Acta Mechanica Sinica

, Volume 19, Issue 3, pp 235–240 | Cite as

MHD unsteady flows due to non-coaxial rotations of a disk and a fluid at infinity

  • T. Hayat
  • S. Mumtaz
  • R. Ellahi
Article

Abstract

Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk and the fluid are in a state of non-coaxial rotation. Such a flow model has a great significance not only due to its own theoretical interest, but also due to applications to geophysics and engineering. The resulting initial value problem has been solved analytically by applying the Laplace transform technique and the explicit expressions for the velocity for steady and unsteady cases have been established. The analysis of the obtained results shows that the flow field is appreciably influenced by the applied magnetic field, the frequency and rotation parameters.

Key Words

general periodic oscillation non-coaxial rotation magnetohydrodynamic flow Laplace transform 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Stangeby PC. A review of the status of MHD power generation technology including suggestions for a Canadian MHD research program. UTIAS Rev, 1974, 39Google Scholar
  2. 2.
    Lielausis OA. Liquid-metal magnetohydrodynamics.Atomic Energy Rev, 1975, 13: 527–581Google Scholar
  3. 3.
    Hunt JCR, Moreau R. Liquid-metal magnetohydrodynamics with strong magnetic fields: a report on Euromec 70.J Fluid Mech, 1976, 78: 261–288MATHCrossRefGoogle Scholar
  4. 4.
    Lyons JM, Turcotte DL. A study of MHD induction devices. AFOSR-TR-1864, 1962Google Scholar
  5. 5.
    Bernstein IB, Fanucci JB, Fischbeck KH, et al. An electrodeless MHD generator. In: 2nd Symposium on the Engineering Aspects of Magnetohydrodynamics, University of Pennsylvania, Philadelphia, 1961Google Scholar
  6. 6.
    Sarpkaya T. Flow of non-Newtonian fluids in a magnetic field.AIChE Journal, 1961, 7: 324–328CrossRefGoogle Scholar
  7. 7.
    Ramamurty G, Shanker B. Magnetohydrodynamic effect on blood flow through a porous channel.Med Biol Eng Comput, 1994, 32: 655–659Google Scholar
  8. 8.
    Berker R. Handbook of Fluid Dynamics, Vol. VIII/3, Berlin: Springer, 1963. 87Google Scholar
  9. 9.
    Coirier J. Rotations non-coaxiales d'un disque et d'un fluide a l'infini.J de Mecanique, 1972, 11: 317–340MATHMathSciNetGoogle Scholar
  10. 10.
    Murthy SN, Ram RKP. Magnetohydrodynamic flow and heat transfer due to eccentric rotations of a porousdisk and a fluid at infinity.Int J Engng Sci, 1978, 16: 943–949CrossRefGoogle Scholar
  11. 11.
    Rajagopal KR. On the flow of a simple fluid in an orthogonal rheometer.Arch Rat Mech Anal, 1982, 79: 39–47MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Rajagopal KR. Flow of viscoelastic fluids between rotating disks.Theor Comput Fluid Dynamics, 1992, 3: 185–206MATHCrossRefGoogle Scholar
  13. 13.
    Kasiviswanathan SR, Rao AR. An unsteady flow due to eccentrically rotating porous disk and a fluid at infinity.Int J Engng Sci, 1987, 25: 1419–1425MATHCrossRefGoogle Scholar
  14. 14.
    Erdogan ME. Unsteady flow of a viscous fluid due to non-coaxial rotations of a disk and a fluid at infinity.Int J Non-Linear Mech, 1997, 32: 285–290MATHCrossRefGoogle Scholar
  15. 15.
    Erdogan ME. Flow induced by non-coaxial rotation of a disk executing non-torsional oscillations and a fluid rotating at infinity.Int J Engng Sci, 2000, 38: 175–196CrossRefGoogle Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 2003

Authors and Affiliations

  • T. Hayat
    • 1
  • S. Mumtaz
    • 1
  • R. Ellahi
    • 1
  1. 1.Islamic International Engineering College c/o Head Office IIMCThe Mall Rawalpindi CanntPakistan

Personalised recommendations