Regular perturbation solution of the Elenbaas-Heller equation
- Mechanical and Aeronautical Engineering Department, University of California, Davis, California 95616 (United States)
The Elenbaas-Heller equation is nondimensionalized and solved using regular perturbation theory to provide closed-form analytical solutions to describe structures of cylindrically symmetrical steady electric arc discharges with negligible radiant heat transfer. Based on available data, it is assumed that the electrical conductivity varies with the heat-flux potential in an Arrhenius fashion. The leading-order solution is equivalent to an asymptotic solution proposed by Kuiken [J. Appl. Phys. 58, 1833 (1991)]. Higher-order terms are also derived in the present paper, and it is shown that quantitatively accurate analytical solutions can be developed when higher-order terms are included. Analysis shows that appreciable Joule heating is restricted to an inner zone when a dimensionless parameter is large relative to unity, leading to arc-channel models suggested by previous investigators.
- OSTI ID:
- 20787873
- Journal Information:
- Journal of Applied Physics, Vol. 99, Issue 3; Other Information: DOI: 10.1063/1.2168026; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-8979
- Country of Publication:
- United States
- Language:
- English
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