Surface film deformation by melt moving in an alternating magnetic field and the integral criterion of such film stability

Abstract

The paper concerns some aspects of the induction melting technology improvement. The generalized mathematical model is presented which contains governing equations for the alternating magnetic field (AMF) diffusion into the liquid metal, heat and mass transfer in the melt and elastic deformation of the dielectric film covering partially the melt surface. The integral strain criterion is suggested which describes the total stress excited in the film by the melt motion. The model validation results are described. The influence of the film size on its stress–strain state is studied numerically for different values of external AMF frequency and strength. We calculate and classify realizable surface flow regimes depending on the AMF frequency and model, how this near-surface flow deforms the film of different sizes. An integral strain criterion is introduced, which lets to estimate the film break condition. The map of regimes is drawn which demonstrates the possible film radii at which the film does not break and does not deform depending on the AMF frequency and strength. It is shown, that integral strain criterion predicts well the film stress–strain state and conforms to the map of regimes. The results of numerical modeling, technique of the integral strain criterion calculation and examples of its application are given.