Abstract
A mathematical model of heat transfer that is complicated by phase transitions in a moving layer is proposed. An analytical solution is obtained using fractional differential-integral calculus. An expression for the temperature in the front as a function of the phase-transition boundary velocity is derived, from which an expression for the front velocity is found. The theoretical expression of the front velocity fits experimental data. A method for estimating the activation energy is proposed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Pfann, W.G., Zone Melting, New York: Wiley, 1966. Translated under the title Zonnaya plavka, Moscow: Mir, 1970.
Maksimov, E.I., Dokl. Akad. Nauk SSSR, 1970, vol. 191, no.4, pp. 1091–1093.
Pomogailo, A.D., Davtyan, S.P., Tomchak, A.A., Dzhardimalieva, G.I., Savost’yanov, V.S., and Ivanchenko, P.A., Solid-Phase Frontal Polymerization of Metal-Containing Monomers, Mater. VIII Vsesoyuz. simp. po goreniyu i vzryvu “Kinetika i gorenie” (Proc. VIII All-Union Symp. on Combustion and Explosion “Kinetics and Combus-tion”), Chernogolovka, 1986, pp. 8–9.
Dzhardimalieva, G.I., Pomogailo, A.D., and Volpert, V.A., Frontal Polymerization of Metal-Containing Monomer, J. Inorg. Organometal. Polymers, 2002, vol. 12, nos.1–2, pp. 1–9.
Wohrle, D. and Pomogailo, A.D., Metal Complexes and Metals in Macromolecules. Synthesis, Structures, and Properties, Weinheim: Wiley-VCH, 2003.
Kholpanov, L.P., Zakiev, S.E., and Fedotov, V.A., Neumann-Lame-Clapeyron-Stefan Problem and Its Solution Using Fractional Differential-Integral Calculus, Teor. Osn. Khim. Tekhnol., 2003, vol. 37, no.2, pp. 128–137 [Theor. Found. Chem. Eng. (Engl. Transl.), vol. 37, no. 2, pp. 113–121].
Babenko, Yu.I., Teplomassoobmen. Metod rascheta teplovykh i diffuzionnykh potokov (Heat and Mass Transfer: A Method for Calculation of Heat and Diffusion Fluxes), Leningrad: Khimiya, 1986.
Samko, S.G., Kilbas, A.A., and Marichev, O.I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya (Fractional Integrals and Derivatives and Some of Its Applications), Minsk: Nauka i Tekhnika, 1987.
Ditkin, V.A. and Prudnikov, A.P., Operatsionnoe ischislenie (Operational Calculus), Moscow: Vysshaya Shkola, 1966.
Author information
Authors and Affiliations
Additional information
__________
Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 3, 2005, pp. 243–250.
Original Russian Text Copyright © 2005 by Kholpanov, Zakiev, Pomogailo.
Rights and permissions
About this article
Cite this article
Kholpanov, L.P., Zakiev, S.E. & Pomogailo, A.D. Heat Transfer Complicated by Phase Transitions in a Moving Layer. Theor Found Chem Eng 39, 225–231 (2005). https://doi.org/10.1007/s11236-005-0068-6
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11236-005-0068-6