Temperature Distribution Along a Filament

Abstract

A method has been developed for adapting a new integrating machine to the solution of: (1) the integral equation which applies to the distribution of thermionic emission along the central portion of a long filament in an evacuated vessel, the effect of the thermionic emission upon the filament temperature (by changing the heating current as well as by a direct cooling action) being considered; (2) the differential equation which applies to the temperature distribution near the end of a long filament from which the thermionic emission is negligible compared with the filament heating current; (3) The integro-differential equation which applies to the distribution of temperature and thermionic emission along an entire filament heated, in an evacuated vessel, by a direct current. This takes into account the effects of thermionic emission as well as cooling due to thermal conduction. All these solutions fully account for the variation of the following quantities with temperature, graphical relations being used throughout: (a) thermal conductivity; (b) thermionic emission; (c) resistivity; (d) radiation. The method has been applied to various typical cases of tungsten and thoriated tungsten filaments, and in those cases where an experimental check was possible it was found that the results were in good agreement with the measured quantities.