Two-dimensional viscous MHD flows in coaxial ducts

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

Abstract
An investigation is conducted into the two-dimensional laminar developed flow of a conducting fluid v(v_r, 0, v_z) in an axially symmetric annular MHD duct with continuous impermeable ideally conducting walls that are slightly curved along the longitudinal axis z. An external magnetic field B(0, B_θ, 0) is produced by the current in the center electrode, and it varies according to B_θ=1/r. A potential difference U_el is applied to the side walls. The scalar conductivity is assumed to be a function of the radius; the density _0, the viscosity _0, and the electron mobility _e are assumed to be constant. Two cases are considered: ^2=_e^2_e^2=0 (the Hall effect is absent) and ^2 1 (an appreciable Hall effect). The magnetic Reynolds number is assumed to be small. The end effects at the inlet and outlet are not considered, which corresponds to a flow in the regions of a MHD duct that are far from the inlet and outlet. An analytic solution is obtained for the two−dimensional problem by expanding in a power series of the small parameter 1 which characterizes the meridian curvature of the generatrices of the side walls. The influence of the duct shape, the Reynolds Re and Hartmann Ha numbers, the Hall parameter , the load factor, and the conductivity profile (r) on the flow hydrodynamics and the potential difference are investigated for an annular MHD duct. The calculations are used to explain the characteristics of the hydrodynamic break (in the absence of a magnetic field) and the electromagnetic break due to the inhomogeneity of the MHD retardation over the duct cross section and to the Hall effect. The velocity and potential distributions in annular MHD ducts are given for various parameters Re, Ha, , and (r)