Numerical simulation of a thermo-electromagneto-hydrodynamic problem in an induction heating furnace

This paper deals with mathematical modelling and numerical simulation of induction heating furnaces with axisymmetric geometries. The mathematical model consists of a coupled thermo-electromagneto-hydrodynamic problem with phase change. For the numerical solution, we propose finite element methods combined with boundary element methods (BEM/FEM) for the electromagnetic model, and with the method of characteristics for the flow equations. Moreover, an iterative fixed point-like algorithm is established for the whole coupling. Some numerical results for an industrial furnace are shown.