﻿ Evaluation of Effective Heat Conductivity of Composite Materials by the Moments Method | Herald of the Bauman Moscow State Technical University. Natural Sciences
|

# Evaluation of Effective Heat Conductivity of Composite Materials by the Moments Method

 Authors: Pugachev O.V., Han Zaw Htun Published: 10.08.2016 Published in issue: #4(67)/2016 DOI: 10.18698/1812-3368-2016-4-28-39 Category: Physics | Chapter: Physics and Technology of Nanostructures, Nuclear and Molecular Physics Keywords: effective heat conductivity coefficient, composite material, computer simulation, momentum of heat energy, random motion, confidence interval

The purpose of the research was to elaborate a new method of finding the effective heat conductivity coefficient of a composite material. As an example, we consider a matrix with ball inclusions of a material having another heat conductivity, the heat contact being ideal. The process of heat conduction is modeled via random motion of virtual heat particles. The speed of diffusion in each material is proportional to its temperature conductivity coefficient. When a particle is passing from one material to another, one having smaller heat conductivity, it is reflected from the frontier with a certain probability. We formulate an estimate of heat conductivity via moment of heat energy, this value is exactly known for a homogeneous material, and this estimate is statistically evaluated for composite materials. A computing experiment models the process of heat conduction through a layer of a composite material, having heated one side of the layer at the start. For a layer of a composite, we perform a multiple computational experiment modeling heat conduction, and, having processed the experiment results statistically, we obtain confidence intervals for the effective temperature conductivity and heat conductivity coefficients. We have considered inclusions of materials with heat conductivity coefficients differing from those of the matrix in 3 times up or down, and with zero heat conductivity. Ball inclusions of equal size were situated in a cubic order or chaotically. In series of 4300 randomly moving particles, in all cases considered, the difference between the effective heat conductivity coefficients and those calculated by other methods does not exceed a statistical error. The method elaborated makes it possible to obtain effective heat conductivity coefficients for composites with inclusions of any size and shape; it can be applied also in a case of inclusions of several materials. The results obtained are reliable, their exactness is limited only by the power of computers.

## References

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

[2] Missenard Andre. Conductivite thermique des solides, liquides, gas et de leurs melanges. Lditions eyrolles, Paris, 1965.

[3] Shermergor T.D. Teoriya uprugosti mikroneodnorodnykh sred [Theory of elasticity of micro-inhomogeneous media]. Moscow, Nauka Publ., 1977. 399 p.

[4] Zarubin V.S. Inzhenernye metody resheniya zadach teploprovodnosti [Engineering methods for solving problems of thermal conductivity]. Moscow, Energoatomizdat Publ., 1983. 328 p.

[5] Khoroshun L.P., Soltanov N.S. Termouprugost’ dvukhkomponentnykh smesey [Thermoelasticity of two-component mixtures]. Kiev, Nauk. dumka Publ., 1984. 111 p.

[6] Zarubin V.S., Kuvyrkin G.N., Savel’eva I.Yu. The effective thermal conductivity of composites with spherical inclusions. Teplovye protsessy v tekhnike [Thermal Processes in Engineering], 2012, no. 10, pp. 470-474 (in Russ.).

[7] Zarubin V.S., Kuvyrkin G.N., Savel’eva I.Yu. Evaluation of effective thermal conductivity of composites with ball inclusions by the method of self-consistency. Nauka i obrazovanie. MGTU im. N.E. Baumana [Science & Education of the Bauman MSTU. Electronic Journal], 2013, no. 9. DOI: 10.7463/0913.0601512 Available at: http://technomag.bmstu.ru/en/doc/601512.html

[8] Zarubin V.S., Kotovich A.V., Kuvyrkin G.N. Estimates of the effective coefficient of heat conductivity of a composite with anisotropic ball inclusions. Izvestiya RAN. Energetika [Proceedings of RAS. Power Engineering], 2012, no. 6, pp. 118-126 (in Russ.).

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

[10] Zarubin V.S., Kuvyrkin G.N., Savel’eva I.Yu. Comparative analysis of estimations of heat conduction of a composite with ball inclusions. Nauka i obrazovanie. MGTU im. N.E. Baumana [Science & Education of the Bauman MSTU. Electronic Journal], 2013, no. 7. DOI: 10.7463/0713.0569319 Available at: http://technomag.bmstu.ru/en/doc/569319.html

[11] Yankovskiy A.P. Numerical-analytical modeling of thermal conductivity in a spatially reinforced composites under intense heat impact. Teplovye protsessy v tekhnike [Therm. Processes Eng.], 2011, vol. 3, no. 11, pp. 500-516 (in Russ.).

[12] Chen Y.-M., Ting J.-M. Ultra high thermal conductivity polymer composites. Carbon, 2002, vol. 40, pp. 359-362.

[13] Nan C.-W., Birringer R., Clarke D.R., Gleiter H. Effective thermal conductivity of particulate composites with interfacial thermal resistance. J. Appl. Phys., 1997, vol. 81, pp. 6692-6699.

[14] Pugachev O.V., Han Z.T. Heat conductivity of composite materials with included balls of zero heat conductivity. Nauka i obrazovanie. MGTU im. N.E. Baumana [Science & Education of the Bauman MSTU. Electronic Journal], 2015, no. 5. DOI: 10.7463/0515.0776224 Available at: http://technomag.bmstu.ru/en/doc/776224.html

[15] Pugachev O.V., Han Z.T. Effective heat conductivity of composite materials with ball inclusions. Nauka i obrazovanie. MGTU im. N.E. Baumana [Science & Education of the Bauman MSTU. Electronic Journal], 2015, no. 6. DOI: 10.7463/0615.0778049 Available at: http://technomag.bmstu.ru/en/doc/778049.html

[16] Tikhonov A.N., Samarskiy A.A. Uravneniya matematicheskoy fiziki [Equations of mathematical physics]. Moscow, MGU im. M.V. Lomonosova Publ., 1999. 799 p.