On longitudinal electromagnetic stirring in the continuous casting of steel blooms

Recent work highlighting an anomaly in the modelling of rotary electromagnetic stirring (EMS) in the continuous casting of round steel billets is extended to the case of longitudinal stirring for rectangular blooms. An earlier, still often-cited, model forms the basis of the current analysis, which uses asymptotic methods on the three-dimensional (3D) Maxwell equations and demonstrates how the earlier result for the components of the Lorentz force is but a particular case of a more general form. Time-dependent 3D computations using finite-element methods are also performed to verify the validity of the asymptotic analysis, and the relevance of the results to modulated EMS is noted.