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The article is devoted to mathematical modelling of the plasma temperature field taking into account the temperature dependence of thermal conductivity. The channel model was taken as a basis. Neglecting a very small fraction of the energy received by the ions during their acceleration in the longitudinal field, it can be assumed that all the energy taken by the arc discharge from an external source in the arc column passes directly to the plasma electrons. To find the temperature field by the integration method, the equation of thermal conductivity was solved. At the same time, the arc column is considered as a cylindrical continuous conductive rod in which all the supplied electrical energy is diverted due to thermal conductivity to the cooled walls of the discharge tube. The arc itself is represented by two regions: conductive and non-conductive. Based on mathematical modelling, the law of temperature field change in the arc cross-section was obtained. A formula was also derived to determine the effective radius of an electrically conductive channel.

The existing experimental methods do not allow us to accurately determine the limiting temperature stresses that cause the destruction of brittle bodies. In this work, a method of testing for thermal resistance is proposed and investigated, which is similar to the method of radiation heating. However, in this case, external heating of samples of electrically conductive materials is carried out by high-frequency currents, which significantly expands the possibilities of obtaining representative experimental results and simplifies the technique of the experiment itself.

The work is devoted to mathematical modeling of the plasma temperature field. To do this, it was represented as a conducting sphere under boundary conditions of the third kind. The simulation of the thermal process is based on the numerical integration of the heat equation. This takes into account the change in the thermal conductivity of the plasma and convective heat transfer. Also, based on the obtained result, an analysis of the behavior of the temperature field was carried out.

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