Abstract: This study focuses on a magnetically stabilized gliding arc (MGA) plasma. Two fully coupled flow-plasma models (in 3D and 2D) are presented. The 3D model is applied to compare the arc dynamics of the MGA with a traditional gas-driven gliding arc. The 2D model is used for a detailed parametric study on the effect of the external magnetic field. The results show that the relative velocity between the plasma and feed gas is generated due to the Lorentz force, which can increase the plasma-treated gas fraction. The magnetic field also helps to decrease the gas temperature by enhancing heat transfer and to increase the electron number density. This work shows the potential of an external magnetic field to control the gliding arc behavior, for enhanced gas conversion at low gas flow rates.