Steady rotation of a sphere in a paramagnetic fluid

The steady rotation of a non-conducting sphere in an unbounded electrically non-conducting incompressible paramagnetic fluid was investigated. An external magnetic field acted parallel to the axis of rotation. The non-dimensional partial differential equations governing the magnetic field, magnetization and velocity were solved numerically. The magnetic field is comparatively weak in the radial direction and strong in the transverse direction over regions nearer the sphere. At points equidistant from the sphere the radial component of the magnetic field is maximum at an angle 14° from the axis. At points equidistant from the centre of the sphere the transverse component of the magnetic field is maximum at points near the equator and minimum at points near the axis. The magnetization increases with the applied magnetic field. At points near the equator and the axis the dipoles are oriented almost parallel to the applied magnetic field. In the remaining region they make an angle with the direction of the applied field which decreases with increasing applied magnetic field until at saturation magnetization they are oriented in the direction of the applied field. At points very near to the sphere the velocity is not affected by the magnetic field. Away from the sphere magnetization retards the flow.