An analytical 1D model for computing low-frequency electromagnetic fields in material layers: Application to metallurgical furnaces

An analytical one-dimensional model for the distribution of electric fields within multiple material layers is developed and analyzed. The model originates from the study of large three-phase electric smelting furnaces for ferroalloys and is derived from the low-frequency time-harmonic Maxwell's equations. A solution is obtained for a general case with N layers of material with different electromagnetic properties. A practical demonstration of the utility of the model is given through an application to a multilayer configuration representing the lining and casing in a FeMn furnace, with validation against 2D simulations. In addition, for a specific two-layer scenario with a highly conductive material, an approximate solution for the adjacent layer is derived. This approximation allows the distribution of the adjacent layer to depend only on its individual properties, and shows that the dissipated power reaches a maximum value when the skin depth/thickness ratio is around one. Comparative analysis between the analytical model and 2D simulations shows good qualitative agreement.