Extensions of the two-dimensional constant property arc

Abstract

Our Galerkin approximate analysis of two-dimensional arc properties and arc shape has been extended from planar constant property arcs to axisymmetric constant property arcs and to planar arcs with thermal and electrical conductivity variations. Axisymmetric constant property arcs are qualitatively similar to planar constant property arcs. Local temperature maxima occur on the arc axis about halfway between the central plane and the electrodes, and increase in magnitude as the arc slenderness ratio increases. When the electrical conductivity increases as a power of n of the heat flux potential, the arc gets thinner and cooler with increasing n for larger currents, but for small currents the arc gets thicker and hotter with increasing n. Since conductivity increases rapidly with heat flux potential ?, when this is greater than unity, high enough conductivities can be obtained at lower temperatures and with thinner arcs. On the other hand, when current ? is small, ?<1, so larger n corresponds to smaller conductivities. Thus higher temperatures and thicker arcs (as n increases) are required in order to pass small currents.