Understanding the particle injection into the gas flow issuing from an APS torch is necessary to optimize the spraying parameters. In order to solve numerically this task, the distribution of gas velocity and temperature at the torch outlet is required. In this work this is achieved by developing a model which not only delivers the solution for the electrically charged gas flow within the torch, but also includes the thermodynamical condition of minimum entropy production. This additional condition fixes the size of the electric arc inside the torch, whose radius is particularly responsible for the form of the calculated velocity and temperature profiles at the torch nozzle. The velocity and viscosity of the gas flow near the torch outlet mainly control the trajectory of particles injected into the gas flow. For the typical gas mass flow and torch power used in APS, the resulting temperatures at the gas core are slightly above the ionization temperature of the gas species. The radial location of the viscosity maximum corresponding to the ionization temperature is calculated, since this maximum strongly influences the particle trajectory. Finally, the influence of plasma fluctuations on the heat transfer to the injected particles is discussed.