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A magnetohydrodynamic model of a plasma torch that describes the complete torch system from the gas injection, through the arc region, and out into the plasma plume is presented. It is a two‐dimensional model but includes a swirl component of the flow and the K‐ϵ model of turbulence and assumes local thermodynamic equilibrium. Temperatures in the plume of a plasma torch have been determined spectroscopically by measuring the emission from neutral argon atoms, and these temperatures have been compared with the predictions of the model.