A system of partial differential equations describing the thermal behavior of aluminium cell coupled with magnetohydrodynamic effects is numerically solved. The thermal model is considered its a two-phases Stefan problem which consists of a non-linear convection-diffusion heat equation with Joule effect as a source. The magnetohydrodynamic fields are governed by Navier-Stokes and by static Maxwell equations. A pseudo-evolutionary scheme (Chernoff) is used to obtain the stationary solution giving the temperature and the frozen layer profile for the simulation of the ledges in the cell. A numerical approximation using a finite element method is formulated to obtain the fluid velocity, electrical potential, magnetic induction and temperature. An iterative algorithm and 3-D numerical results are presented. (C) 2008 Elsevier Inc. All rights reserved.