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Abstract <p>The motion of viscous electrically conducting incompressible liquid is investigated, in circumstances where the liquid rotates initially in a solid mass at constant speed together with a porous boundary wall (plate) until the instantaneous onset of longitudinal vibrations in the wall. The wall is at an arbitrary angle with respect to the axis of rotation. An unsteady flux is induced by the following factors: the longitudinal vibrations; injection (removal) of the liquid perpendicular to the surface of the porous wall; and a constant magnetic field perpendicular to the wall, which is also switched on instantaneously. Exact equations are derived for the velocity field and pressure field of the liquid. The magnetic field induced in the flux of electrically conducting liquid is determined. A hydrodynamic paradox is established on the basis of the results.</p>

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Motion of an Electrically Conducting Viscous Liquid at a Porous Wall with Liquid Injection

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • N. D. Vysk,
  • A. A. Gurchenkov,
  • A. M. Romanenkov

摘要

Abstract

The motion of viscous electrically conducting incompressible liquid is investigated, in circumstances where the liquid rotates initially in a solid mass at constant speed together with a porous boundary wall (plate) until the instantaneous onset of longitudinal vibrations in the wall. The wall is at an arbitrary angle with respect to the axis of rotation. An unsteady flux is induced by the following factors: the longitudinal vibrations; injection (removal) of the liquid perpendicular to the surface of the porous wall; and a constant magnetic field perpendicular to the wall, which is also switched on instantaneously. Exact equations are derived for the velocity field and pressure field of the liquid. The magnetic field induced in the flux of electrically conducting liquid is determined. A hydrodynamic paradox is established on the basis of the results.