“…In such a system, the slag flow and heat transfer are governed by conservation equations of mass, momentum, and energy, while both momentum and energy equations should be coupled with a set of Maxwell's field equations and Ohm's law. For the sake of brevity, the transport equations can be written in coordinate free tensor notation: [1] [2] [3] Here, B denotes the magnetic flux density, C p the specific heat, E the electric field density, g the gravitational acceleration, h the enthalpy, J the current density, k the thermal conductivity, p the pressure, T the temperature, V the velocity, the slag density, eff ϭ ϩ t , the dynamic viscosity, t the turbulent viscosity, the electrical conductivity of the slag, h the turbulent Prandtl number, and  the thermal expansion coefficient. The Ohm's law applies: [4] The electric field can be written as the gradient of an electric potential: The electric potential satisfies [6] Because the Rayleigh number is estimated to be about 2.7 ϫ 10 11 for the furnace considered, the slag flow is turbulent.…”