Ignition of reacting substances

  • A. M. Grishin


For the solution of problems in the ignition of reacting substances great mathematical difficulties have to be surmounted. An analytic solution is known for only one problem of this type [1]. In the present work with the example of a solution of two different problems in ignition theory, of independent interest, it was shown that all the mathematical difficulties can be overcome by the method of Shvets [2].


Mathematical Modeling Mechanical Engineer Industrial Mathematic Independent Interest Mathematical Difficulty 
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  1. 1.
    Ya. B. Zel'dovich, “Ignition theory,” Dokl. AN SSSR, vol. 150, no. 2, 1963.Google Scholar
  2. 2.
    M. E. Shvets, “Approximate solution of some problems in boundary layer hydrodynamics,” PMM, vol. 3, no. 3, 1949.Google Scholar
  3. 3.
    V. N. Vilyunov and O. V. Sidonskii, “Theory of ignition of condensed systems by hot surface,” Dokl. AN SSSR, vol. 152, no. 1, 1963.Google Scholar
  4. 4.
    A. E. Averson, V. V. Barzykin, and A. G. Merzhanov, “Ignition relationships for condensed explosive systems under ideal heat exchange at the surface,” Inzh. Fiz. Zh. [Journal of Engineering Physics], vol. 9, no. 2, 1965.Google Scholar
  5. 5.
    D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics [in Russian], Izd. AN SSSR, 1947.Google Scholar
  6. 6.
    L. S. Gandin, “Convergence of Shvets method,” PMM, vol. 14, no. 4, 1950.Google Scholar
  7. 7.
    H. C. Carslaw and J. C. Jager, Conduction of Heat in Solids, Oxford, Clarendon Press, 1959.Google Scholar
  8. 8.
    Ya. B. Zel'dovich, “Theory of ignition by hot surface,” Zh. Eksperim. i Teor. Fiz., no. 12, 1939.Google Scholar
  9. 9.
    Ya. B. Zel'dovich, “Flame propagation theory,” Zh. Fiz. Khim., vol. 22, no. 1, 1948.Google Scholar
  10. 10.
    D. B. Spalding, “Theory of laminar flame propagation,” Combustion and Flame, vol. 1, 287, 1957.Google Scholar
  11. 11.
    G. Rosen, “On the classification of the chemistry in combustion experiments,” Jet Propulsion, vol. 28, 839, 1958.Google Scholar
  12. 12.
    Ya. B. Zel'dovich, “Combustion theory of powders and explosives,” Zh. Eksperim. i Teor. Fiz., nos. 11–12, 1942.Google Scholar
  13. 13.
    V. B. Librovich, “Ignition of powders and explosives,” PMTF, no. 6, 1963.Google Scholar

Copyright information

© The Faraday Press, Inc. 1969

Authors and Affiliations

  • A. M. Grishin
    • 1
  1. 1.Saratov

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