A note on the steady longitudinal motion of an insulating cylinder in a conducting fluid

Extract

This note examines one particular feature of the motion produced by an infinitely long insulating circular cylinder moving parallel to its axis in a conducting fluid permeated by a uniform transverse magnetic field. The particular aspect examined is that of determining, for large values of the Hartmann number, the flow in the neighbourhood of those points on the cylinder where the applied field is tangential.

The problem of determining the fields in these regions is very similar to that of calculating the acoustic potential in the neighbourhood of glancing incidence for a plane wave normally incident on a sound soft circular cylinder. An elegant method of treating this latter problem has been given by Jones [1] and the purpose of this note is to indicate the way in which Jones' method has to be modified to treat the magnetohydrodynamic problem. The basis of the approach is to determine a solution which satisfies the boundary conditions in the tangential regions and this can be achieved by conventional integral representation methods.