The effect of a very strong magnetic cross-field on steady motion through a slightly conducting fluid

Abstract

The flow engendered by the steady motion of a cylindrical insulator through an inviscid, incompressible fluid of small conductivity σ is not close to potential flow when the applied magnetic cross-fieldH₀is sufficiently strong. Here we determine the limiting form of this flow as σ → 0 with$\sigma H^2_0 \rightarrow \infty$, the latter representing the ponderomotive force.The limit equations do not have a unique solution, but it is possible to make a selection by taking into account the inertia of the fluid during the limiting process, i.e. without recourse to considerations of how the motion was set up from rest. The forces on the cylinder are found to be asymptotically proportional to$\surd {\sigma} H_0$.The case of an elliptic cylinder and that of a flat plate are worked out in detail.