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**Closed-form exact solutions of MHD viscous flow over a shrinking sheet.**
*(English)*
Zbl 1221.76142

Summary: The magnetohydrodynamic (MHD) flow over a shrinking sheet is solved analytically. The solution is given in a closed-form equation and is an exact solution of the full governing Navier–Stokes equations for the problem. Interesting solution behavior is observed with multiple solution branches for certain parameter domain.

### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76W05 | Magnetohydrodynamics and electrohydrodynamics |

### Keywords:

similarity solution; stretching surface; shrinking sheet; Navier; Stokes equations; analytical solution; exact solution; magnetohydrodynamics
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\textit{T. Fang} and \textit{J. Zhang}, Commun. Nonlinear Sci. Numer. Simul. 14, No. 7, 2853--2857 (2009; Zbl 1221.76142)

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### References:

[1] | Altan, T.; Oh, S.; Gegel, H., Metal forming fundamentals and applications, (1979), American Society of Metals Metals Park, OH |

[2] | Fisher, E.G., Extrusion of plastics, (1976), Wiley New York |

[3] | Tadmor, Z.; Klein, I., Engineering principles of plasticating extrusion, Polymer science and engineering series, (1970), Van Nostrand Reinhold New York |

[4] | Sakiadis, B.C., Boundary-layer behavior on continuous solid surface: I. boundary-layer equations for two-dimensional and axisymmetric flow, J aiche, 7, 26-28, (1961) |

[5] | Sakiadis, B.C., Boundary-layer behavior on continuous solid surface: II. boundary-layer equations for two-dimensional and axisymmetric flow, J aiche, 7, 221-225, (1961) |

[6] | Tsou, F.K.; Sparrow, E.M.; Goldstain, R.J., Flow and heat transfer in the boundary-layer on a continuous moving surface, Int J heat mass transfer, 10, 219-235, (1967) |

[7] | Crane, L.J., Flow past a stretching plate, Z angew math phys, 21, 4, 645, (1970) |

[8] | Banks, W.H.H., Similarity solutions of the boundary-layer equations for a stretching wall, J mech theor appl, 2, 375-392, (1983) · Zbl 0538.76039 |

[9] | Dutta, B.K.; Roy, P.; Gupta, A.S., Temperature field in flow over a stretching sheet with uniform heat flux, Int commun heat mass trans, 12, 89-94, (1985) |

[10] | Grubka, L.J.; Bobba, K.M., Heat transfer characteristics of a continuous stretching surface with variable temperature, ASME J heat transfer, 107, 248-250, (1985) |

[11] | Chen, C.K.; Char, M.I., Heat transfer of a continuous stretching surface with suction and blowing, J math anal appl, 135, 568-580, (1988) · Zbl 0652.76062 |

[12] | Ali, M.E., On thermal boundary-layer on a power-law stretched surface with suction or injection, Int J heat fluid flow, 16, 280-290, (1995) |

[13] | Elbashbeshy, E.M.A., Heat transfer over a stretching surface with variable surface heat flux, J phys D: appl phys, 31, 1951-1954, (1998) |

[14] | Magyari, E.; Keller, B., Heat and mass transfer in the boundary-layers on an exponentially stretching continuous surface, J phys D: appl phys, 32, 5, 577-585, (1999) |

[15] | Magyari, E.; Keller, B., Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls, Euro J mech B: fluid, 19, 1, 109-122, (2000) · Zbl 0976.76021 |

[16] | Magyari, E.; Ali, M.E.; Keller, B., Heat and mass transfer characteristics of the self-similar boundary-layer flows induced by continuous surfaces stretched with rapidly decreasing velocities, Heat mass transfer, 38, 1-2, 65-74, (2001) |

[17] | Liao, S.J., A new branch of solutions of boundary-layer flows over a stretching flat plate, Int J heat mass transfer, 49, 12, 2529-2539, (2005) · Zbl 1189.76142 |

[18] | Liao, S.J., A new branch of solution of boundary-layer flows over a permeable stretching plate, Int J non-linear mech, 42, 819-830, (2007) · Zbl 1200.76046 |

[19] | Wang, C.Y., Exact solutions of the steady state navier – stokes equations, Ann rev fluid mech, 23, 159-177, (1991) |

[20] | Miklavcic, M.; Wang, C.Y., Viscous flow due to a shrinking sheet, Quart appl math, 64, 2, 283-290, (2006) · Zbl 1169.76018 |

[21] | Fang, T., Boundary layer flow over a shrinking sheet with power-law velocity, Int J heat mass transfer, 51, 25-26, 5838-5843, (2008) · Zbl 1157.76010 |

[22] | Hayat, T.; Abbas, Z.; Sajid, M., On the analytic solution of magnetohydrodynamic flow of a second grade fluid over a shrinking sheet, J appl mech: trans ASME, 74, 6, 1165-1171, (2007) |

[23] | Sajid, M.; Hayat, T.; Javed, T., MHD rotating flow of a viscous fluid over a shrinking surface, Non-linear dyn, 51, 1-2, 259-265, (2008) · Zbl 1170.76366 |

[24] | Sajid, M.; Hayat, T., The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet, Chaos, soliton fractals, (2007) · Zbl 1197.76100 |

[25] | Chakrabarti, A.; Gupta, A.S., Hydromagnetic flow and heat transfer over a stretching sheet, Quart appl math, 37, 73-78, (1979) · Zbl 0402.76012 |

[26] | Andersson, H.I., An exact solution of the navier – stokes equations for magnetohydrodynamic flow, Acta mech, 113, 241-244, (1995) · Zbl 0863.76089 |

[27] | Pop, I.; Na, T.Y., A note on MHD flow over a stretching permeable surface, Mech res commun, 25, 3, 263-269, (1998) · Zbl 0979.76097 |

[28] | Liao, S.J., On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet, J fluid mech, 488, 189-212, (2003) · Zbl 1063.76671 |

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