On the slow rotation of axisymmetric solids in magnetohydrodynamics

Abstract

The motion of a solid in a viscous conducting fluid permeated by a magnetic field has been the subject of a number of papers. Using the Stokes approximation Chester (3) first derived an expansion in powers of the Hartmann number for the drag on a sphere translating uniformly through a fluid, parallel to the applied magnetic field. In a subsequent paper (4) the same author treated the high Hartmann number limit. Later, Chang (2) considered, in the low Hartmann number regime, the motion of an axisymmetric body translating slowly along the axis of a fluid filled tube, and was able to calculate a drag formula which includes the lowest order wall effect term. An alternative treatment of this class of problems has recently been given by Williams (13), using an intergral equation formulation.