Russian Aeronautics

, Volume 61, Issue 2, pp 252–256 | Cite as

Critical Conditions of Thermal Explosion Considering Space-Temporal Nonlocality

  • V. A. KudinovEmail author
  • A. V. Eremin
  • I. V. Kudinov
  • V. V. Zhukov
Aircraft and Rocket Engine Theory


The equation for locally non-equilibrium heat exchange with nonlinear internal heat source was obtained by using Fourier’s law formula with the relaxation of heat flux and temperature gradient. The thermal conductivity problem for the infinite plate was studied by the numerical method at nonsymmetrical boundary conditions of the third kind. The conclusion was made that the thermal explosion delay time considerably increased as compared to the case of neglecting the space-temporal nonlocality.


local non-equilibrium heat exchange nonlinear internal heat source relaxation factors estimation of thermal explosion possibility 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kudinov, V.A., Eremin, A.V., and Stefanyuk, E.V., Critical Conditions for Thermal Explosion in a Plate with a Nonlinear Heat Source, Problemy Mashinostroeniya i Nadezhnosti Mashin, 2016, no. 1, pp. 38–43.Google Scholar
  2. 2.
    Kudinov, V.A., Eremin, A.V., and Zhukov, V.V., Mathematical Models of Heat Ignition and Explosion Considering Local Non-Equilibrium of Processes, Journal of Physics: Conference Series, 2017, vol. 891, pp. 1–4.Google Scholar
  3. 3.
    Sobolev, S.L., Transport Processes and Traveling Waves in Systems with Local Nonequilibrium, Uspekhi Fizicheskikh Nauk, 1991, vol. 161, no. 3, pp. 5–29.CrossRefGoogle Scholar
  4. 4.
    Sobolev, S.L., Local Non-Equilibrium Transport Models, Uspekhi Fizicheskikh Nauk, 1997, vol. 167, no. 10, pp. 1095–1106.CrossRefGoogle Scholar
  5. 5.
    Jou, D., Lebon, G., and Casas-Vázquez, J., Extended Irreversible Thermodynamics, Springer-Verlag Berlin Heidelberg, 2001.CrossRefzbMATHGoogle Scholar
  6. 6.
    Kirsanov, Yu.A., Kirsanov, A.Yu., Gil’fanov, K.Kh., and Yudakhin, A.E., On Measurement of the Thermal Relaxation Time in Transient Thermal Processes of Solids, Izv. Vuz. Av. Tekhnika, 2015, vol. 58, no. 3, pp. 3–8 [Russian Aeronautics (Engl. Transl.), vol. 58, no. 3, pp. 251–257].Google Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  • V. A. Kudinov
    • 1
    Email author
  • A. V. Eremin
    • 1
  • I. V. Kudinov
    • 1
  • V. V. Zhukov
    • 1
  1. 1.Samara State Technical UniversitySamaraRussia

Personalised recommendations