536.2 Effective thermal conductivity of a composite in case of inclusions shape deviations from spherical ones

Zarubin V. S. (Bauman Moscow State Technical University), Kuvyrkin G. N. (Bauman Moscow State Technical University), Savelyeva I. Y. (Bauman Moscow State Technical University)


doi: 10.18698/2309-3684-2014-4-317

On the basis of mathematical model of thermal interaction between inclusion and the matrix we estimated influence of inclusions deviations from spherical shape on the effective thermal conductivity coefficient of the composite and associated with such deviation a possible occurrence of the anisotropy of the composite with respect to the property of thermal conductivity. Using the dual variational formulation of the stationary problem of heat conduction in an inhomogeneous body we built bilateral estimates of effective thermal conductivity.

[1] Chudnovskiy A.F. Thermophysical characteristics of dispersed materials. Moscow, Fizmatgiz
Publ., 1962, 456 p.
[2] Missenard A. Conductivité thermique des solides, liquides, gaz et de leurs
mélanges. Editions Eyrolles, Paris, 1965 464 p.
[3] Dul'nev G.N., Zarichnyak Yu.P. Heat conductivity of mixes and composite materials. Leningrad,
Energiya Publ., 1974, 264 p.
[4] Han Z., Fina A. Thermal conductivity of carbon nanotubes and their polymer nanocomposites: A review. Progress in Polymer Science, vol. 7, 2011, pp. 914–944.
[5] Pierson H.O. Handbook of Carbon, Graphite, Diamond and Fullerences: Properties, Processing and Applications. New Jersey, Noyes Publications, 1993.
[6] Wypych G. Handbook of Fillers: Physical Properties of Fillers and Filled Materials. Toronto, ChemTec Publishing, 2000.
[7] Wang J., Carson J.K., North M.F., Cleland D.J. A new structural model of effective thermal conductivity for 92 heterogeneous materials with cocontinuous phases. Int. J. Heat Mass. Trans., 2008, vol. 51, рр. 2389−2397.
[8] Kats E.A. Fullerena, carbon nanotubes and nanoclusters. Family tree of forms and ideas. Moscow, LKI Publ., 2008, 296 p.
[9] Dresselhaus M.S., Dresselhaus G., Eklund P.C. Science of fullerenes and carbon nanotubes. San Diego, Academic Press, 1996.
[10] Zarubin V.S. Mathematical modeling in equipment. Moscow, BMSTU Publ., 2010, 496 p.
[11] Zarubin V.S., Kuvyrkin G.N. Mathematical models of mechanics and electrodynamics of continuous medium. Moscow, BMSTU Publ., 2008, 512 p.
[12] Maxwell C. Treatise on electricity and magnetism. Oxford, 1873.
[13] Carslaw H., Jaeger J. Conduction of Heat in Solids. 2nd ed. Oxford University Press, USA, 1959, 510 p.
[14] Eshelby J.D. Continual theory of dislocations. Coll. articles. Moscow, Inostrannaya literatura Publ.,
1963, 248 p.
[15] Zarubin V.S., Kuvyrkin G.N. Herald of the Bauman Moscow State Technical University. Series: Natural sciences, 2012, no. 3, pp. 76–85.
[16] Zarubin V.S., Kuvyrkin G.N., Savel'eva I.Yu. Heat conductivity of composites with spherical
inclusions. Saarbrucken, Deutschland: LAMBERT Academic Publishing, 2013, 77 p.
[17] Zarubin V.S. Engineering methods of the solution of problems of heat conductivity. Moscow,
Energoatomizdat Publ., 1983, 328 p.
[18] Zarubin V.S., Kuvyrkin G.N. Matematicheskoe modelirovanie i chislennye
metody. Mathematical Modeling and Computational Methods, 2014, no. 1, pp. 5–17.
[19] Abramovits M., Stigan I., reds. Directory of Functions
with Formulas, Graphs, and Mathematical Tables. Moscow, Nauka, 1979, 832 p.
[20] Shermergor T.D. Theory of elasticity of micronon-uniform environments. Moscow, Nauka, 1977, 400 p.

Zarubin V., Kuvyrkin G., Savelyeva I. Effective thermal conductivity of a composite in case of inclusions shape deviations from spherical ones. Маthematical Modeling and Coтputational Methods, 2014, №4 (4), pp. 3-17

Download article

Количество скачиваний: 681