Influence of asymmetry of an external magnetic field on viscous fluid flow in an annular MHD duct

L. K. Kovalev - S. M.-A. Koneev

Abstract
An investigation is conducted into the developed laminar one-component flow v(0,0,v) of an incompressible viscous fluid with constant conductivity σ in an annular duct with a difference potential U_el applied to the cylindrical ideally conducting walls. An asymmetric external tangential magnetic field B(B_r, B_θ, 0) is produced by the current in the center electrode, which is separated from the geometrical axis of the duct by the small quantity δ. It is assumed that the Hall effect is absent and the magnetic Reynolds number is small. An analytic solution is obtained for a two-dimensional flow by expanding in a power series of the small parameter δ << 1. The expressions obtained for the velocity and potential in the duct in zero-order and first-order approximations are used to calculate the flow parameters for various Hartmann numbers. The calculations indicate a possible periodic variation in the radial velocity and potential in a duct with an asymmetric magnetic field for Ha >~1000.