Homogenised model for the electrical current distribution within a submerged arc furnace for silicon production

Silicon is produced in submerged arc furnaces which are heated by electric currents passing through the furnace. It important to understand distribution of heating within furnace order accurately model silicon production process, yet many existing studies neglect aspects this current flow. In present paper, we formulate a that couples electrical thermal, material flow and chemical processes We then exploit disparate timescales homogenise over timescale alternating current, deriving averaged equations for slow evolution system. Our numerical simulations predict minimum applied required obtain steady-state solutions homogenised show high enough currents, two spatially heterogeneous exist, with distinct crater sizes. system evolves steady state larger radius explain behaviour terms overall power balance typically found find industrial practice stoking increases rate consumption furnace, thereby improving efficiency production.