Thermal and electrical characteristics of a two-dimensional tanh-conductivity arc

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Abstract
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.

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