Two full 3D steady mathematical models are developed by finite element method (FEM) to calculate coupled physics fields: the electro-magnetic model is built and solved first and so is the fluid motion model with the acquired electromagnetic force as source body forces in Navier-Stokes equations. Effects caused by the ferromagnetic shell, busbar system around, and open boundary problem as well as inside induced current were considered in terms of the magnetic field. Furthermore, a new modeling method is found to set up solid models and then mesh them entirely with so-called structuralized grids, namely hex-mesh. Examples of 75kA prebaked cell with two kinds of busbar arrangements are presented. Results agree with those disclosed in the literature and confirm that the coupled simulation is valid. It is also concluded that the usage of these models facilitates the consistent analysis of the electric field to magnetic field and then flow motion to the greater extent, local distributions of current density and magnetic flux density are very much dependent on the cell structure, the steel shell is a shield to reduce the magnetic field and flow patt is two dimensional in the main body of the metal pad.