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Numerical modeling has been used to investigate the influence of electromagnetic stirring on melting of a single piece of scrap in an eccentric bottom tapping (EBT) electric arc furnace (EAF). The heat transfer and fluid flow in the melt for both conditions with and without electromagnetic stirring were studied. The buoyancy and electromagnetic forces were considered as the source terms for momentum transfer in the studied conditions. The enthalpy-porosity technique was applied to track the phase change of a scrap piece defined in the EBT region of the furnace. Different scrap sizes, preheating temperatures, stirring directions and force magnitudes were considered, and the heat transfer coefficient was estimated from the heat transfer rate at the melt-scrap interface. The results showed that electromagnetic stirring led to a reduced melting time and an increased heat transfer coefficient by a factor of four. The results for Nusselt number versus Grashof number for natural convection and Reynolds number for electromagnetic stirring were compared with those obtained through correlations from previous studies.

Streamer branching in liquid dielectrics is driven by stochastic and deterministic factors. The presence of stochastic causes of streamer branching such as inhomogeneities inherited from noisy initial states, impurities, or charge carrier density fluctuations is inevitable in any dielectric. A fully three-dimensional streamer model presented in this paper indicates that deterministic origins of branching are intrinsic attributes of streamers, which in some cases make the branching inevitable depending on shape and velocity of the volume charge at the streamer frontier. Specifically, any given inhomogeneous perturbation can result in streamer branching if the volume charge layer at the original streamer head is relatively thin and slow enough. Furthermore, discrete nature of electrons at the leading edge of an ionization front always guarantees the existence of a non-zero inhomogeneous perturbation ahead of the streamer head propagating even in perfectly homogeneous dielectric. Based on the modeling results for streamers propagating in a liquid dielectric, a gauge on the streamer head geometry is introduced that determines whether the branching occurs under particular inhomogeneous circumstances. Estimated number, diameter, and velocity of the born branches agree qualitatively with experimental images of the streamer branching. V

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