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As a first step towards a computer simulation of the fluid dynamics in the falling film plasma reactor, two-temperature swirl flow equations are developed allowing the detailed handling of the working gas using the code for thermodynamic equilibrium in a multi-component system and for the electrical and thermal conductivity in a gas. There is an easy way to incorporate the detailed radiation data into the integration process. It is important because radiation heat loss dominates over the convective one at a substantial length of a plasmatron of the kind under consideration. The matching of the calculated data to the available experimental data is obtained using quite reasonable coefficients in the heat transfer terms.