Thermal and electrical characteristics of a twoâ•’dimensional tanhâ•’conductivity arc

The two-dimensional variable-property arc has been studied through the use of the tanh-conductivity model. Results that describe the thermal and electric arc characteristics for various values of the electrode temperatures and aspect ratios are given. The numerical evaluation is carried out by the use of a Galerkin technique. The results exhibit several novel and interesting features depending on the arc parameters. For large aspect ratios (ratio of the interelectrode distance to that between the bounding walls) and small electrode temperatures, the current---electric-field characteristics tend toward those of a slender arc. However, at a given aspect ratio with large enough electrode temperatures, the distinct minimum noted in the slender-arc characteristics does not occur. Also, for a given aspect ratio and large enough differences in electrode potential, the electric-field-current characteristic is nearly linear and is independent of the electrode temperature. The transverse electrostatic potential is found to have no significant variation in cross-sectional planes. The qualitative nature of the thermal characteristics are similar to those of a constant-property arc although significant differences in quantitative results exist. Wall and electrode heat transfer rates are provided. Disciplines Engineering | Mechanical Engineering Comments Suggested Citation: Ayyaswarmy, Portonovas S., G.C. Das and Ira M. Cohen (1978) Thermal and electrical characteristics of a twodimensional tanh-conductivity arc. Journal of Applied Physics. Vol. 49(1). Copyright (1978) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Applied Physics and may be found at http://link.aip.org/link/ JAPIAU/v49/i1/p160/s1 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/189 Thermal and electrical characteristics of a two-dimensional tanh-conductivity arc P. S. Ayyaswamy, G.C. Das, and I. M. Cohen Department of Mechanical Engineering and Applied Mechanics. University of Pennsylvania, Philadelphia, Pennsylvania 19104 (Received 6 January 1977; accepted for publication 5 April 1977) The two-dimensional variable-property arc has been studied through the use of the tanh-conductivity model. Results that describe the thermal and electric arc characteristics for various values of the electrode temperatures and aspect ratios are given. The numerical evaluation is carried out by the use of a Galerkin technique. The results exhibit several novel and interesting features depending on the arc parameters. For large aspect ratios (ratio of the interelectrode distance to that between the bounding walls) and small electrode temperatures, the current---electric-field characteristics tend toward those of a slender arc. However, at a given aspect ratio with large enough electrode temperatures, the distinct minimum noted in the slender-arc characteristics does not occur. Also, for a given aspect ratio and large enough differences in electrode potential, the electric-field-current characteristic is nearly linear and is independent of the electrode temperature. The transverse electrostatic potential is found to have no significant variation in cross-sectional planes. The qualitative nature of the thermal characteristics are similar to those of a constant-property arc although significant differences in quantitative results exist. Wall and electrode heat transfer rates are provided. PACS numbers: S2.80.Mg