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

Authors:
W. Nachbar, F. Williams and S. S. Penner

Journal:
Quart. Appl. Math. **17** (1959), 43-54

MSC:
Primary 76.00

DOI:
https://doi.org/10.1090/qam/102982

MathSciNet review:
102982

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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.

**[1]**Hans Wolfgang Liepmann and Allen E. Puckett,*Introduction to Aerodynamics of a Compressible Fluid*, John Wiley & Sons, Inc., New York, 1947. MR**0021780****[2]**S. Goldstein,*Modern developments in fluid dynamics*, vol. I, Clarendon Press, Oxford, 1938, pp. 95-105**[3]**L. Prandtl,*Essentials of fluid dynamics*, Blackie and Sons, Ltd., Glasgow, 1952, chap. II etc.**[4]**S. Chapman and T. G. Cowling,*The mathematical theory of non-uniform gases*, Cambridge University Press, Cambridge, 1953, chap. 3**[5]**J. O. Hirschfelder, C. F. Curtiss and R. B. Bird,*Molecular theory of gases and liquids*, John Wiley and Sons, New York, 1954, chap. 7**[6]**Th. von Kármán,*Sorbonne Lectures*, Paris, France, 1950-51**[7]**S. S. Penner,*Introduction to the study of chemical reactions in flow systems*, Butterworths' Scientific Publications, London, 1955, chap. 2**[8]**For related treatments, see the following: J. Stefan, Sitzber, Akad, Wiss. Wien**63**, 63 (1871); C. Eckart, Phys. Rev.**58**, 267 (1940); C. Truesdell, J. Rational Mech. Anal.**1**, 125 (1952)**[9]**R. Courant and K. O. Friedrichs,*Supersonic Flow and Shock Waves*, Interscience Publishers, Inc., New York, N. Y., 1948. MR**0029615**

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DOI:
https://doi.org/10.1090/qam/102982

Article copyright:
© Copyright 1959
American Mathematical Society