Skip to main content
SpringerLink
Log in

Nonstationary Flow of a Viscous Incompressible Electrically Conductive Fluid on a Rotating Plate

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

In this work, the evolution of a flow of a viscous electrically conductive fluid on a rotating plate in the presence of a magnetic field is studied. The analytical solution of three-dimensional unsteady equations of magnetohydrodynamics is presented. The velocity field and the induced magnetic field in the flow of a viscous electrically conductive fluid filling a half-space bounded by a flat wall are determined. The fluid, together with the bounding plane, rotates as a whole with a constant angular velocity around a direction not perpendicular to the plane. An unsteady flux is induced by suddenly beginning vibrations of the wall and an applied magnetic field directed perpendicular to the plane. A number of special cases of the wall motion are considered. Based on the results obtained, the individual structures of the boundary layers near the wall are investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Similar content being viewed by others

REFERENCES

  1. Slezkin, N.A., Dynamics of a Viscous Incompressible Fluid, Moscow: Gostekhizdat, 1955.

    Google Scholar 

  2. Thornley, Cl., On stokes and rayleigh layers in a rotating system, Quantum J. Mech. Appl. Math., 1968, vol. 21, no. 4, pp. 455–462.

    MATH  Google Scholar 

  3. Gurchenkov, A.A. and Yalamov, Yu.I., Unsteady flow on a porous plate in the presence of injection (suction) of the medium, Prikl. Mat. Tekh. Fiz., 1980, no. 4, pp. 66–69.

  4. Gurchenkov, A.A., Unsteady motion of a viscous fluid between rotating parallel walls, J. Appl. Math. Mech. (Engl. Transl.), 2002, vol. 66, no. 2, p. 239–243.

  5. Kholodova, E.S., Doctoral Sci. (Phys.-Math.) Dissertation, St. Petersburg: St. Petersburg. Univ., 2019.

  6. Gurchenkov, A.A., Swirling Fluid Dynamics in the Cavity of a Rotating Body, Moscow: Fizmatlit, 2010.

    Google Scholar 

  7. Doetsch, G., Anleitung zum praktischen Gebrauch der Laplace-Transformation und der Z-Transformation, München, Wien: R. Oldenbourg, 1967.

    MATH  Google Scholar 

  8. Korn, G.A. and Korn, T.M., Mathematical Handbook for Scientists and Engineers, McGraw-Hill, 1961.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Federal Research Center Computer Science and Control, Russian Academy of Sciences, 119333, Moscow, Russia

    A. A. Gurchenkov

  2. National Research University “Moscow Aviation Institute,”, 125993, Moscow, Russia

    A. A. Gurchenkov

Authors
  1. A. A. Gurchenkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Gurchenkov.

Additional information

Translated by N. Semenova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gurchenkov, A.A. Nonstationary Flow of a Viscous Incompressible Electrically Conductive Fluid on a Rotating Plate. Fluid Dyn 56, 943–953 (2021). https://doi.org/10.1134/S0015462821070041

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462821070041

Keywords:

Search

Navigation