Eigenschaften und Parameterabhängigkeit der Temperaturverteilung und der Charakteristik eines zylindersymmetrischen Stickstoffbogens

Abstract

The purpose of this work is to examine the properties and dependence upon parameters of the temperature distribution, and to ascertain the characteristic of a stationary, cylindersymmetrical nitrogen arc with negligible convection. Proceeding from the local balance of energy (the Elenbaas-Heller differential equation), the article makes known a process designed to determine the axial field strength in the arc discharge tube explicity with the aid of the boundary conditions of the temperature and the material functions. To this end, the differential equation is converted to a nonlinear integral equation. This equation can then, provided that the material functions are known and the parameters — radius of discharge tube, axis temperature, wall temperature — are established, be solved either numerically or graphically by a method analogous with the Picard's method of successive approximations. The numerical results, parameter limitations, and assumptions concerning material functions, enable the graphic and analytical relationship between temperature distribution and characteristic to be ascertained within a predetermined range of parameters. Thus we are enabled to interpret and theoretically record a few empirical beginnings and laws.