Russian Journal of Physical Chemistry B

, Volume 12, Issue 1, pp 91–97 | Cite as

Dual Variational Form of the Model of Thermal Explosion in a Quiescent Medium with Temperature-Dependent Thermal Conductivity

  • A. V. Attetkov
  • V. S. Zarubin
  • G. N. Kuvyrkin
Combustion, Explosion, and Shock Waves


Based on the dual variational formulation of the nonlinear stationary heat conduction problem, a mathematical model is constructed that describes the temperature state of a stationary medium in a volume of an arbitrary shape. The thermal conductivity of the medium and the volumetric energy release depend on the temperature. This model is applied to analyzing the conditions of thermal explosion in an infinitely long circular cylinder for exponential temperature dependences of the above parameters. In the particular case of constant thermal conductivity of this cylinder, a comparison with the published results is carried out.


thermal explosion variational approach alternative functionals 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • A. V. Attetkov
    • 1
  • V. S. Zarubin
    • 1
  • G. N. Kuvyrkin
    • 1
  1. 1.Bauman Moscow State Technical UniversityMoscowRussia

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