Stability of MHD Viscous Flow in a Curved Channel

Abstract

The purpose of this paper is to consider by the method of small perturbations how an external magnetic field suppresses the onset of a secondary vortex flow in a two-dimensional, incompressible, electrically conducting viscous flow in a curved channel. The magnetic field is applied in the direction perpendicular to the channel walls. The results show: (1) the critical Dean number K_C begins to increase as the Hartmann number H_a becomes larger than about 2, and in the limit H_a → ∞ the Dean number K_C tends to a relation proportinal to H_a^3/2; (2) the associated dimensionless wavenumber σ_C of the vortices also increases with H_a, and the location of the vortex center comes closer to the outer concave wall. In addition the effect of electrical conductivity of the wall material on the present stability problem is discussed.