Effective Thermal Conductivity Coefficients of the Composites with Spheroidal Inclusions

Composites find broad application as structural and functional materials in different instrument devices. A substantial number of works are devoted to investigation of heat conduction ofcomposites. However the calculation formulas in these works are obtained, as a rule, either as a result of processing of experimental data as applied to particular materials or by means of a priori specification of the temperature distribution and the heat flow in models of heterogeneous bodies. The mathematical model of thermal energy transfer in the composite with inclusions of spheroidal shape is constructed. Based on the model, the effective thermal conductivity coefficients of this composite are found. To estimate the possible error of the obtained results, the dual variational formulation of the stationary heat conduction is applied. The results can be used for prediction of effective thermal conductivity coefficients of the composites modified with nanostructural elements (e.g., with fullerenes).

References

[1] Arzamasov B.N., Krasheninnikov A.I., Pastukhova Zh.P, A.G. Rakhshtadt Nauchnye osnovy materialovedeniya [Scientific fundamentals of materials science]. Moscow, MGTU im. N.E. Baumana Publ., 1994. 366 p.

[2] Van Vleck J.H. The theory of electric and magnetic susceptibilities. Oxford University Press, 1965. 384 p. (Russ. ed.: Van Flek L. Teoreticheskoe i prikladnoe materialovedenie. Moscow, Atomizdat Publ., 1975. 472 p.).

[3] Kats E.A. Fullereny, uglerodnye nanotrubki i nanoklastery. Rodoslovnaya form i idey [Fullerenes, carbon nanotubes and nanoclusters. Pedigree of forms and ideas]. Moscow, LKI Publ., 2008. 296 p.

[4] Cahn R.W., Haasen P. Physical metallurgy. Vol. 2. Amsterdam, North-Holland Physics Publ., 1983. 1040 p. (Russ. ed.: Kan R.U. Khaazen P. Fizicheskoe metallovedenie. T. 2. Moscow, Metallurgiya Publ., 1987. 624 p.).

[5] Carslaw H.S., Jaeger J.C. Conduction of heat in solids. Oxford, Clarendon Press, 1959. 520 p. (Russ. ed.: Karslou G., Eger D. Teploprovodnost’ tverdykh tel. Moscow, Nauka Publ., 1964. 488 p.).

[6] Zarubin V.S., Kuvyrkin G.N. The effective thermal conductivity of composites with ellipsoidal inclusions. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Ser. Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ. Ser. Nat. Sci.], 2012, no. 3, pp. 76-85 (in Russ.).

[7] Zarubin V.S., Kuvyrkin G.N., Savel’eva I.Yu. The effective thermal conductivity of composites with spherical inclusions. Tepl. Protsessy Tekh. [Therm. Processes Eng.], 2012. no. 10, pp. 470-474 (in Russ.).

[8] Zarubin V.S. Inzhenernye metody resheniya zadach teploprovodnosti [Engineering methods for solving problems of heat conduction]. Moscow, Energoatomizdat Publ., 1983. 329 p.

[9] 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.

[10] Adamesku R.A., Gel’d P.V., Mityushov E.A. Anizotropiya fizicheskikh svoystv metallov [Anisotropy of physical properties of metals]. Moscow, Metallurgiya Publ., 1985. 136 p.

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