A magneto-hydrodynamic Stokes flow

Abstract This paper considers the slow flow of a viscous, conducting fluid past a non-conducting sphere at whose centre is a magnetic pole. The magnetic Reynolds number is assumed to be small, and the modifications to the classical Stokes flow and the free magnetic pole field are obtained for an arbitrary Hartmann number. The total drag D on the sphere has been calculated, and the ratio D/Ds determined as a function of the Hartmann number M, where Ds is the Stokes drag. In particular (D — Ds)/Ds = 37/210M2+O(M4) for small M and (D — Ds)/Ds ~ 0·7205M - 1 as M → ∞.