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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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| Published in: | Journal of applied physics 2006-02, Vol.99 (3), p.034906-034906-6 |
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| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c312t-976281a313948a9da87eb84b8279d4ec97f453617a42531b28a59584d3ba80c13 |
| container_end_page | 034906-6 |
| container_issue | 3 |
| container_start_page | 034906 |
| container_title | Journal of applied physics |
| container_volume | 99 |
| creator | Shaw, B. D. |
| description | 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. |
| doi_str_mv | 10.1063/1.2168026 |
| format | article |
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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.</description><identifier>ISSN: 0021-8979</identifier><identifier>EISSN: 1089-7550</identifier><identifier>DOI: 10.1063/1.2168026</identifier><identifier>CODEN: JAPIAU</identifier><language>eng</language><publisher>United States: American Institute of Physics</publisher><subject>ANALYTICAL SOLUTION ; ASYMPTOTIC SOLUTIONS ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; ELECTRIC ARCS ; ELECTRIC CONDUCTIVITY ; EQUATIONS ; HEAT FLUX ; JOULE HEATING ; PERTURBATION THEORY ; RADIANT HEAT TRANSFER</subject><ispartof>Journal of applied physics, 2006-02, Vol.99 (3), p.034906-034906-6</ispartof><rights>2006 American Institute of Physics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c312t-976281a313948a9da87eb84b8279d4ec97f453617a42531b28a59584d3ba80c13</citedby><cites>FETCH-LOGICAL-c312t-976281a313948a9da87eb84b8279d4ec97f453617a42531b28a59584d3ba80c13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/20787873$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Shaw, B. D.</creatorcontrib><title>Regular perturbation solution of the Elenbaas-Heller equation</title><title>Journal of applied physics</title><description>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.</description><subject>ANALYTICAL SOLUTION</subject><subject>ASYMPTOTIC SOLUTIONS</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>ELECTRIC ARCS</subject><subject>ELECTRIC CONDUCTIVITY</subject><subject>EQUATIONS</subject><subject>HEAT FLUX</subject><subject>JOULE HEATING</subject><subject>PERTURBATION THEORY</subject><subject>RADIANT HEAT TRANSFER</subject><issn>0021-8979</issn><issn>1089-7550</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><recordid>eNp1kEFLw0AQhRdRsFYP_oOAJw-pO7tJdvagIKVaoSCInpfNZmIjMam7m4P_vm3agxeZw5vDx4P3MXYNfAa8kHcwE1AgF8UJmwBHnao856dswrmAFLXS5-wihC_OAVDqCbt_o8-htT7ZkI-DL21s-i4JfTuMT18ncU3JoqWutDakS2pb8gn9DCN4yc5q2wa6OuaUfTwt3ufLdPX6_DJ_XKVOgoipVoVAsBKkztDqyqKiErMShdJVRk6rOstlAcpmIpdQCrS5zjGrZGmRO5BTdnPo7UNsTHBNJLd2fdeRi0ZwhbuTO-r2QDnfh-CpNhvffFv_a4CbvR0D5mhnxz4c2H3ZuOV_-KjI_FUktxWMauM</recordid><startdate>20060201</startdate><enddate>20060201</enddate><creator>Shaw, B. D.</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>20060201</creationdate><title>Regular perturbation solution of the Elenbaas-Heller equation</title><author>Shaw, B. D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c312t-976281a313948a9da87eb84b8279d4ec97f453617a42531b28a59584d3ba80c13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>ANALYTICAL SOLUTION</topic><topic>ASYMPTOTIC SOLUTIONS</topic><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>ELECTRIC ARCS</topic><topic>ELECTRIC CONDUCTIVITY</topic><topic>EQUATIONS</topic><topic>HEAT FLUX</topic><topic>JOULE HEATING</topic><topic>PERTURBATION THEORY</topic><topic>RADIANT HEAT TRANSFER</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shaw, B. D.</creatorcontrib><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>Journal of applied physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shaw, B. D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Regular perturbation solution of the Elenbaas-Heller equation</atitle><jtitle>Journal of applied physics</jtitle><date>2006-02-01</date><risdate>2006</risdate><volume>99</volume><issue>3</issue><spage>034906</spage><epage>034906-6</epage><pages>034906-034906-6</pages><issn>0021-8979</issn><eissn>1089-7550</eissn><coden>JAPIAU</coden><abstract>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.</abstract><cop>United States</cop><pub>American Institute of Physics</pub><doi>10.1063/1.2168026</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-8979 |
| ispartof | Journal of applied physics, 2006-02, Vol.99 (3), p.034906-034906-6 |
| issn | 0021-8979 1089-7550 |
| language | eng |
| recordid | cdi_osti_scitechconnect_20787873 |
| source | American Institute of Physics:Jisc Collections:Transitional Journals Agreement 2021-23 (Reading list) |
| 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 |
| title | Regular perturbation solution of the Elenbaas-Heller equation |
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