Electric smelting furnace (ESF) is increasingly adopted as an alternative to conventional cupola furnace for mineral wool production. The application of freeze lining to protect the refractory lining from erosion by molten slag has become a prevalent industrial practice. In this study, a three-dimensional (3D) full-scale mathematical model of a three-phase alternating current (AC) ESF is developed, which incorporates electromagnetism, heat transfer, and solid–liquid phase transitions. The model is used to simulate freeze lining formation and assess the impacts of process parameters. The time-averaged electromagnetic field (EMF) distribution is derived from Maxwell's equations using the finite volume method. The temperature field and phase transitions are modelled through the energy conservation equation, integrated with enthalpy-porous medium model. To optimise control over freeze lining thickness, this study analyzes three critical parameters: pitch circle diameter (PCD), melt pool height (MPH), and sidewall refractory thickness (SRT). Results demonstrate that the model effectively predicts the EMF distribution within the furnace, coupled heat transfer between the solid linings and the melt pool, and the morphology of the freeze lining. Under identical cooling conditions, increasing PCD and MPH slightly reduces freeze lining thickness, while an increasing in SRT complicates its formation. For optimal freeze lining maintenance, it is recommended that PCD, MPH, and SRT be set at 1.5 m, 1.2 m and 50 mm, respectively.
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