Simulation of the Averaged Flow of a Metal Melt in an Alternating Magnetic Field with Variable Amplitude and Frequency

Abstract

The movement of a metal melt in an inhomogeneous high-frequency magnetic field is considered. A system of equations with boundary conditions defining the diffusion of the magnetic field and the heat conduction in such a melt in the Boussinesq approximation with account of the Joule heat released in the melt and the volume Lorentz forces acting in it is presented. The correctness of the mathematical model proposed is demonstrated. The amplitude distributions of the magnetic fields of the eddy currents induced in a metal melt, the velocity distributions of the heat flows in it, and the distribution of temperatures in the melt were calculated for the control parameters of its flow determined by the frequency and amplitude of the alternating magnetic field acting on it. The conditions under which the structure of this flow is completely determined by the parameters of the magnetic field and the problem on determination of the heat and mass transfer in the metal melt can be reduced to the calculation of its forced convection in the Lorentz force field and the temperature distribution in the melt at a definite velocity of its flow were determined.