Abstract
A method is proposed to determine the moment of ignition of a semi-infinite massif of a condensed material exposed to an external heat flux specified as an arbitrary function of time. The method uses the fractional-differentiation formalism. For large values of the heat flux, the calculation results coincide with the results obtained using well-known methods.
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References
A. G. Merzhanov and A. E. Averson, “The present state of the thermal ignition theory,” Combust. Flame, 16, 89–124 (1971).
A. E. Averson, “Ignition theory,” in: A. G. Merzhanov (ed.), Heat and Mass Transfer in Combustion Processes [in Russian], Chernogolovka (1980), pp. 16–36.
V. N. Vilyunov, Ignition Theory for Condensed Materials [in Russian], Nauka, Novosibirsk (1984).
R. S. Burkina and V. N. Vilyunov, Asymptotics of Problems of Combustion Theory [in Russian], Izd. Tomsk. Univ., Tomsk (1982).
R. S. Burkina, “Ignition of a porous solid by a radiation source,” Combust., Expl., Shock Waves, 31, No. 6, 627–634 (1995).
Yu. I. Babenko, Heat and Mass Transfer. A Method for Calculating Heat and Diffusion Fluxes [in Russian], Khimiya, Leningrad (1986).
D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics [in Russian], Nauka, Moscow (1987).
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives and Some of Their Applications [in Russian], Nauka Tekhnika, Minsk (1987).
R. R. Nigmatullin and M. Kh. Salakhov, “Regularized algorithm for calculating fractional derivatives,” Avtometriya, No. 6, 92–96 (1987).
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Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 2, pp. 23–28, March–April, 2006.
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Babenko, Y.I. Approximate method for solving problems of ignition theory. Combust Explos Shock Waves 42, 144–148 (2006). https://doi.org/10.1007/s10573-006-0032-8
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DOI: https://doi.org/10.1007/s10573-006-0032-8