Mathematical model of magnetic hydrodynamics and heat transfer in aluminium reduction cell

The paper presents a new nonstationary three-dimensional mathematical model of an aluminium reduction cell which makes it possible to perform coupled thermoelectric and magnetohydrodynamic calculations taking into account sideledge formation. The model considers the nonlinear dependence of material electrical conductivity and thermal conductivity coefficients on temperature, and the nonlinear dependence of magnetization on the magnetic field strength for ferromagnetic materials. Heat transfer coefficients on outer surfaces included the radiant and convective components of heat transfer and were functions of the ambient temperature and the local surface temperature. The energy equation took into account internal heat sources due to the electric current flow, exothermic reactions and additional thermal effects associated with the raw material loading and phase transitions. The control volume method was used to obtain a numerical solution. The developed mathematical model was experimentally tested at the S8BME aluminium reduction cell. The paper presents the calculated and experimental data of magnetic, electric, thermal and hydrodynamic fields. The comparison of calculation results with the results of industrial experiments showed that the developed model reflects physical processes taking place in the aluminium reduction cell with accuracy sufficient for engineering calculations. The calculated values of electrical voltage, magnetic induction and temperature practically coincide with the measured ones. Velocity directions in the metal and the sideledge profile shape obtained by calculation have insignificant differences from experimental values. The developed model can be used to estimate operation specifications and design parameters for new and modernized aluminium reduction cells. Further studies will be aimed at refining the calculated results by improving the developed mathematical model.