Acta Mechanica

, Volume 113, Issue 1–4, pp 241–244 | Cite as

An exact solution of the Navier-Stokes equations for magnetohydrodynamic flow

  • H. I. Andersson
Note

Summary

Viscous flow past a stretching sheet in the presence of a uniform magnetic field is considered. An exact similarity solution for velocity and pressure of the two-dimensional Navier-Stokes equations is presented, which is formally valid for all Reynolds numbers. The solution for the velocity field turns out to be the identical solution derived earlier by Pavlov [1] within the framework of high-Reynolds-number boundary layer theory, in which the pressure distribution cannot be determined.

Keywords

Magnetic Field Boundary Layer Dynamical System Reynolds Number Exact Solution 
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References

  1. [1]
    Pavlov, K. B.: Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface. Magnitnaya Gidrodinamika (U.S.S.R.)4, 146–147 (1974).Google Scholar
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    Chakrabarti, A., Gupta, A. S.: Hydromagnetic flow and heat transfer over a stretching sheet. Q. Appl. Math.37, 73–78 (1979).Google Scholar
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    Takhar, H. S., Ali, M. A., Gupta, A. S.: Stability of magnetohydrodynamic flow over a stretching sheet. In. Liquid metal hydrodynamics (Lielpeteris, J., Moreau, R., eds.), pp. 465–471. Dordrecht: Kluwer 1989.Google Scholar
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    Andersson, H. I.: MHD flow of a viscoelastic fluid past a stretching surface. Acta Mech.95, 227–230 (1992).Google Scholar
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    Andersson, H. I., Bech, K. H., Dandapat, B. S.: Magnetohydrodynamic flow of a power-law fluid over a stretching sheet. Int. J. Non-Linear Mech.27, 929–936 (1992).Google Scholar
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    Wang, C. Y.: Exact solutions of the steady-state Navier-Stokes equations. Ann. Rev. Fluid Mech.23, 159–177 (1991)Google Scholar
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    Shercliff, J. A.: A textbook of magnetohydrodynamics. Oxford: Pergamon Press 1965.Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • H. I. Andersson
    • 1
  1. 1.Department of Applied Mechanics, Thermo- and FluiddynamicsThe Norwegian Institute of TechnologyTrondheimNorway

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