Magnetohydrodynamics of laminar flow in slowly varying tubes in an axial magnetic field

Abstract

Laminar flow of a conducting fluid in round, straight tubes with axially varying radius, with a uniform magnetic field applied parallel to the tube axis, is treated theoretically as a regular perturbation problem at finite hydrodynamic Reynolds number, finite magnetic Reynolds number, and Hartmann numbers as large as O(α−1/2), where α is a small parameter characteristic of the slope of the tube wall. The first-order solution is examined numerically for local tube dilations and for local constrictions. Flow separation along both converging and diverging sections of the tube is discussed. Pressure, current density, and induced magnetic field distributions are also presented.