A mathematical model was established to describe the electromagnetic, heat flow and fluid flow phenomena within a combined plasma arc. In the development of the model allowance was made for the conservation of mass, momentum, energy and the Maxwell equations. With the ANSYS finite analysis software, specific calculations were presented for a pure argon system, operating in a laminar mode. The distributions of the current density and velocity of combined plasma arc were gotten. In addition, the influences of process parameters, including arc current, argon gas flow rate and the distance from the nozzle outlet to the anode workpiece, on the velocity along the axial direction and current density distribution along radial direction were evaluated, respectively. The results shows that the velocity and current density of combined plasma arc are much dependent on the working current, while are less sensitive to the argon flow rate and the distance from the nozzle outlet to the workpiece anode.