Estimations of the parameters of a thermal explosion in a triaxial ellipsoid

Abstract

The formulation of the nonlinear problem corresponding to the process of stationary heat conduction in homogeneous triaxial ellipsoid with increasing temperature and intensity of volumetric energy release was used to build a variational form of a mathematical model of this process. This form includes a functional defined on a set of continuous and piecewise differentiable functions that approximate the temperature distribution in the volume of an ellipsoid and take a given value of temperature on its surface. An analysis of the stationary points of the functional makes it possible to estimate the combination of determining parameters corresponding to the temperature distribution in the ellipsoid before the occurrence of a thermal explosion. Comparison of the integral error caused by the use of various approximating functions allows to choose the function that most accurately describes the temperature state of the ellipsoid preceding the thermal explosion. Estimations of the parameters of the thermal explosion are obtained under the assumption of an exponential increase in the intensity of volumetric energy release in an ellipsoid with increasing temperature.

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Acknowledgements

This work was supported by Ministry of Science and Higher Education of the Russian Federation [grant nos. 0705-2020-0032].

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Correspondence to I. Y. Savelyeva.

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Kuvyrkin, G.N., Savelyeva, I.Y. & Zarubin, V.S. Estimations of the parameters of a thermal explosion in a triaxial ellipsoid. Z. Angew. Math. Phys. 71, 113 (2020). https://doi.org/10.1007/s00033-020-01340-6

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Keywords

  • Variational form of the model
  • Stationary functional point
  • Thermal explosion
  • Temperature state

Mathematics Subject Classification

  • Primary 80M30
  • Secondary 97M50