Dimensional analysis and effects of dimensionless numbers on the iron removal process in electromagnetic induction heating furnaces

In the iron removal process by melting reduction of aluminosilicate solid waste, induction heating furnace can provide the heat source for fast melting solid wastes and carbothermal reduction, and drive the melt flow by electromagnetic force, which enhances the heat and mass transfer and improves the reduction and separation efficiency of the iron oxide impurities in the melt. In this work, based on the multi-physics real-time coupling model that integrates carbothermal reduction and interfacial mass transfer between two-phase melts in the induction furnace, several dimensionless numbers are derived by dimensional analysis of the magnetohydrodynamic equations and governing equations of physical fields, i.e., magnetic Reynolds number (Rem), Reynolds number (Re), Prandtl number (Pr), Hartmann number (Ha), Froude number (Fr), Weber number (We) and Peclet number (Pe). Combined with the physical significance of these dimensionless numbers, the constraints between different parameters and physical fields were analyzed, as well as the influences of dimensionless numbers on the two evaluation indexes of reduction degree and energy consumption. The correlation models between the dimensionless numbers and the reduction degree of iron oxides were obtained by data regression. Since the dimensionless numbers in the correlation models coupled the synergistic influences of multiple parameters on the transport processes, it can not only provide theoretical guidance for the inverse selection of design or operating parameters, but also greatly improve the applicability of the model.