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Meccanica

, Volume 32, Issue 2, pp 157–163 | Cite as

Similarity Solution of Unsteady Boundary Layer Equations with a Magnetic Field

  • H.S. TAKHAR
  • G. NATH
Article

Abstract

The unsteady laminar incompressible boundary layer flow of an electricallyconducting fluid in the stagnation region of two-dimensional and axisymmetricbodies with an applied magnetic field has been studied. The boundary layerequations which are parabolic partial differential equations with threeindependent variables have been reduced to a system of ordinary differential equations by using suitable transformations and then solved numerically using a shooting method. Here, we have obtained new solutions which are solutions of both the boundary layer and Navier-Stokes equations.

Unsteady flow Boundary layers MHD Fluid mechanics. 

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References

  1. 1.
    Blasius, H., 'Grenzschichten in Flüssigkeiten mit Kleiner Reibung', Z. Angew Math. Phys., 56(1908), 1–37.Google Scholar
  2. 2.
    Hiemenz, K., 'Die Grenzschicht an einem in den gleich formigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder', Dinglers Polytech. J., 326(1911), 321–324.Google Scholar
  3. 3.
    Rayleigh, Lord, 'On the motion of solid bodies through viscous liquids', Phil. Mag. 21(1911), 697–711.Google Scholar
  4. 4.
    Falkner, V.M., Skan, S.W., 'Some approximate solutions of the boundary layer equations', Phil. Mag. 12 (1931), 865–896.Google Scholar
  5. 5.
    Glauert, M.B., 'The laminar boundary layer on oscillating plates and cylilnders', J. Fluid Mech. 1(1956), 97–110.Google Scholar
  6. 6.
    Rott, N., 'Unsteady viscous flow in the vicinity of a stagnation point', Quart. Appl. Math. 13(1956), 444–451.Google Scholar
  7. 7.
    Yang, K.T., 'Unsteady laminar boundary layers in an incompressible stagnation flow', J. Appl. Mech., 25 (1958), 421–427.Google Scholar
  8. 8.
    Birkoff, G., Hydrodynamics: A study in Logic, Fact and Similitude, Princeton University Press, Princeton, 1960.Google Scholar
  9. 9.
    Rosenhead, L. (Ed.) Laminar Boundary Layers, Clarendon Press, Oxford, 1963.Google Scholar
  10. 10.
    Williams, J.C. and Johnson, W.D., 'Semi-similar solutions to unsteady boundary layer flows including separation', AIAA J. 12(1974), 1388–1393.Google Scholar
  11. 11.
    Ma, P.K.H., and Hui, W.H., 'Similarity solutions of the two-dimensional unsteady boundary layer equations', J. Fluid Mech., 216(1990), 537–559.Google Scholar
  12. 12.
    Takhar, H.S., 'Free convection from a flat plate', J. Fluid Mech., 34(1968), 81–89.Google Scholar
  13. 13.
    Katagiri, M., 'Unsteady magnetohydrodynamic flow at the forward stagnation point', J. Phys. Soc. Japan, 27(1969), 1662–1688.Google Scholar
  14. 14.
    Pop, I., 'MHD flow near an asymmetric plane stagnation point', Z. Angew Math. Mech., 65(1983), 380–383.Google Scholar
  15. 15.
    Takhar, H.S., 'Hydromagnetic free convection from a flat plate', Indian J. Phys. 45(1971), 289–311.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • H.S. TAKHAR
    • 1
  • G. NATH
    • 2
  1. 1.School of EngineeringUniversity of ManchesterManchesterU.K
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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