The Self-Consistent Scheme Estimation of Effective Thermal Conductivity for the Transversally Isotropic Composite with Isotropic Ellipsoidal Inclusions
Authors: Zarubin V.S., Kuvyrkin G.N., Savelyeva I.Yu. | Published: 17.06.2015 |
Published in issue: #3(60)/2015 | |
DOI: 10.18698/1812-3368-2015-3-99-109 | |
Category: Physics | Chapter: Thermal Physics and Theoretical Heat Engineering | |
Keywords: self-consistent scheme, composite, ellipsoidal inclusions, effective thermal conductivity tensor |
The article presents the estimation of effective thermal conductivity tensor components for the transversally isotropic composite with isotropic ellipsoidal inclusions. The estimation is performed by using the self-consistent method. For its implementation a mathematical model of the thermal interaction between an inclusion and a homogeneous medium is developed. The quantitative analysis of the obtained calculation correlations is performed. They are supposed to be used for estimating effective conductivity coefficients of a composite with ellipsoidal inclusions.
References
[1] Hill R. A self-consistent mechanics of composite materials. J. Mech. Phys. Solids, 1965, vol. 13, no. 4, pp. 213-222.
[2] Pan’kov A.A. Metody samosoglasovaniya mekhaniki kompozitov [Self-Consistent Methods of Composite Mechanics]. Perm’, Perm. Gos. Tekhn. Univ. Publ., 2008. 253 p.
[3] Eshelby J.D. Solid State Phisics, vol. 3. N.Y., Academic Press, 1956 (Russ. ed.: Kontinual’naya teoriya dislokatsiy. Moscow, In. Lit. Publ., 1963. 248 p.).
[4] Shermergor T.D. Teoriya uprugosti mikroneodnorodnykh sred [Theory of Microinhomogeneous Medium Elasticity]. Moscow, Nauka Publ., 1977. 400 p.
[5] Hershey A.V. The elasticity of anisotropic aggregate of anisotropic cubic crystals. J. Appl. Mech., 1954, vol. 21, no. 3, pp. 236.
[6] Zarubin V.S. Prikladnye zadachi termoprochnosti elementov konstruktsiy [Applied Problems of Structural Element Thermal Strength]. Moscow, Mashinostroenie Publ., 1985. 296 p.
[7] Sarychev A.K., Shalaev V.M. Electrodynamics of metamaterials. Singapore: World Scientific, 2007. 227 p.
[8] Apresyan L.A., Vlasov D.V. Factors of Anisotropic Ellipsoid Depolarization in an Anisotropic Medium. Zh. Tekh. Fiz. [J. Appl. Phys], 2014, vol. 84, no. 12, pp. 23-28 (in Russ.).
[9] Zarubin V.S., Kuvyrkin G.N., Savel’eva I.Yu. Estimation of the Effective Thermal Conductivity of the Composite with Spherical Inclusions by the Self-Consistent Method. Jelektr. Nauchno-Tehn. Izd "Nauka i obrazovanie" [El. Sc.-Tech. Publ. Science and Education], 2013, no. 9, pp. 435-444. DOI: 10.7463/0913.0601512
[10] Landau L.D., Lifshits E.M. Teoreticheskaya fizika. V 10 t. T. 8. Elektrodinamika sploshnykh sred [Theoretical Physics. In 10 volumes, vol. 8. Electrodynamics of Continuum]. Moscow, Nauka Publ., 1992. 664 p.
[11] Carslaw H.S., Jaeger J.C. Conduction of heat in solids. Oxford University Press, London, 1959.
[12] Zarubin V.S., Kuvyrkin G.N., Savel’eva I.Yu. Effective Coefficients of Thermal Conductivity of a Composite with Prolate Spheroid Inclusions. Teplovye protsessy v tekhnike [Thermal Processes in Engineering], 2013, vol. 5, no. 6, pp. 276-282 (in Russ.).
[13] Zarubin V.S., Savel’eva I.Yu. Effective Thermal Conductivity Coefficients of the Composites with Spheroidal Inclusions. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2013, no. 4, pp. 116-126 (in Russ.).
[14] 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.).