Analytical models of rotary clectromagnetic stirring

Electromagnetic stirring (EMS) is widely used in the steel industry as a means of improving the as-cast structure of a continuously-cast billet. Proponents of the technique have claimed that EMS not only promotes homogeneous grain growth, but also reduces shrinkage porosity and improves surface quality. EMS is less commonly used for grain refining in other metallurgical industries, but frequently appears in welding, vacuum arc refining, and single-crystal pulling. In this paper, we shall consider rotary magnetic stirring. We shall show that, for many geometries, the magnitude and distribution of the induced flow may be predicted without recourse to numerical simulations. Moreover, we shall show that the same magnetic body force can lead to entirely different velocity fields, depending on the shape of the liquid pool.