A two-dimensional mathematical model was developed to describe the heat transfer and fluid flow in an AC arc zone of a ferrosilicon submerged arc furnace.In this model,the time-dependent conservation equations of mass,momentum,and energy in the specified domain of plasma zone were numerically solved by coupling with the Maxwell and Laplace equations for magnetic filed and electric potential,respectively.A control volume-based finite difference method was used to solve the governing equations in cylindrical coordinates.The reliability of the developed model was checked by experimental data from the previous available literature.The results of present model were in good agreement with the given data comparing with other models,because of solving the Maxwell and Laplace equations simultaneously in order to calculate current density.In addition,parametric studies were carried out to evaluate the effects of electrical current and arc length on flow field and temperature distribution within the arc.According to the computed results,a lower power input led to a higher arc efficiency. A two-dimensional mathematical model was developed to describe the heat transfer and fluid flow in an AC arc zone of a ferrosilicon submerged arc furnace. In this model, the time-dependent conservation equations of mass, momentum, and energy in the specified domain of plasma zone were numerically solved by coupling with the Maxwell and Laplace equations for magnetic filed and electric potential, respectively. A control volume-based finite difference method was used to solve the governing equations in cylindrical coordinates. reliability of the developed model was checked by experimental data from the previous available literature. the results of present model were in good agreement with the given data comparing with other models, because of the solving of Maxwell and Laplace equations simultaneously in order to calculate current density.In addition, parametric studies were carried out to evaluate the effects of electrical current and arc length on flow field and temperature distribution within the arc. According to the computed results, a lower power input led to a higher arc efficiency.