Abstract
A direct relation in the form of a first‐order differential equation is obtained between the phase‐transformation depth (phase‐boundary position) and the Frank‐Kamenetskii parameter characterizing the intensity of chemical heat release. As a particular case, this equation yields a solution of the problem obtained previously for cylindrical and plane‐parallel reactors. The presence of a stable intermediate position of the interphase boundary is generalized to symmetric regions of an arbitrary (even fractional) dimension, which appears to have some physical meaning.
Similar content being viewed by others
REFERENCES
S. I. Khudyaev and A. M. Stolin, “Analysis of self-ignition conditions in a cylindrical volume in the frontal phase transformation,” Khim. Fiz., 3, No. 11, 1616-1621 (1984).
S. I. Khudyaev, A. M. Stolin, and S. V. Maklakov, “Thermal explosion under phase transformation conditions,” Combust. Expl. Shock Waves, 19, No. 5, 610-614 (1983).
D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics [in Russian], Nauka, Moscow (1987).
A. I. Volpert and S. I. Khudyaev, Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics [in Russian], Nauka, Moscow (1975).
S. I. Khudyaev, “Some estimates of eigenfunctions of spherically symmetric problems,” in: Numerical Methods of Solving Problems of Mathematical Physics [in Russian], Nauka, Moscow (1966), pp. 68-74.
S. A. Bostandzhiyan, A. G. Merzhanov, and S. I. Khudyaev, “Hydrodynamic thermal explosion,” Dokl. Akad. Nauk SSSR, 163, No. 1, 133-136 (1965).
S. A. Bostandzhiyan, A. G. Merzhanov, and S. I. Khudyaev, “Some problems of nonisothermal steady flow of a viscous liquid,” J. Appl. Mech. Tech. Phys., No. 5, 30-33 (1965).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Khudyaev, S.I. Effect of the Phase Transition on the Ignition Process. Combustion, Explosion, and Shock Waves 39, 644–649 (2003). https://doi.org/10.1023/B:CESW.0000007676.33964.03
Issue Date:
DOI: https://doi.org/10.1023/B:CESW.0000007676.33964.03