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

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...

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Bibliographic Details
Published in:High temperature 2018-03, Vol.56 (2), p.223-228
Main Authors: Zarubin, V. S., Kuvyrkin, G. N., Savel’eva, I. Yu
Format: Article
Language:English
Subjects:
Atoms and Molecules in Strong Fields
Classical and Continuum Physics
Explosions
Heat and Mass Transfer and Physical Gasdynamics
Heat conductivity
Heat transfer
Industrial Chemistry/Chemical Engineering
Laser Matter Interaction
Materials Science
Mathematical models
Physical Chemistry
Physics
Physics and Astronomy
Quantitative analysis
Temperature
Temperature dependence
Thermal conductivity
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Summary: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.
ISSN:0018-151X
1608-3156
DOI:10.1134/S0018151X18010212