Kinetic Theory Description of Rarefied Gas Flow
In an early paper with H. Bolza and Max Born, von Karman examined the relation between the "collision-dominated" and "collision-free" regimes in the simple case of steady flow or steady heat conduction through a porous medium. Von Karman also formulated the boundary condition at...
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| Veröffentlicht in: | Journal of the Society for Industrial and Applied Mathematics 1965-03, Vol.13 (1), p.278-311 |
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| creator | Lees, Lester |
| description | In an early paper with H. Bolza and Max Born, von Karman examined the relation between the "collision-dominated" and "collision-free" regimes in the simple case of steady flow or steady heat conduction through a porous medium. Von Karman also formulated the boundary condition at a gas-solid interface, and showed that the temperature "jump" arises quite naturally from the two-sidedness of the velocity distribution function, independently of any statements about the thermal accommodation coefficient. We reexamine this question of the transition between gas-kinetics and gasdynamics with the aid of the Maxwell moment method, utilizing a two-sided Maxwellian-type distribution as weighting function. The main features deduced from this approach are illustrated by considering two simple examples: (1) steady heat conduction between two concentric cylinders, and between two concentric spheres; (2) the "signaling problem" generated by the sudden motion and heating of an infinite flat plate. |
| doi_str_mv | 10.1137/0113017 |
| format | Article |
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Bolza and Max Born, von Karman examined the relation between the "collision-dominated" and "collision-free" regimes in the simple case of steady flow or steady heat conduction through a porous medium. Von Karman also formulated the boundary condition at a gas-solid interface, and showed that the temperature "jump" arises quite naturally from the two-sidedness of the velocity distribution function, independently of any statements about the thermal accommodation coefficient. We reexamine this question of the transition between gas-kinetics and gasdynamics with the aid of the Maxwell moment method, utilizing a two-sided Maxwellian-type distribution as weighting function. The main features deduced from this approach are illustrated by considering two simple examples: (1) steady heat conduction between two concentric cylinders, and between two concentric spheres; (2) the "signaling problem" generated by the sudden motion and heating of an infinite flat plate.</description><identifier>ISSN: 0368-4245</identifier><identifier>ISSN: 0036-1399</identifier><identifier>EISSN: 2168-3484</identifier><identifier>EISSN: 1095-712X</identifier><identifier>DOI: 10.1137/0113017</identifier><language>eng</language><publisher>Philadelphia: Society for Industrial and Applied Mathematics</publisher><subject>Boundary conditions ; Cylinders ; Flow velocity ; Fluid mechanics ; Gas flow ; Gases ; Heat ; Heat flux ; Heat transfer ; Kinetic theory ; Rarefied gases ; Shear stress ; Spheres ; Temperature ; Velocity ; Wave fronts ; Weighting functions</subject><ispartof>Journal of the Society for Industrial and Applied Mathematics, 1965-03, Vol.13 (1), p.278-311</ispartof><rights>Copyright 1965 Society for Industrial and Applied Mathematics</rights><rights>[Copyright] © 1965 Society for Industrial and Applied Mathematics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c203t-bd93800c136dd3a7d112a1c89156f07d033d75d79c839d9c60778429cf1b5d503</citedby><cites>FETCH-LOGICAL-c203t-bd93800c136dd3a7d112a1c89156f07d033d75d79c839d9c60778429cf1b5d503</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2946405$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/2946405$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,3184,27923,27924,58016,58020,58249,58253</link.rule.ids></links><search><creatorcontrib>Lees, Lester</creatorcontrib><title>Kinetic Theory Description of Rarefied Gas Flow</title><title>Journal of the Society for Industrial and Applied Mathematics</title><description>In an early paper with H. Bolza and Max Born, von Karman examined the relation between the "collision-dominated" and "collision-free" regimes in the simple case of steady flow or steady heat conduction through a porous medium. Von Karman also formulated the boundary condition at a gas-solid interface, and showed that the temperature "jump" arises quite naturally from the two-sidedness of the velocity distribution function, independently of any statements about the thermal accommodation coefficient. We reexamine this question of the transition between gas-kinetics and gasdynamics with the aid of the Maxwell moment method, utilizing a two-sided Maxwellian-type distribution as weighting function. The main features deduced from this approach are illustrated by considering two simple examples: (1) steady heat conduction between two concentric cylinders, and between two concentric spheres; (2) the "signaling problem" generated by the sudden motion and heating of an infinite flat plate.</description><subject>Boundary conditions</subject><subject>Cylinders</subject><subject>Flow velocity</subject><subject>Fluid mechanics</subject><subject>Gas flow</subject><subject>Gases</subject><subject>Heat</subject><subject>Heat flux</subject><subject>Heat transfer</subject><subject>Kinetic theory</subject><subject>Rarefied gases</subject><subject>Shear stress</subject><subject>Spheres</subject><subject>Temperature</subject><subject>Velocity</subject><subject>Wave fronts</subject><subject>Weighting 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Lester</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Kinetic Theory Description of Rarefied Gas Flow</atitle><jtitle>Journal of the Society for Industrial and Applied Mathematics</jtitle><date>1965-03-01</date><risdate>1965</risdate><volume>13</volume><issue>1</issue><spage>278</spage><epage>311</epage><pages>278-311</pages><issn>0368-4245</issn><issn>0036-1399</issn><eissn>2168-3484</eissn><eissn>1095-712X</eissn><abstract>In an early paper with H. Bolza and Max Born, von Karman examined the relation between the "collision-dominated" and "collision-free" regimes in the simple case of steady flow or steady heat conduction through a porous medium. Von Karman also formulated the boundary condition at a gas-solid interface, and showed that the temperature "jump" arises quite naturally from the two-sidedness of the velocity distribution function, independently of any statements about the thermal accommodation coefficient. We reexamine this question of the transition between gas-kinetics and gasdynamics with the aid of the Maxwell moment method, utilizing a two-sided Maxwellian-type distribution as weighting function. The main features deduced from this approach are illustrated by considering two simple examples: (1) steady heat conduction between two concentric cylinders, and between two concentric spheres; (2) the "signaling problem" generated by the sudden motion and heating of an infinite flat plate.</abstract><cop>Philadelphia</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/0113017</doi><tpages>34</tpages></addata></record> |
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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; LOCUS - SIAM's Online Journal Archive |
| subjects | Boundary conditions Cylinders Flow velocity Fluid mechanics Gas flow Gases Heat Heat flux Heat transfer Kinetic theory Rarefied gases Shear stress Spheres Temperature Velocity Wave fronts Weighting functions |
| title | Kinetic Theory Description of Rarefied Gas Flow |
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