Conducting fluid flowing through the electromagnetic field can generate a force called electromagnetic force. The electromagnetic force can change the flow of conducting fluid. This paper models and simulates the incompressible, viscous, conducting fluid flowing with different applied conditions. The numerical results show that: (1) The electromagnetic force is related to the applied electric and magnetic field. The electromagnetic force will be varied when the applied electric and magnetic field are different. Specifically, for the flowing between two electrode plates where the applied magnetic field is perpendicular to, the electromagnetic force increases with the increase of the applied electric and magnetic field. While when the inlet velocity becomes higher, the influence of electromagnetic force will become smaller. (2) The phenomenon of edge effect near the electrodes will affect the conducting fluid flow.%导电流体在磁场中会受到电磁力的作用而导致流体运动发生改变。本文模拟了不可压缩粘性导电流体在不同外加条件下的流动状况。模拟结果表明：（1）电磁力与外加磁场和外加电场有关，对于不同的外加磁场和外加电场，导电流体所受到的电磁力作用也不同。对于外加垂直方向均匀磁场的导电流体在两电极间的流动，外加磁场和外加电场越大，电磁力越大；在外加电场和外加磁场相同的情况下，对于不同的进口流动速度，入口速度越大，导电流体的流动受电磁力影响越小。（2）在电极附近会产生端部效应影响导电流体的流动。
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