Over the decades, computational methods have been used to model and describe the flow and ionization dynamics in plasma torches. However, the impact of the operational parameters such as gas flow rate, swirl number and input current density on flow is still inexplicit. In this study, the flow in a non-transferred plasma torch is modelled using COMSOL Multiphysics, and the influence of these parameters is studied. The analysis is carried out on an axisymmetric geometry with the conical-shaped cathode, nozzle-shaped anode, and Argon is used as the plasma gas. A thermal plasma (equilibrium discharges) is considered, i.e., the plasma is under partial to complete local thermodynamic equilibrium in which the magnetohydrodynamic (MHD) equations are solved. This is treated in the Equilibrium Discharge Interface in COMSOL’s plasma module that has been used in the present study. The laminar flow analysis is performed for low-velocity cases and turbulent flow analysis for higher velocities. It was found that the velocity increase across the plasma arc due to ionization and gas expansion, could be observed only for sufficiently high plasma inflow velocities. The position of the plasma arc is determined for different operating conditions. It was further found that the velocity has a negligible effect on the length of the plasma arc, whereas the dependency of the arc length and attachment point on the anode wall, to the input current density and cathode tip temperature is well explained. The paper concludes by presenting the variations in temperature and velocity of plasma arc due to swirling inflow