On the thermal boundary layer on an electrode

Abstract

In the present paper we consider the approximate calculation of the temperature distribution in a MHD channel operating in the accelerator regime with account for the dependence of the electrical conductance and thermal conductance coefficients on the temperature and with account for Joule dissipation. If the plasma temperature in the channel is about 10^4∘ K, then the Prandtl number is much less than unity. Therefore the length of the inlet dynamic segment is much greater than the inlet thermal segment, and we can neglect the transverse velocity component. This permits solving the problem without imposing any constraint on the longitudinal velocity and density. Moreover, under certain conditions we can neglect the term with the pressure gradient in comparison with the Joulean dissipation in the heat transport equation, which permits separation of the thermal problem from the dynamic. In the study we investigate the length of the inlet thermal segment, the heat exchange at the channel wall as a function of the wall temperature, and we also analyze the applicability of the suggested method of calculation.