Skip to main content
Log in

On the bounds of the thickness of a steady shock wave

  • Published:
Applied Scientific Research, Section A Aims and scope Submit manuscript

Summary

Following the reasoning of von Mises, the author attempts to answer the question, “Does the use of higher order Burnett terms from the solution of the Boltzmann equation in the von Mises approach improve the bounds of the thickness of steady shock?” The answer is a negative one.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Becker, R., Z. Phys.8 (1922) 361; Impact Waves and Detonation, Part. I. NACA, T. M. 505, 1929.

    ADS  Google Scholar 

  2. Bethe, H. A. and E. Teller, Deviations from Thermal Equilibrium in Shock Waves. Ballistic Research Laboratories Rep. X-117, Aberdeen Proving Grounds, Md.

  3. Broer, L. J. F., Appl. Sci. Res.A 2 (1951) 447; Appl. Sci. Res.A 3 (1952) 349.

    Article  MATH  MathSciNet  Google Scholar 

  4. Broer, L. J. F. and A. C. van den Bergen, Appl. Sci. Res.A 3 (1954) 157.

    Google Scholar 

  5. Chapman, S. and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, Cambridge Univ. Press 1939.

  6. Courant, R. and K. O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Co., New York 1948.

    MATH  Google Scholar 

  7. Cowan, R. and D. F. Hornig, J. Chem. Phys.18 (1950) 1008.

    Article  ADS  Google Scholar 

  8. Eggers, A. J. Jr., One-Dimensional Flows of an Imperfect Diatomic Gas, NACA T.N. 1861, Apr. 1949.

  9. Gilbarg, D., Amer. J. Math.73 (1951) 256.

    Article  MATH  MathSciNet  Google Scholar 

  10. Gilbarg, D. and D. Paolucci, J. Ration. Mech. Anal.2 (1953) 617.

    MathSciNet  Google Scholar 

  11. Grad, H., Comm. Pure Appl. Math.2 (1949) 331; Comm. Pure Appl. Math.5 (1952) 257.

    Article  MATH  MathSciNet  Google Scholar 

  12. Green, E. F., G. R. Cowan and D. F. Hornig, J. Chem. Phys.19 (1951) 427.

    Article  ADS  Google Scholar 

  13. Green, E. F. and D. F. Hornig, J. Chem. Phys.21 (1953) 617.

    Article  ADS  Google Scholar 

  14. Khosla, G., Some Considerations on the Influence of higher Order Terms on the Thickness of a steady Shock Wave. Thesis, Un. Illinois, Dept. Aero. Engng. 1952. (Unpublished).

  15. Ludford, G. S. S., J. Aero.18 (1951).

  16. Meyerhoff, L., J. Aero. Sci.17 (1950) 775.

    MATH  MathSciNet  Google Scholar 

  17. Meyerhoff, L. and H. J. Reissner, The standing one-dimensional Shock Wave under the Influence of temperature dependent Viscosity, Heat Conduction and Specific Heat; PIBAL, No. 150, Contr. N6ori-206, T.O.I., June 1949.

  18. Mises, v. R., J. Aero Sci.17 (1950) 551.

    Google Scholar 

  19. Morduchow, M. and P. A. Libby, J. Aero. Sci.16 (1949) 674.

    MathSciNet  Google Scholar 

  20. Mott-Smith, H. M., Phys. Rev.82 (1951) 885.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. Prandtl, L., Z. f. fas Ges. Turbinen-Wesen3 (1906) 241.

    Google Scholar 

  22. Primakoff, H., J. Acoust. Soc. Amer.14 (1942) 14.

    Article  ADS  Google Scholar 

  23. Puckett, A. E. and H. J. Stewart, Quart. Appl. Mathem.7 (1950) 457.

    MATH  MathSciNet  Google Scholar 

  24. Rankine, W. J. M., Proc. Roy. Soc. London18 (1870) 80.

    Google Scholar 

  25. Rayleigh, Lord J., Proc. Roy. Soc. LondonA 84 (1910) 247.

    Article  ADS  Google Scholar 

  26. Reissner, H.J. and L. Meterhoff, On the Structure of Shock Waves in a viscous, heat conducting compressible Flow; Part I: Shock Waves in one dimensional Flow with constant coefficients of Viscosity and Conductivity; Report submitted to Project Squid, Princeton, N.J., Febr. 1948; A Contribution to the exact Solutions of the Problem of a one-dimensional Shock Wave in a viscous, heat conducting Fluid. PIBAL, No. 138, Contr. N6ori-206, T.O.I., Nov. 1948.

  27. Shapiro, A. H. and S. J. Kline, J. Appl. Mech.21 (1954) 185.

    MATH  Google Scholar 

  28. Taylor, G. I., Proc. Roy. Soc. LondonA 84 (1910) 371.

    Article  ADS  Google Scholar 

  29. Thomas, L. H., J. Chem. Phys.12 (1944) 449.

    Article  ADS  Google Scholar 

  30. Vileta, F., On some Singularities in the Theory of Shocks based on Kinetic Theory of Gases; Thesis, University of Illinois, Dept. Aero. Engng, Febr. 1957 (unpublished).

  31. Wang Chang, C. S., On the Theory of the Thickness of weak Shock Waves; Univ. Michigan, Dept. Engng. Research, Rep. UMH-3-F (APL/JHU CM-503), 1948.

  32. Weyl, H., Comm. Pure Appl. Math.2 (1949).

  33. Rosen, P., J. Chem. Phys.22 (1954) 1045.

    Article  MathSciNet  ADS  Google Scholar 

  34. Broer, L. J. F., Appl. Sci. Res.A 5 ((1955) 76.

    MathSciNet  Google Scholar 

  35. Flook, W. M. Jr. and D. F. Hornig, J. Chem. Phys.23 (1955) 816.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

v. Krzywoblocki, M.Z. On the bounds of the thickness of a steady shock wave. Appl. sci. Res. 6, 337–350 (1957). https://doi.org/10.1007/BF03185039

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03185039

Keywords

Navigation