Magnetohydrodynamic Effects on the Formation of Couette Flow

Abstract

This paper is concerned with the problem of the formation of Couette flow—i.e., the problem of how the velocity profile varies with the time tending asymptotically to that of the steady flow of an electrically conducting viscous fluid in the presence of a magnetic field. The governing equations and boundary conditions are established and discussed. The cases of both vanishing and nonvanishing mean induced electric field strengths are solved in terms of complimentary error functions as well as some elementary functions. I t is shown tha t the solutions are reducible to tha t of the steady case as the time approaches infinity, and to that of the nonmagnetic field as the Hartmann number becomes zero. Some numerical calculations are given. The results indicate that in the presence of a magnetic field the flow rate is reduced depending on the magnitude of the Hartmann number, and tha t the magnetic field assists the flow to reach its steady condition.