Numerical calculation of the temperature distribution in the melt of induction crucible furnaces

In induction furnaces, power losses from the eddy currents in the melt are used to heat the charged metal. Nearly all of the induced heating power is generated inside the melt within the small depth of penetration. On the other hand, the electromagnetic Lorentz forces on the molten metal cause heat transport by forced convection. The question is wether the influence of convection is strong enough to homogenize the temperature of the melt. This paper deals with a method to calculate numerically the steady state temperature distribution within the melt, taking into account the heat transport by conduction, convection and radiation. The calculations were done for a 800 kg steel furnace with a filling level of 125 %, an induced power of 50 kW at 500 Hz; any other combinations can be calculated