The stability of combined plane Poiseuille and Couette flow in the presence of a transverse magnetic field

Abstract

M. Takashima. Department of Physics, Faculty of Science, Osaka City University, Osaka 558, Japan. FAX: 06 6605-2532 Abstract: The stability of combined plane Poiseuille and Couette ow of an electrically conducting uid under a transverse magnetic þeld is investigated using linear stability theory. In deriving the equations governing the stability, the so-called magnetic Stokes approximation is made using the fact that the magnetic Prandtl number Prm for most electrically conducting uids is extremely small. The Chebyshev collocation method is adopted to obtain the eigenvalue equation, which is then solved numerically. The critical Reynolds number Rec, the critical wave number ac, and the critical wave speed cc are obtained for wide ranges of the Hartmann number Ha and the parameter k › U0U(U0 + v0), where U0 is the maximum velocity of pure Couette ow and v0 is the maximum velocity of pure Poiseuille ow. It is found that a transverse magnetic þeld has both stabilizing and destabilizing effects on the ow depending on the value of k.