Magnetohydrodynamic Stokes flows for rotating solids of revolution

Abstract

Riley (1) has considered a magnetohydrodyriamic Stokes flow in which the modifications to the well-known Stokes flow past a fixed sphere were investigated for the case in which there is a magnetic pole situated at its centre. Again, Barthel and Lykoudis (2) and Ludford and Murray (3) have considered the low Reynolds number flow and inviscid flow respectively, past a sphere in the presence of a magnetic field due to a dipole situated at the centre of the sphere and directed parallel to the uniform stream. For the viscous problem, the velocity field and induced magnetic field were calculated for small values of the Hartmann number M and an expression found for the total drag on the sphere. Tamada and Sone (5) have also considered the same problem for a viscous conducting fluid at small Reynolds numbers and calculated the solution for small values of M while an asymptotic solution was found for large values of M. For small values of M they show that, since the Lorentz force retards the fluid motion, the viscous forces are reduced and hence the drag on the sphere is also reduced. However, the magnetic stresses contribute a force on the boundary which actually results in a net increase for the total drag on the sphere.