Regular perturbation solution of the Elenbaas-Heller equation

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...

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Bibliographic Details
Published in:Journal of applied physics 2006-02, Vol.99 (3), p.034906-034906-6
Main Author: Shaw, B. D.
Format: Article
Language:English
Subjects:
ANALYTICAL SOLUTION
ASYMPTOTIC SOLUTIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
ELECTRIC ARCS
ELECTRIC CONDUCTIVITY
EQUATIONS
HEAT FLUX
JOULE HEATING
PERTURBATION THEORY
RADIANT HEAT TRANSFER
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Summary: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.
ISSN:0021-8979
1089-7550
DOI:10.1063/1.2168026