In the solidification with a magnetic field, both thermoelectric magnetohydrodynamic (TEMHD) effect and magnetogydrodynamic (MHD) effect exist simultaneously. The two effects have different influence on the fluid flow, leading to drive flow or brake flow. In this paper, a 2D model which is based on a combination of the Vc++ and the commercial finite volume package Fluent is proposed, for simulation of the magnetic driven fluid flow. This paper will focus on the relationship between TEMHD effect and MHD effe...