Transverse Magnetohydrodynamic Flow Past a Semi-Infinite Plate

Abstract

A viscous, incompressible, conducting fluid flows past a semi‐infinite flat plate; the free‐stream velocity of the fluid is taken parallel to the plate, and there is an applied magnetic field perpendicular to the plate. Physical arguments are given for a certain linearization of the basic steady‐state equations, and the linearized equations are solved by an approximation method based on the Wiener‐Hopf technique. An error estimate for the approximation is derived. The induced magnetic field, measured at the plate, is found to differ from the applied magnetic field by a multiplicative factor, whose value depends on the physical properties of the fluid and is constant for any given fluid. If the conducting fluid is a liquid metal (mercury or liquid sodium), edge effects can reasonably be neglected in calculating skin friction at the plate. An experimental study of the physical conclusions should be relatively manageable.