Three-dimensional flow of a viscous conducting liquid in coaxial MHD channels with an asymmetric magnetic field

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

Abstract
The results of theoretical investigations of three-dimensional laminar extended MHD flows of conducting liquid in coaxial MHD channels with curvilinear conduct- ing walls r₁ (εz) and r₂ (εz), when an external asymmetric magnetic field is produced by a longitudinal current I, which is a distance Z = δr_o from the geometrical axis of the channel (where r_o is the radius of the internal electrode at the input), are presented. Assuming the parameters ε and δ, which characterize, respectively, the asymmetry of the applied magnetic field and the meridional curvature of the ring electrodes, to be small (ε << 1, δ << I, and ε ∼ δ), the solution of the three-dimensional problem reduces to the solution of appropriate twodimensional problems. The analytical solutions obtained in the zeroth and first approximations with respect to ε and δ are illustrated by calculations of the three-dimensional velocity and potential distributions in an MHD channel.