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The conservation equations for independent coexistent continua and for multicomponent reacting gas mixtures

Nachbar, W. and Williams, F. and Penner, S. S. (1959) The conservation equations for independent coexistent continua and for multicomponent reacting gas mixtures. Quarterly of Applied Mathematics, 17 (1). pp. 43-54. ISSN 0033-569X. http://resolver.caltech.edu/CaltechAUTHORS:20110125-094239088

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Abstract

The equations for conservation of mass, momentum, and energy are derived for a set of independent, coexistent continua obeying the laws of dynamics and thermodynamics. The idea of a control volume and a control surface for each continuum is used in the analysis. The derived results are practically identical with relations obtained previously by Th. von Kármán. A direct comparison is conducted between the continuum theory results and those obtained from kinetic theory by assuming that, for each of the species, the kinetic theory definitions apply. It is found that the new terms appearing in the conservation equations derived from continuum theory are precisely those which are required to make these equations identical with the results obtained from the kinetic theory of multicomponent, reacting gas mixtures. However, the continuum theory forms of the equations are not useful because they require knowledge of the transport properties for individual species in the mixture.


Item Type:Article
Additional Information:© 1959 Brown University. Received December 13, 1957. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract AF 18(603)-146.
Group:Guggenheim Jet Propulsion Center
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Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)AF 18(603)-146
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Guggenheim Jet Propulsion Center UNSPECIFIED
Record Number:CaltechAUTHORS:20110125-094239088
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20110125-094239088
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:21876
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:25 Jan 2011 22:14
Last Modified:26 Dec 2012 12:52

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