A mathematical 2D representation is developed describing the temperature and the velocity profiles in a DC plasma torch and in the resulting plume. It is based on the resolution of conservation equations using the Simple method after Patankar. In the first part, we illustrate the effects of the turbulence, using, on the one hand, two Prandtl’s mixing length models and, on the other hand, a standard k - epsilon model. We also show the influence of physical parameters like the inlet mass flow rate, the current intensity, and the kind of gas (argon or air) on the characteristics of the plasma. The second part of this study presents a comparison of the model with experimental results encountered in the literature. The profiles obtained at the exit of the torch are compared to the mathematical formulation used as boundary condition by the models taking into account only the plasma jet.