A stability criterion for an infinitely long Hall-Héroult cell

This study is concerned with the stability of a Hall-Héroult cell which is assumed to be infinitely long. The modelling used leans on the magnetohydrodynamic theory for incompressible fluids. The presence of longitudinal electrical current inside the cell are taken into account. The influences of these last ones, on the stability of the cell, are studied. delling is obtained through a linearization of Navier-Stokes and Maxwell equations around a stationary solution. The problem defined by this process is solved with the help of a method related to the conservation of the energy flux. It allows in particular to establish a stability criterion related to the intensity of the longitudinal electrical currents. ar features of possible unstable modes are analytically obtained. ial results confirm the existence of such unstable modes.