Fields, Power Density and Effective Resistance in the Electrode and Furnace of an Electric Smelter

摘要

A model is presented of an electric smelting furnace, in which a single electrode is in contact with a cylindrical furnace. Starting from Maxwell's equations, solutions for the electro-magnetic fields are expressed in terms of Bessel series and exponentials. The coefficients of the series are computed numerically. The current density distribution, its time dependence and its phase angle are comprehensively discussed; the spread of the total current in the furnace and the power density distribution are also investigated. Finally, the effective resistance is calculated for various values of parameters. Approximate power laws are given, expressing the resistance in terms of powers of electrode radius or furnace height.