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The magnetic fields, current densitites, metal and electrolyte velocities, current efficiencies and topography of the electrolyte-metal interface within the Hall-Hroult cell used to produce aluminum have been predicted from first principles. The computation of current densities was carried out by solving Ohms law enabling the calculation of magnetic field vectors from the Biot-Savart law. The cross product of the current densities and magnetic fields then yielded the electromagnetic stirring forces acting on the molten metal and electrolyte. By employing a turbulence model and the time averaged Navier-Stokes equations, velocities within these two liquids could be calculated. The solution of the fluid flow equations yielded the pressure distribution within both elecrolyte and metal, permitting the calculation of the shape of the interface between these two liquids.

A Mathematical model for prediction of currents, magnetic fields, melt velocities, melt topography and current efficiency in Hall-Héroult cells