. 37, 623-627 (1996)
[15] Chaudhary, M. A.; Merkin, J. H.; Pop, I.: Similarity solutions in free-convection boundary layer flows adjacent to vertical permeable surfaces in porous media. I. prescribed surface temperature. Eur. J. Mech. B fluids 14, 217-237 (1995) · Zbl 0835.76100
[16] Cheng, P.; Minkowycz, W. J.: Free-convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. J. geophys. Res. 82, 2040-2044 (1977)
[17] 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
[18] Coppel, W. A.: On a differential equation of boundary layer theory. Philos. trans. Royal soc. London ser. A 253, 101-136 (1960) · Zbl 0093.19105
[19] Cortel, R.: Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to suction and to a transverse magnetic field. Int. J. Heat mass transfer 49, 1851-1856 (2006) · Zbl 1189.76778
[20] Elbarbary, E. M. E.: Chebyshev finite difference method for the solution of boundary-layer equations. Appl. math. Comput. 160, 487-498 (2005) · Zbl 1059.76043
[21] Elbarbary, E. M. E.; El-Kady, M.: Chebyshev finite difference approximation for the boundary value problems. Appl. math. Comput. 139, 513-523 (2003) · Zbl 1027.65098
[22] Elbarbary, E. M. E.; El-Sayed, S. M.: Higher order pseudospectral differentiation matrices. Appl. numer. Math. 55, 425-438 (2005) · Zbl 1086.65016
[23] Fox, L.; Parker, I. B.: Chebyshev polynomials in numerical analysis. (1968) · Zbl 0153.17502
[24] Gottlieb, D.; Orszag, S. A.: Numerical analysis of spectral methods: theory and applications, CBMS-NSF regional conference series. Applied mathematics 26 (1977) · Zbl 0412.65058
[25] Greengard, L.: Spectral integration and two-point boundary value problems. SIAM J. Numer. anal. 28, 1071-1080 (1991) · Zbl 0731.65064
[26] Guedda, M.: Similarity solutions of differential equations for boundary layer approximations in porous media, ZAMP. J. appl. Math. phys. 56, 749-762 (2005) · Zbl 1084.34034
[27] Guedda, M.: Multiple solutions of mixed convection boundary-layer approximations in a porous medium. Appl. math. Lett. 19, 63-68 (2006) · Zbl 1125.34006
[28] Ingham, D. B.; Brown, S. N.: Flow past a suddenly heated vertical plate in a porous medium. J. proc. R. soc. London A 403, 51-80 (1986) · Zbl 0586.76151
[29] Kidder, L. E.; Scheel, M. A.; Teukolsky, S. A.; Carlson, E. D.; Cook, G. B.: Black hole evolution by spectral methods. Phys. rev. D 62, 1-20 (2000)
[30] Magyari, E.; Aly, E. H.: Exact analytical solution for a thermal boundary layer in a saturated porous medium. Appl. math. Lett. 19, 1351-1355 (2006) · Zbl 1154.76049
[31] Magyari, E.; Aly, E. H.: Mechanical and thermal characteristics of a mixed convection boundary-layer flow in a saturated porous medium. Int. J. Heat mass transfer 49, 3855-3865 (2006) · Zbl 1099.76059
[32] Magyari, E.; Keller, B.: Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls. Eur. J. Mech. B fluids 19, 109-122 (2000) · Zbl 0976.76021
[33] Nazar, R.; Amin, N.; Pop, I.: Unsteady mixed convection boundary-layer flow near the stagnation point over a vertical surface in a porous medium. Int. J. Heat mass transfer 47, 2681-2688 (2004) · Zbl 1079.76637
[34] Peyret, R.: Spectral methods for incompressible viscous flow. (2002) · Zbl 1005.76001
[35] Pop, I.; Na, T. Y.: A note on MHD flow over a stretching permeable surface. Mech. res. Commun. 25, 263-269 (1998) · Zbl 0979.76097
[36] Raptis, A.; Perdikis, C.; Takhar, H. S.: Effect of thermal radiation on MHD flow. Appl. math. Comput. 153, 645-649 (2004) · Zbl 1050.76061
[37] Snyder, M. A.: Chebyshev methods in numerical approximation. (1966) · Zbl 0173.44102
[38] Takhar, H. S.: Hydromagnetic free convection from a flat plate. Indian J. Phys. 45, 289-311 (1971)
[39] Takhar, H. S.; Chamkha, A. J.; Nath, G.: Flow and mass transfer on a stretching sheet with a magnetic field and chemically reactive species. Int. J. Eng. sci. 38, 1303-1314 (2000) · Zbl 1210.76205
[40] Takhar, H. S.; Nath, G.: Similarity solutions of unsteady boundary layer equations with a magnetic field. Mecanica 32, 157-163 (1997) · Zbl 0877.76083
[41] Voigt, R. G.; Gottlieb, D.; Hussaini, M. Y.: Spectral methods for partial differential equations. (1984) · Zbl 0534.00017
[42] Yang, H. H.; Seymour, B. R.; Shizgal, B. D.: A Chebyshev pseudospectral multi-domain method for steady flow past a cylinder, up to re=150. Comput. fluids 23, 829-851 (1994) · Zbl 0817.76064