Boundary element analysis of electromagnetic confinement applications

A boundary integral equation (BIE) formulation is derived to represent a mathematical model for a molten metal in a two-ton crucible induction furnace with an induction coil shielded by a nonconducting magnetic yoke. In this formulation, the impedance boundary condition relation is applied in the molten metal region and a special BIE formulation is derived for the yoke region. The strong singularities appearing in this formulation are treated numerically. An iterative procedure based on this formulation is developed to predict the equilibrium shape of the free surface for the molten metal by fulfilling the balance between the electromagnetic and gravitational pressures. Numerical results for the equilibrium shape are presented. The effects of the current supply and the level of the melt on the equilibrium shape are considered. Profiles of the equilibrium shape are compared with published results obtained by using the finite-difference method. The effect of using the yoke on the equilibrium free-surface shape of the melt is discussed