A mathematical model for the dynamic behavior of melts subjected to electromagnetic forces: Part I. Model development and comparison of predictions with published experimental results

A mathematical model was developed to predict electromagnetically driven flow and (particularly) free surface behavior in melts subject to electromagnetic forces. Such melts appear in electromagnetic casters, induction furnaces, and other metal processing units. The calculations started with Maxwell's equations and Ohm's law, which were solved by a novel ''modified hybrid technique.'' The Instantaneous continuity and Navier-Stokes equations (rather than their time-averaged versions) were then solved with electromagnetic forces as input. The calculations allowed for the dynamic behavior of the free surface of the melt, and electromagnetic fields were recomputed as the free surface changed. In this first part of a two-part article, the model predictions are compared with the experimental measurements of induced current, magnetic field, melt velocity, and free surface deformation reported by others.