PurposeThe purpose of this paper is to present a 3D finite element model of the electromagnetic fields in an AC three‐phase electric arc furnace (EAF). The model includes the electrodes, arcs, and molten bath.Design/methodology/approachThe electromagnetic field in terms of time in AC arc is also modeled, utilizing a 3D finite element method (3D FEM). The arc is supposed to be an electro‐thermal unit with electrical power as input and thermal power as output. The average Joule power, calculated during the transient electromagnetic analysis of the AC arc furnace, can be used as a thermal source for the thermal analysis of the inner part of furnace. Then, by attention to different mechanisms of heat transfer in the furnace (convection and radiation from arc to bath, radiation from arc to the inner part of furnace and radiation from the bath to the sidewall and roof panel of the furnace), the temperature distribution in different parts of the furnace is calculated. The thermal model consists of the roof and sidewall panels, electrodes, bath, refractory, and arc. The thermal problem is solved in the steady state for the furnace without slag and with different depths of slag.FindingsCurrent density, voltage and magnetic field intensity in the arcs, molten bath and electrodes are predicted as a result of applying the three‐phase AC voltages to the EAF. The temperature distribution in different parts of the furnace is also evaluated as a result of the electromagnetic field analysis.Research limitations/implicationsThis paper considers an ideal condition for the AC arc. Non‐linearity of the arc during the melting, which leads to power quality disturbances, is not considered. In most prior researches on the electrical arc furnace, a non‐linear circuit model is usually used for calculation of power quality phenomena distributions. In this paper, the FEM is used instead of non‐linear circuits, and calculated voltage and current densities in the linear arc model. The FEM results directly depend on the physical properties considered for the arc.Originality/valueSteady‐state arc shapes, based on the Bowman model, are used to calculate and evaluate the geometry of the arc in a real and practical three‐phase AC arc furnace. A new approach to modeling AC arcs is developed, assuming that the instantaneous geometry of the AC arc at any time is constant and is similar to the geometry of a DC arc with the root mean square value of the current waveform of the AC arc. A time‐stepping 3D FEM is utilized to calculate the electromagnetic field in the AC arc as a function of time.
Electromagnetic Field and Three-Phase-Lag in a Compressed Rotating Isotropic Homogeneous Micropolar Thermo-Viscoelastic Half-Space