A three-dimensional mathematical model has been developed and an analysis of inhomogeneous distribution of magnetic and temperature fields have been made in the lined inductor of melting-holding furnace for copper melting and in the copper template. The analysis was done considering a complex geometry of the inductor (which typical dimensions of the elements differ significantly), nonlinear dependence of the copper conductivity on temperature, ferromagnetic properties of a steel magnetic core and an availability of water cooling of the
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