High Temperature

, Volume 56, Issue 2, pp 223–228 | Cite as

The Variational Form of the Mathematical Model of a Thermal Explosion in a Solid Body with Temperature-Dependent Thermal Conductivity

  • V. S. Zarubin
  • G. N. Kuvyrkin
  • I. Yu. Savel’eva
Heat and Mass Transfer and Physical Gasdynamics
  • 7 Downloads

Abstract

The variational form of a mathematical model of a thermal explosion has been developed based on a variational formulation of a nonlinear problem of stationary thermal conductivity in a homogeneous solid body. The model takes the temperature dependence of the thermal conductivity of a solid body into account. The presented example of quantitative analysis of the model demonstrates a method for finding the combination of parameters for determining a thermal explosion in a plate with an exponential temperature dependence of the thermal conductivity. At the same time, the analysis allows one to identify the number of steadystate temperature distributions inside a body whose energy release intensifies with a temperature increase.

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • V. S. Zarubin
    • 1
  • G. N. Kuvyrkin
    • 1
  • I. Yu. Savel’eva
    • 1
  1. 1.Bauman Moscow State Technical UniversityMoscowRussia

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