We study the processes of thermodiffusion with regard for the decay of a substance in a two-phase randomly inhomogeneous layered strip. The statement of a contact-boundary-value problem is formulated on the basis of the theory of binary systems with conditions of perfect contact for temperature and imperfect conditions for concentration. The system of equations of thermodiffusion of decaying particles is obtained for the entire body. The system of integrodifferential equations equivalent to the source contact boundary-value problem is formulated. Its solution is constructed by the method of successive approximations. The random fields of temperature and concentration of decaying particles are found in the form of Neumann series. The conditions of absolute and uniform convergence of the series are established. The procedure of averaging of the random fields is carried out over the ensemble of phase configurations with uniform distribution function.
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References
D. K. Belashchenko, Transfer Phenomena in Liquid Metals and Semiconductors [in Russian], Atomizdat, Moscow (1970).
Ya. Yo. Burak, E. Ya. Chaplya, and O. Yu. Chernukha, Continual Thermodynamic Models of the Mechanics of Solid Solutions [in Ukrainian], Naukova Dumka, Kiev (2006).
V. S. Vladimirov, Equations of Mathematical Physics, M. Dekker, New York (1971).
A. V. Lykov and Yu. A. Mikhailov, Theory of Heat and Mass Transfer, Israel Program for Sci. Translations, Jerusalem (1965).
A. Münster, Chemische Thermodynamik, Chemie, Berlin (1969).
B. V. Savinykh and F. M. Gumerov, “Mutual diffusion of liquids in electric fields,” Khim. Komp. Model. Butler. Soobshch., No. 10 (Spec. Issue, Suppl.), 213–220 (2002).
R. A. Sadykov, “Numerical analysis of the thermal engineering characteristics of enveloping structures with regard for thermal diffusion and moisture filtration,” in: Materials of Internat. Sci.-Eng. Confer. “Theoretical Foundations of Heat-Gas-Supply and Ventilation (November 23–25, 2005, Moscow),” Moscow State Building Univ., Moscow (2005), pp. 115–121.
L. P. Khoroshun, “Methods of theory of random functions in problems of macroscopic properties of microinhomogeneous media,” Prikl. Mekh., 14, No. 2, 3–17 (1978); English translation: Int. Appl. Mech., 14, No. 2, 113–124 (1978).
E. Ya. Chaplya, O. Yu. Chernukha, V. E. Honcharuk, and A. R. Tors’kyi, Processes of Transfer of Decaying Substances in Heterogeneous Media [in Ukrainian], Evrosvit, Lviv (2010).
D. Łydżba, “Homogenization theories applied to porous media mechanics,” J. Theor. Appl. Mech. (Poland), 36, No. 3, 657–679 (1998).
D. Reith and F. Müller-Plathe, “On the nature of thermal diffusion in binary Lennard–Jones liquids,” J. Chem. Phys., 112, No. 5, 2436–2443 (2000).
M. R. Sørensen, K. W. Jacobsen, and H. Jónsson, “Thermal diffusion processes in metal-tip-surface interactions: contact formation and adatom mobility,” Phys. Rev. Lett., 77, No. 25, 5067–5070 (1996).
L.-Z. Zhang and S.-M. Huang, “Coupled heat and mass transfer in a counter flow hollow fiber membrane module for air humidification,” Int. J. Heat Mass Transf., 54, Nos. 5-6, 1055–1063 (2011).
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 57, No. 3, pp. 143–154, July–September, 2014.
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Chernukha, O.Y., Goncharuk, V.E. & Davydok, A.E. Mathematical Modeling of the Processes of Thermodiffusion of the Decaying Substance in a Stochastically Inhomogeneous Layered Strip. J Math Sci 217, 312–329 (2016). https://doi.org/10.1007/s10958-016-2975-y
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DOI: https://doi.org/10.1007/s10958-016-2975-y