MATHEMATICAL MODEL OF THE PROCESSES OF HEAT AND MASS TRANSFER AND DIFFUSION OF THE MAGNETIC FIELD IN AN INDUCTION FURNACE

We propose a mathematical model describing the motion of a metal melt in a variable inhomogeneous magnetic field of a short solenoid. In formulating the problem, we made estimates and showed the possibility of splitting the complete magnetohydrodynamical problem into two subproblems: a magnetic fi eld diffusion problem where the distributions of the external and induced magnetic fi elds and currents are determined, and a heat and mass transfer problem with known distributions of volume sources of heat and forces. The dimensionless form of the heat and mass transfer equation was obtained with the use of averaging and multiscale methods, which permitted writing and solving separately the equations for averaged fl ows and temperature fi elds and their oscillations. For the heat and mass transfer problem, the boundary conditions for a real technological facility are discussed. The dimensionless form of the magnetic fi eld diffusion equation is presented, and the experimental computational procedure and results of the numerical simulation of the magnetic fi eld structure in the melt for various magnetic Reynolds numbers are
described. The extreme dependence of heat release on the magnetic Reynolds number has been interpreted.
   
Author:  A. V. Perminov and I. L. Nikulin
Keywords:  induction melting, superalloy, variable magnetic fi eld, magnetic fi eld diffusion, inductive current, heat and mass transfer, convection, multiscale method, averaging method
Page:  397