Some electrically driven flows in magnetohydrodynamics Part 2. Theory and experiment

Abstract

In this part we first extend the theory of part 1 to analyse the distribution of velocity and electric current in an electrically conducting liquid between two circular electrodes of finite diameter, when a current is passed between them. The electrodes are set opposite to each other in insulating planes and a magnetic field is applied perpendicular to these planes. When the Hartmann number M [Gt ] 1 we find that the current is confined to the cylinder of fluid joining the electrodes. This effect is accounted for by the velocity which is induced in thin layers of thickness O(M−½), at the circumference of the cylinder. In our analysis we concentrate on these interesting layers and, amongst other results, we find that in the limit M → ∞ the resistance of the fluid between the electrodes becomes that of the cylinder of fluid joining the electrodes.We then describe some experiments to test the validity of this theory. In these experiments we measured, as a function of the magnetic field, (a) the potential difference between the copper electrodes, the fluid being mercury, (b) the electric potential distribution in the fluid between the disks and in the thin layers between the electrode edges, by means of an electric potential probe, and (c) the velocities induced in the layers using a Pilot tube. Our conclusions were: (i) the overall predictions of the theory were correct; (ii) the results of the two probes approximately correlated with each other, despite the theory still having some limitations and the behaviour of these probes still being somewhat uncertain.