On the flow of a conducting fluid past a magnetized sphere

Abstract

In the steady flow of an incompressible, inviscid, conducting fluid past a magnetized sphere, the first-order effects of the magnetic field and the conductivity are studied. Paraboloidal wakes of vorticity and magnetic intensity are formed, the former being half the size of the latter. The vorticity, generated by the non-conservative electromagnetic force, is logarithmically infinite on the sphere. For the case of a dipole of moment M at the centre of a sphere of radius a, the drag coefficient is $C_D = \frac {144 \mu^{\prime 2}}{5(2\mu + \mu^{\prime})^2} \beta R_M,$ where μ and μ′ are the permeabilities of the fluid and sphere, respectively, β is the ratio of the representative magnetic pressure μM²/2a⁶ to the free-stream dynamic pressure, and R_M is the magnetic Reynolds number.