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


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.


Magnetic Field Boundary Layer Dynamical System Reynolds Number Exact Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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
  2. [2]
    Chakrabarti, A., Gupta, A. S.: Hydromagnetic flow and heat transfer over a stretching sheet. Q. Appl. Math.37, 73–78 (1979).Google Scholar
  3. [3]
    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
  4. [4]
    Andersson, H. I.: MHD flow of a viscoelastic fluid past a stretching surface. Acta Mech.95, 227–230 (1992).Google Scholar
  5. [5]
    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
  6. [6]
    Wang, C. Y.: Exact solutions of the steady-state Navier-Stokes equations. Ann. Rev. Fluid Mech.23, 159–177 (1991)Google Scholar
  7. [7]
    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

Personalised recommendations