In this paper a commercial CFD (computational fluid dynamics) code FLUENT has been used and modified for the axisymmetric swirl and time-dependent simulation of an atmospheric pressure argon arc in an exteal axial magnetic field (AMF).The computational domain includes the arc itself and the anodic region.Numerical results demonstrate that the AMF substantially increases the tangential component of the plasma velocity.The resulting centrifugal force for the plasma rotation impels it to travel to the arc mantel and as a result,a low-pressure region appears at the arc core.With the AMF,the arc presents a hollow bell shape and correspondingly,the maximal values of the temperature,pressure and current density on the anode surface are departing from the arc centreline.