Visnyk of the Lviv University. Series Physics
56 (2019) ñ. 76-83
DOI: https://doi.org/10.30970/vph.56.2019.76 ## The use of mathematical modelling while studying thermophysical properties of carbon fiber-reinforced plasticsK. A. Yeriomina, O. I. Burya |

Materials based on aromatic polyamide phenylone are designed to work at elevated (up to 523 K) temperatures in all climatic zones. Their thermal coefficient of linear expansion is stable enough in the range of working temperatures and 2 - 3 times lower comparing with other unfilled plastics. Thus, the scientific interest was the study of the influence of carbon fiber on the thermophysical characteristics of carbon fiber-reinforced plastics based on phenylone, because many details of technical devices from polymeric composite materials are used in the unstationary thermal processes. \\ \indent The results of the researches on thermophysical properties of carbon fiber-reinforced plastics based on phenylone aromatic polyamide depending on the degree of filling it with carbon fiber and ambient temperature are given in the article. The researches on thermophysical properties of carbon fiber-reinforced plastics were carried out using the methods of mathematical statistics, because experimental studies connected with the material content optimization are usually bulky and multifactorial that leads to huge loss of time and resources. Such methods allow us to evaluate studied processes adequately with fewer experiments. Mathematical models, which adequately describe the dependence of specific heat and thermal conductivity of carbon fiber-reinforced plastics on the ambient temperature and content of carbon fiber, were found using mathematical planning of the experiment The analysis of obtained mathematical models in studied range of factors variation shows that ambient temperature has the greatest impact on specific heat and thermal conductivity of carbon fiber-reinforced plastics. The effect of the amount of carbon fiber in polymer matrix on the studied thermophysical properties is ambiguous. It is showed that maximal ambient temperature and content of the filler account for the maximum of optimization parameter.

- Y. Chen J. Guan and H. Hu et all, Journal of Applied Spectroscopy.
**83**(3), 500(1)-500(7)(2016). - V. A Goldade S. V. Zotov K. V. Ovchinnikov and V. M. Shapovalov, Chrezvichainie sytuatsyy: obrazovanye y nauka.
**10**(1), 9-16(2015). - E. A. Belyaeva A. F. Kosolapov and S. V. Shatsky et all, Uspekhy v khymyy y khymycheskoi tekhnolohyy.
**29**(10), 11-13(2015). - A. N. Ponomarev and A. S. Rassokhin, Ynzhenerno-stroytelnyi zhurnal, 8(68), 45-57(2016).
- S. O. Mesita, Pop plast.
**4**(29), 27-29(1984). - Pryorytety myrovykh tsentrov nauchno-tekhnycheskoho razvytyia. http://www.consultant.ru/document/ cons\textunderscore doc\textunderscore LAW\textunderscore 144190/fc6952971442f3f583 4ab9e3506cf0d2ef7b3249/
- A. A. Spiridonov and N. G. Vasiliev, Planyrovanye eksperymenta, 1st ed. (S. M. KirovYPI, Svrdlovsk, 1975), pp 149.
- L. N. Bolshev, N. V. Smyrnov, Tablytsu matematycheskoi statystyky, 1st ed. (Hlavnaia redaktsyia fyzyko-matematycheskoi lyteratu, 1983), pp. 416.