Field structures including electromagnetic, concentration of ions, and flow fields in an ESR-like process composed of a graphite crucible containing a molten slag, air, and an iron electrode are computed. Both CaF 2-(mass pct 2) CaO and CaF 2-(mass pct 2) Al 2 O 3 slags are examined. Tertiary current distribution is calculated. Therefore, polarization overpotential and Faradic reactions at metal-slag interface are considered using Tafel law, whereas transport of ions in the bulk of slag is determined through Nernst-Planck equations. The main goal is to shed light on the invisible phenomena such as magnetohydrodynamics caused by transport of ions, electrical conductivity of CaF 2-based slag using additives (e.g., CaO or Al 2 O 3), and the role of complexation of ions (e.g., AlO 3À 3) in the molten slag applied to the ESR. An explanation is given for the observation of higher oxygen content in the metal using Al 2 O 3 than that using equivalent amount of CaO in the CaF 2-based slag of a DC-operated ESR.