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TVT, 2018, Volume 56, Issue 2, Pages 235–240 (Mi tvt10796)  

Heat and Mass Transfer and Physical Gasdynamics

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. Savelyeva

Bauman Moscow State Technical University

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 steady-state temperature distributions inside a body whose energy release intensifies with a temperature increase.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 9.7784.2017/ΑΧ
9.2422.2017/ΟΧ
This work was supported by the Ministry of Education and Science of the Russian Federation (state tasks 9.7784.2017/BCh and 9.2422.2017/PCh).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.7868/S0040364418020102

Full text: PDF file (381 kB)
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English version:
High Temperature, 2018, 56:2, 223–228

Bibliographic databases:

UDC: 536.2
Received: 19.12.2016
Accepted:18.04.2017

Citation: V. S. Zarubin, G. N. Kuvyrkin, I. Yu. Savelyeva, “The variational form of the mathematical model of a thermal explosion in a solid body with temperature-dependent thermal conductivity”, TVT, 56:2 (2018), 235–240; High Temperature, 56:2 (2018), 223–228

Citation in format AMSBIB
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