One of the most sensitive factors for the simulation of the gas flow outside the plasma torch is the determination of the velocity and temperature profiles at the torch outlet. It requires the solution of the flow and electric potential equations within the torch. In this work this problem is solved through numerical simulations, with two free parameters: the radius of the plasma core near to the cathode and the length of the electric arc (or alternatively the potential between cathode and anode). In order to reduce the number of the free parameters to only one, an analytical model is also developed, which solves the same equations as the numerical simulations but in a simplified way. The reduction of parameters is achieved in this simple model through the additional condition that the physical plasma corresponds to an extremal value in the entropy production. Since the results of the simplified analytical model are compared to more detailed numerical simulations, the free parameter can be adjusted. The effect of high hydrogen content on the gas flow is thus studied, showing that the velocity profile at the outlet displays a more pronounced peak, as expected experimentally.

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