Electric Arc Furnace

What is modelled

A charge of scrap steel is heated from ambient to the melting point, melted, then superheated to the tapping temperature. The electric power is P = √3 V I cosφ; only a fraction η_arc reaches the bath. Oxygen and fuel add chemical power, while water-cooled panels and off-gas remove heat at a roughly constant rate. The net power sets the time to reach the required enthalpy.

Equations

• Electrical power P = √3 V I cosφ (V line-to-line).
• Enthalpy per kg h = ∫ cs(T) dT + L + cl(Ttap − Tm), with c_s rising with temperature.
• Net power Pnet = η P + Pchem − Ploss; time t = m h / Pnet.
• Specific electrical energy e = P t / m in kWh per tonne.

Checks run in the page

• Enthalpy from numerical integration of c_p(T) against the analytic value.
• Three-phase power from V and I against the set power.
• Time stepping reaches the tap temperature at the closed-form power-on time.
• Energy balance: input equals bath enthalpy plus losses at the moment of tap.

Honest simplifications

Lumped bath, constant efficiency and loss rate, constant latent heat, no slag, no scrap preheat or charge-by-charge details, and a fixed chemical power. Typical real furnaces use roughly 350 to 450 kWh per tonne of electricity; the numbers here are illustrative.

• Choose Oxygen assisted and see the electricity per tonne fall as chemical heat replaces it.
• Choose Poor power factor and watch the apparent power rise for the same arc power.
• Raise the panel heat loss and watch the tap time stretch.