On accounting for thermal resistance between inclusions and matrix in effective thermal conductivity prediction of composites


Аuthors

Lavrov I. V.1, Kochetygov A. A.1*, Bardushkin V. V.2**, Yakovlev V. B.1***

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. Institute of Nanotechnology of Microelectronics of the Russian Academy of Sciences, Moscow, Russia

*e-mail: aakcht@gmail.com
**e-mail: bardushkin@mail.ru
***e-mail: yakvb@mail.ru

Abstract

The article considers the problem of matrix composite effective thermal conductivity in the presence of contact thermal resistance at the boundary between the matrix and inclusions. In the beginning, the variants of generalization of Maxwell and Maxwell-Garnett approximations pro- posed by earlier explorers in the event of accounting for contact thermal resistance in the matrix composite with spherical single-type inclusions were discussed. A technique for accounting for thermal resistance at the boundary between the matrix and inclusions in the composite, based on the composite model with inclusions with thin shell was proposed hereafter. The thickness and thermal conductivity of the inclusions shells are being selected based on the contact thermal re- sistance. The generalized effective-field approximation, previously developed by the authors, is used for the composite effective thermal conductivity calculation.



The equation for effective thermal conductivity of the composite with single-type spherical inclusions in on dependence thermal conductivities of the matrix, shells and cores of inclusions was obtained. Model calculations were carried out for the ED-20 composite as a matrix and spherical inclusions from the aluminum-borosilicate glass. The inclusions radius was being as- sumed as 0.5 μm. The effective thermal conductivity of the said composite was computed de- pending on relative shell thickness as well as volume fraction of the inclusions.

The article demonstrates conformance of the results, obtained on the base of the generalized effective-field approximation for the model of the composite with inclusions with shell, with computational results on the Maxwell-Garnett approximation generalizing with account for the contact thermal resistance. The article shows as well that despite the fact that the inclusions ma- terial has higher thermal conductivity, with the poor contact between the inclusions and matrix the inclusions volume fraction increase may lead to the effective thermal conductivity decrease.

Keywords:

effective thermal conductivity, contact thermal resistance, composite, matrix, in- clusion with shell, Maxwell-Garnett approximation, generalized effective-field approximation

References

  1. Kolesnikov V.I. Teplofizicheskie protsessy v metallopo- limernykh tribosistemakh [Thermophysical processes in metal-polymeric tribosystems]. Moscow, Nauka, 2003, 279 p. In Russ.

  2. Every A.G., Tzou Y., Hasselman D.P.H., Raj R. The ef- fect of particle size on the thermal conductivity of ZnS/diamond composites. Acta Metall. Mater., 1992, vol. 40, no. 1, pp. 123.

  3. Devpura A., Phelan P.E., Prasher R.S. Size effects on the thermal conductivity of polymers laden with highly conduc- tive filler particles. Microscale Thermophysical Engineering, 2001, vol. 5, no. 3, pp. 177–189. http://dx.doi.org/ 10.1080/108939501753222869

  4. Kidalov S.V., Shakhov F.M. Thermal conductivity of dia- mond composites. Materials, 2009, vol. 2, pp. 2467–2495. DOI:10.3390/ma2042467

  5. Pietrak K., Wiśniewski T.S. A review of models for effec- tive thermal conductivity of composite materials. Journal of Power Technologies, 2015, vol. 95, no. 1, pp. 14–24.

  6. Pietrak K., Wiśniewski T.S. Methods for experimental de- termination of solid-solid interfacial thermal resistance with application to composite materials. Journal of Power Tech- nologies, 2014, vol. 94, no. 4, pp. 270–285.

  7. Pietrak K., Kubiś M., Langowski M., Kropielnicki M., Wultański P. Effect of particle shape and imperfect filler- matrix interface on effective thermal conductivity of epoxy- aluminum composite. Composites Theory and Practice, 2017, no. 4, pp. 183–188. DOI: 10.5281/zenodo.1188082

  8. Kapitza P.L. The study of heat transfer in Helium II .

  9. J. Phys. USSR, 1941, vol. 4, pp. 181.

  10. Hasselman D.P.H., Johnson L.F. Effective thermal con- ductivity of composites with interfacial thermal barrier re- sistance. J. Compos. Mater., 1987, vol. 21, no. 6, pp. 508— 515. DOI: 10.1177/002199838702100602

  11. Benveniste Y., Miloh T. The effective conductivity of compo- sites with imperfect thermal contact at constituent interfaces. Int. J. Eng. Sci., 1986, vol. 24, no. 9, pp. 1537–1552.

  12. Benveniste Y. Effective thermal conductivity of composites with a thermal contact resistance between the constituents: Nondilute case. J. Appl. Phys., 1987, vol. 61, no. 8, pp. 2840–2843.

  13. Maxwell J.C. Treatise on Electricity and Magnetism. Ox- ford, Clarendon Press, 1873, V. 1. 431 p.

  14. Wait J.R. Geo-electromagnetism. New-York, London: Academic Press, 1982. 268 p.

  16. Kolesnikov V.I., Bardushkin V.V., Lavrov I.V., Sy- chev A.P., Yakovlev V.B. A generalized effective-field ap- proximation for an inhomogeneous medium with coated in- clusions. Dokl. Phys., 2017, vol. 62, no. 9, pp. 415–419. DOI: 10.1134/S1028335817090087

  17. Maxwell Garnett J.C. Colours in metal glasses and in me- tallic films. Phil. Trans. R. Soc. London, 1904, vol. 203, pp. 385–420.

  18. Kartashov E.M., Kudinov V.A. Analiticheskiye metody teorii teploprovodnosti i yeyo prilozheniy [Analytical meth- ods of the theory of thermal conductance and its applica- tions]. Moscow: LENAND, 2018. 1072 p. In Russ.

  19. Tikhonov A.N., Samarskiy A.A. Uravneniya matemati- cheskoy fiziki [The equations of mathematical physics]. Moscow: Nauka, 1966. 724 p. In Russ.

  20. Lavrov I.V., Bardushkin V.V., Sychev A.P., Yakovlev V.B., Kirillov D.A. O vychislenii effectivnoy teploprovodnosti teksturirovannyh tribokompozitov [On calculation of the ef- fective thermal conductivity of textured tribocomposites]. Ekologicheskiy vestnik naucnyh centrov Chernomorskogo ekonomicheskogo sotrudnichestva — Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2017, no. 2, pp. 48–56. In Russ.

  21. Lavrov I.V., Bardushkin V.V., Sychev A.P., Yakovlev V.B., Kochetygov A.A. Predicting the effective thermal conduc- tivity of tribocomposites with coated antifrictional inclu- sions. Russian Engineering Research, 2019, vol. 39, no. 2, pp. 117–121. DOI: 10.3103/S1068798X19020217

  22. Kolesnikov V.I., Lavrov I.V., Bardushkin V.V., Sy- chev A.P., Yakovlev V.B. Metod otsenki raspredeleniy lo- kal’nykh temperaturnykh poley v mnogokomponentnykh kom- pozitakh [A method of the estimation of the local thermal fields distribution in multicomponent composites]. Nauka Yuga Rossii —Science in the South of Russia, 2017, vol. 13, no. 2, pp. 13–20. DOI: 10.23885/2500-0640-2017-13-2-13-20. In Russ.

  23. Bragg W.L., Pippard A.B. The form birefringence of macro- molecules. Acta Cryst., 1953, vol. 6, no. 11–12, pp. 865–867.

  24. Bohren C.F., Huffman D.R. Absorption and Scattering of Light by Small Particles. Weinheim: Wiley-VCH Publ., 1998. 544 p.

  25. Spanoudaki A., Pelster R. The dependence on effective di- electric properties of composite materials: the particle size distribution. Phys. Rev. B, 2001, vol. 64, pp. 064205-1— 064205-6. DOI: 10.1103/PhysRevB.64.064205

  26. Grigor’ev I.S., Meilikhov E.Z. (eds.) Fizicheskie veli- chiny: Spravochnik [Physical Quantities: A Handbook]. Moscow: Energoatomizdat, 1991. 1232 p. In Russ.

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