Mathematical modeling of the temperature field of the arc of a conductive channel taking into account the temperature dependence of thermal conductivity

Abstract

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.

Criteria for evaluating the laser resistance of crystals under thermoelastic deformation conditions

“…The first term in expression (11) takes into account the distortion of the wave front due to the temperature dependence of the refractive index, the second -the effect of thermal expansion, the third -the effect of photoelasticity.…”

The temperature of the elliptical cross section under boundary conditions of the first and third kind

“…Several works [5][6][7] are devoted to the calculation of temperature fields in bodies of elliptical cross-section in the presence of internal heat sources under various conditions. This article is a continuation of the works [7][8][9][10][11]. The main task of this work is to find the distribution of the temperature field in a hollow body with an elliptical crosssection of infinite length under boundary conditions of the first and third kind.…”