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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Original Russian Text © V.S. Zarubin, G.N. Kuvyrkin, I.Yu. Savel’eva, 2018, published in Teplofizika Vysokikh Temperatur, 2018, Vol. 56, No. 2, pp. 235–240.
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Zarubin, V.S., Kuvyrkin, G.N. & Savel’eva, I.Y. The Variational Form of the Mathematical Model of a Thermal Explosion in a Solid Body with Temperature-Dependent Thermal Conductivity. High Temp 56, 223–228 (2018). https://doi.org/10.1134/S0018151X18010212
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DOI: https://doi.org/10.1134/S0018151X18010212