Circulation in Three-Phase In-Line Electrode-Arc Furnaces

A theory of the circulation in a three-phase in-line electrode-arc furnace with rectangular cross section is derived. It is assumed that the depth of the furnace is infinite and that the length of the electrodes inside the melt is infinite. It isfurther assumed that the melt is electrically homogeneous. Assuming the exponential variation of the electrode current inside the melt, analytical expressions are obtained for the electric and the magnetic fields in the melt. Effects of the walls parallel to the electrode assembly are iincluded in the calculation. With the help of the field expressions the force and circulation are calculated at various points at the surface of the melt for different phasing of the electrode currents. Inclusion of the sidewalls perpendicular to the electrode assembly does not change the results significantly.