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Composites: Mechanics, Computations, Applications: An International Journal
ESCI SJR: 1.182 SNIP: 0.125 CiteScore™: 0.23

ISSN Print: 2152-2057
ISSN Online: 2152-2073

Composites: Mechanics, Computations, Applications: An International Journal

DOI: 10.1615/CompMechComputApplIntJ.v1.i3.30
pages 245-265

AVERAGING OF THE HEAT CONDUCTION EQUATIONS WITH ACCOUNT FOR THE CONVECTIVE MECHANISM OF HEAT TRANSFER

A. N. Vlasov
Institute of Applied Mechanics, Russian Academy of Sciences, 7 Leningradsky Ave., Moscow, 125040, Russian Federation
Viktoria L. Savatorova
University of Nevada Las Vegas, Las Vegas, Nevada; National Research Nuclear University "MEPhI", Moscow, Russia
Alexei V. Talonov
National Research Nuclear University "MEPhI", Moscow, Russia; National University of Science and Technology MISiS, Moscow, Russia

ABSTRACT

Within the framework of asymptotic averaging of differential equations with rapidly oscillating coefficients the asymptotics of the solution of the joint problem of heat conduction and filtration for inhomogeneous media with a periodic structure is being built (up to the terms of the second order of smallness), which allows one to take into account convective heat transfer. The problem is solved in nonlinear statement when the dependence of thermophysical and filtration properties on temperature is taken into consideration. General equations to describe the processes of heat conduction with account for conductive and convective mechanisms of heat transfer, as well as for the possibility of phase transitions are obtained. The solution of the problem on the propagation of heat on heating of a semi-infinite laminated medium has been solved with account for the processes of phase transitions and subsequent filtration of a liquid phase.

REFERENCES

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  2. Landau, L. D. and Lifshits, E. M., Girdodinamika (Hydrodynamics) .

  3. Loitsyanskii, L. G., Mekhanika zhidkosti i gaza (Mechanics of Liquids and Gases) .

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  5. Vlasov, A. N., Savatorova, V. L., and Talonov, A. V., Use of the method of asymptotic averaging for solving the problems of heat conduction with phase transitions.

  6. Kapranov, V. E. and Perlshtein, G. Z., Investigation of the transverse scattering of heat in water-saturated filtering grounds.