Influence of the Mutual Arrangement of Spherical Inclusions on the Thermal Conductivity of the Composite

Composites with spherical inclusions are widely used as constructional and functional materials. Effective thermal conductivity coefficient of this composite depends on location and volume concentration of inclusions. The calculated dependencies which allowed to determine bilateral estimates of the effective thermal conductivity coefficient of matrix structure composite with spherical inclusions are obtained. These dependences take into account the influence of mutual arrangement of inclusions. Options of such locations corresponding repeating cells of simple cubic, body-centered and facet-centered crystal lattices are considered. It was determined by means of calculation that the difference of bilateral estimates is the lowest for the first option of the above. The comparison of these estimates with bilateral estimates defined from the theory of mixes and variation approach and also with the assessment obtained by a method of self-consistency is carried out. Submitted dependencies can be used for prediction of the effective thermal conductivity coefficient of the matrix structure composite.

References

[1] Odelevskiy V.I. Calculation of generalized conductivity of heterogeneous systems. Sov. Phys.: Techn. Phys. [Tech. Phys.], 1951, vol. 21, iss. 6, pp. 667-685 (in Russ.).

[2] Chudnovskiy A.F. Teplofizicheskie kharakteristiki dispersnykh materialov [Thermal and physical properties of dispersed materials]. Moscow, Fizmatlit Publ., 1962.456 p.

[3] Carslaw H., Jaeger J. Conduction of heat in solids. 2nd ed. USA, Oxford University Press, 1959. 510 p. (Russ. ed.: Karslou G., Eger D. Teploprovodnost’ tverdykh tel. Moscow, Nauka Publ., 1964. 488 p.).

[4] Missenard A. Conductivite thermique des solides, liquide, gaz et leurs melanges. Front Cover. Andre Missenard. Editions Eyrolles, 1965. 554 p. (Russ. Ed.: Misnar A. Teploprovodnost’ tverdykh tel, zhidkostey, gazov i ikh kompozitsiy [The heat conductivity of solids, liquids, gases and their compositions]. Moscow, Mir Publ., 1968. 464 p.).

[5] Dul’nev G.N., Zarichnyak Yu.P. Teploprovodnost’ smesey i kompozitsionnykh materialov [The thermal conductivity of composite materials and mixtures] Moscow, Energiya Publ., 1974. 264 p.

[6] Shermergor T.D. Teoriya uprugosti mikroneodnorodnykh sred [The theory of elasticity of micro-inhomogeneous media]. Moscow, Nauka Publ., 1977. 400 p.

[7] Christensen R.M. Mechanics of composite materials. N.Y., Wiley-Interscience Publ., 1979. 348 p. (Russ. ed.: Kristensen R.M. Vvedenie v mekhaniku kompozitov. Moscow, Mir Publ., 1982. 334 p.).

[8] Zarubin V.S., Kuvyrkin G.N., Savel’eva I.Yu. The effective thermal conductivity of composite with spherical inclusions. Tepl. prots. v tekh. [Therm. process. in engineering], 2012, no. 10, pp. 470-474 (in Russ.).

[9] Zarubin V.S., Kuvyrkin G.N., Savel’eva I.Yu. [Comparative analysis of estimations of thermal conduction of a composite with spherical inclusions]. Jelektr. Nauchno-Tehn. Izd. "Nauka i obrazovanie" MGTU im. N.E. Baumana [El. Sc.-Tech. Publ. "Science and Education" of Bauman MSTU], 2013, no. 7 (in Russ.). Available at: http://technomag.edu.ru/doc/569319.html (accessed 17.12.2013) DOI: 10.7463/0713.0569319

[10] Zarubin V.S., Kuvyrkin G.N., Savel’eva I.Yu. Teploprovodnost’ kompozitov s sharovymi vklyucheniyami [The thermal conductivity of composites with spherical inclusions]. Saarbrücken, Deutschland, LAP Publ., 2013. 77 p.

[11] Jackson J.L., Coriell S.R. Transport coefficients of composite materials. J. Appl. Phys., 1968, vol. 39, no. 5, pp. 2349-2354.

[12] Coriell S.R., Jackson J.L. Bounds on transport coefficients of two-phase materials. J. Appl. Phys., 1968, vol. 39, no. 10, pp. 4733-4736.

[13] Zarubin V.S., Zarubin S.V., Kuvyrkin G.N. Mathematical simulation of heat transfer in unidirectional fiber composite. Jelektr. Nauchno-Tehn. Izd. "Nauka i obrazovanie" MGTU im. N.E. Baumana [El. Sc.-Tech. Publ. "Science and Education" of Bauman MSTU], 2014, no. 1 (in Russ.). Available at: http://technomag.edu.ru/doc/657262.html (accessed 05.01.2014). DOI: 10.7463/0114.0657262

[14] Zarubin V.S., Kuvyrkin G.N., Savel’eva I.Yu. The influence of relative position of fibers on the thermal conductivity of unidirectional fiber composites. Izv. Vyssh. Uchebn. Zaved., Mashinostr. [Proc. Univ., Mech. Eng.], 2014, no. 2, pp. 20-28 (in Russ.).

[15] Zarubin V.S. Inzhenernye metody resheniia zadachvteploprovodnosti [Engineering methods for solving problems of heat conduction]. Moscow, Energoatomizdat Publ., 1983. 328 p.

[16] Zarubin V.S., Kuvyrkin G.N. Bilateral estimates of the thermal resistance of an inhomogeneous solid body. Teplofiz. Vys. Temp. [High Temp.], 2013, vol. 51, no. 4, pp. 578-585 (in Russ.).

[17] Zarubin V.S., Kuvyrkin G.N. Matematicheskie modeli mekhaniki i elektrodinamiki sploshnoy sredy [Mathematical models of mechanics and electrodynamics of continuous media]. Moscow, MGTU im. N.E. Baumana Publ., 2008. 512 p.

[18] Gradshteyn I.S., Ryzhik I.M. Tablitsy integralov, summ, ryadov i proizvedeniy [Tables of integrals, sums, series and products]. Moscow, Fizmatgiz Publ., 1963. 1100 p. (Engl. Ed.: Gradshteyn I.S., Ryzhik I.M. Table of integrais, series, and products. Ed. by Alan Jeffrey. 4th ed. New York, Sydney, Academic Press, 1980. 1160 p.).

[19] Golovin N.N., Zarubin V.S., Kuvyrkin G.N. Mixture models of composite mechanics. P. 1. Thermal mechanics and thermoelasticity of multicomponent mixture. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2009, no. 3, pp. 36-49 (in Russ.).

[20] Zarubin VS., Kuvyrkin G.N., Savel’eva I.Yu. Evaluation of effective thermal conductivity of composites with ball inclusions by the method of self-consistency. Jelektr. Nauchno-Tehn. Izd. "Nauka i obrazovanie" MGTU im. N.E. Baumana [El. Sc.-Tech. Publ. "Science and Education" of Bauman MSTU], 2013, no. 9 (in Russ.). Available at: http://technomag.edu.ru/doc/601512.html (accessed 17.12.2013). DOI: 10.7463/0913.0601512