The two-dimensional constant-property arc

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Abstract
The theory of the (one-dimensional) constant property arc has been extended to a planar arc in two dimensions. This makes use of the canal model where the canal boundary temperature T*, at which the electrical conductivity jumps discontinuously from zero to a constant value σ* characteristic of the gas, is specified as a gas property. The Elenbaas-Heller equation is solved for arc temperature distributions subject to Ohm’s law and current conservation. Temperatures on the bounding walls and electrodes are specified. The principal parameters of this study are the length (interelectrode distance) to width (between bounding walls) ratio (a) and the conducting spot size (or maximum temperature) on the electrodes (F0). For a≳1, the central plane electric field is nearly coincident with the one-dimensional value. As a increases beyond 2.0, temperature maxima and arc thickness maxima appear near the electrodes. As F0 increases, arc temperatures increase at each point for fixed current.

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