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.
- Hans Wolfgang Liepmann and Allen E. Puckett, Introduction to Aerodynamics of a Compressible Fluid, John Wiley & Sons, Inc., New York, 1947. MR 0021780
S. Goldstein, Modern developments in fluid dynamics, vol. I, Clarendon Press, Oxford, 1938, pp. 95-105
L. Prandtl, Essentials of fluid dynamics, Blackie and Sons, Ltd., Glasgow, 1952, chap. II etc.
S. Chapman and T. G. Cowling, The mathematical theory of non-uniform gases, Cambridge University Press, Cambridge, 1953, chap. 3
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
Th. von Kármán, Sorbonne Lectures, Paris, France, 1950-51
S. S. Penner, Introduction to the study of chemical reactions in flow systems, Butterworths’ Scientific Publications, London, 1955, chap. 2
For related treatments, see the following: J. Stefan, Sitzber, Akad, Wiss. Wien 63$^{2}$, 63 (1871); C. Eckart, Phys. Rev. 58, 267 (1940); C. Truesdell, J. Rational Mech. Anal. 1, 125 (1952)
- R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Publishers, Inc., New York, N. Y., 1948. MR 0029615
H. W. Liepmann and A. E. Puckett, Introduction to aerodynamics of a compressible fluid, John Wiley and Sons, New York, 1947, chap. 7
S. Goldstein, Modern developments in fluid dynamics, vol. I, Clarendon Press, Oxford, 1938, pp. 95-105
L. Prandtl, Essentials of fluid dynamics, Blackie and Sons, Ltd., Glasgow, 1952, chap. II etc.
S. Chapman and T. G. Cowling, The mathematical theory of non-uniform gases, Cambridge University Press, Cambridge, 1953, chap. 3
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
Th. von Kármán, Sorbonne Lectures, Paris, France, 1950-51
S. S. Penner, Introduction to the study of chemical reactions in flow systems, Butterworths’ Scientific Publications, London, 1955, chap. 2
For related treatments, see the following: J. Stefan, Sitzber, Akad, Wiss. Wien 63$^{2}$, 63 (1871); C. Eckart, Phys. Rev. 58, 267 (1940); C. Truesdell, J. Rational Mech. Anal. 1, 125 (1952)
R. Courant and K. O. Friedrichs, Supersonic flow and shock waves, Interscience Publishers, New York, 1948, Sec. 7
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Article copyright:
© Copyright 1959
American Mathematical Society
