As the primary energy source, the long arc (LA) governs the physical fields and energy transfer in electric arc furnace (EAF). Studying the interaction mechanisms and influence laws among multiple physical fields in LAs is crucial for energy efficiency (η), yet such research remains limited, contributing to LA's status as a typical low-efficiency system. This study investigates how discharge atmosphere affects LA behavior using a magnetohydrodynamic-based electro-thermal-fluid coupling model. Distributions of electromagnetic, temperature, and flow fields under air and nitrogen (N2) are analyzed. Results show that both arcs exhibit bell-shaped profiles, with N2 enhancing plasma convergence near the axis due to lower electrical conductivity, leading to reduced anode receiving area and elevated axial temperatures. Improved synergy between thermal and flow fields in N2 enhances convective heat transfer. Arc current (I) significantly impacts power and efficiency without altering flow distribution. Arc length (L) further affects energy distribution, enhancing power but reducing η. N2 LAs are more sensitive to L and outperform air under extended conditions. Multiple regression models linking anode electric and heat flux densities to I, L, and radius achieve deviations within ±10%. The results highlight the importance of “ordered heat transfer”, which offering insights for optimized EAF control.
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