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APPLICATION OF HEAT-BALANCE INTEGRAL METHOD TO CONJUGATE THERMAL EXPLOSION

ABSTRACT
Conjugate thermal explosion is an extension of the classical theory, proposed and studied recently by the author. The paper reports application of heat-balance integral method for developing phase portraits for systems undergoing conjugate thermal explosion. The heat-balance integral method is used as an averaging method reducing partical differential equation problem to the set of first-order ordinary differential equations. The latter reduced problem allows natural interpretation in appropriately chosen phase space. It is shown that, with the help of heat-balance integral technique, conjugate thermal explosion problem can be described with a good accuracy by the set of non-linear first-order differential equations involving complex error function. Phase trajectories are presented for typical regimes emerging in conjugate thermal explosion. Use of heat-balance integral as a spatial averaging method allows efficient description of system evolution to be developed.
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PAPER SUBMITTED: 2008-01-15
PAPER REVISED: 2008-03-10
PAPER ACCEPTED: 2008-03-10
DOI REFERENCE: https://doi.org/10.2298/TSCI0902073N
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2009, VOLUME 13, ISSUE 2, PAGES [72 - 80]
REFERENCES
  1. Semenov, N. N., On the Theory of Combustion Processes (in Russian), Journal of the Russian Physical and Chemical Society, 60 (1928), pp. 247-250
  2. Frank-Kamenetskii, D. A., Temperature Distribution in a Reactive Vessel and the Steady-State Theory of Thermal Explosion, Journal of Physical Chemistry, 13 (1939), 6, pp. 738-755
  3. Barzykin, V. V., Thermal Regimes of Exothermal Reactions, Institute of Structural Macrokinetics, Russian Academy of Sciences (ISMAN), Chernogolovka, Russia, 2004
  4. Frank-Kamenetskii, D. A., Diffusion and Heat Transfer in Chemical Kinetics, Nauka, Moscow, 1987
  5. Merzhanov, A. G., Dubovitsky, F. I., Modern Theory of Thermal Explosion (in Russian), Progress in Chemistry, 35 (1966), pp. 656-683
  6. Zeldovich, Y. B., et al., Mathematical Theory of Combustion and Explosion, Nauka, Moscow, 1980
  7. Gelfand, I. M., Problems of the Theory of Quasi-Linear Equations (in Russian), Progress in Mathematical Sciences, 14 (1959), 2, pp.137-154
  8. Novozhilov, V., Critical Conditions for Conjugate Thermal Explosion, Combustion Theory and Modelling 12 (2008), 3, pp. 433-449
  9. Goodman, T. R., The Heat Balance Integral and its Application to Problems Involving a Change of Phase - Transactions of ASME, 80 (1958), 2, pp. 335-342

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence