Abstract. The problems of modeling of effective thermal conductivity of three-component compositions on the base of polymer binding agents SKTN-A, Sural-7 and powder mineral fillers SiO2, SiC, Al2O3, AlN in a wide range of values of the volume content of inclusions. The relevance of the selection of compositions with two fillers is said to meet the needs in the development of compounds with the desired conductivity, strength and deformation characteristics. A practical and feasible approach to simulation of thermal conductivity of heterogeneous composites with different content of the two fillers is proposed on the base of experimental determination of effective thermal conductivity of two-component compositions with the same binder and various fillers and further calculating the effective thermal conductivity of three-component mixtures with the use of multiple regression. The adequacy of the model is ensured by checking at several points in the volumetric content of fillers, with the thermal conductivity of corresponding compositions determined experimentally. An interpolation equation that describes thermal conductivity of composites based on polymer binders and having two fillers is presented. A simple formula for practical estimates of effective thermal conductivity of three-component compositions is also proposed; the formula uses effective thermal conductivity for two-component compositions of aggregates of filler particles evaluated from experimental data. 

Keywords: thermal conductivity, polymers, composite, filler, binder, three-component composition, multiple regression

References:

1. Dul'nev G.N., Zarichnyak Yu.P. Teploprovodnost' smesey i kompozitsionnykh materialov (Heat Conductivity of Mixes and Composite Materials), Leningrad, 1974. (in Russ.)
2. Chen H., Ginzburg V. V., Yang J., Yang Y., Liu W., Huang Y., Du L., Chen B. Progress in Polymer Science, http://www.sciencedirect.com/science/article/pii/S0079670016000216.
3. Mikheev V.A., Sulaberidze V.Sh., Mushenko V.D. Izv. vuzov. Priborostroenie, 2016, no. 4(59), pp. 317–332. (in Russ.)
4. Mikheev V.A., Sulaberidze V.Sh., Mushenko V.D. Izv. vuzov. Priborostroenie, 2015, no. 7(58), pp. 167–172. (in Russ.)
5. Mikheev V.A., Sulaberidze V.Sh., Mushenko V.D. The 5th All-Russian and COOMET member-countries Conference on Thermometry "TEMPERATURE-2015", April 21–24, 2015, D.I. Mendeleev All-Russian Institute for Metrology, St. Petersburg, Abstracts of Papers, 2015, рр. 245–247. (in Russ.)
6. Xu J.Z., Gao B.Z., Kang F.Y. Applied Thermal Engineering, 2016, no. 6 (102), pp. 972–979.
7.  Zhou F., Cheng G. Computational Materials Science, 2014, no. 92, pp. 157–165
8. Gao B.Z., Xua J.Z., Pengc J.J., Kanga F.Y., Dua H.D., Lia J., Chianga S.W.,  Xua C.J., Hua N., Ninga X.S. Thermochimica Acta, 2015, no. 20(614), pp. 1–8.
9. Kerber M.L., Vinogradov V.M., Golovkin G.S. Polimernye kompozitsionnye materialy: struktura, svoystva, tekhnologii (Polymeric Composite Materials: Structure, Properties, Technologies), St. Petersburg, 2008. (in Russ.)
10. Agrawal A., Satapathy A. Intern. J. of Thermal Sciences, 2015, no. 89, pp. 203–209.
11. Missenard A. Conductivité thermique des solides, liquides, gaz et de leurs mélanges, Editions Eyrolles, Paris, 1965.
12. Chudnovskiy A.F. Teplofizicheskie kharakteristiki dispersnykh materialov (Thermophysical Characteristics of Disperse Materials), Moscow, 1962. (in Russ.)
13. Xua J., Gaoa B., Dua H., Kanga F. Intern. J. of Thermal Sciences, 2016, no. 104, pp. 348–356.