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A cell model of thermal conductivity in a two-component lubricant

A.N. Belyakov, V.P. Zhukov, A.V. Ogurtsov, E.V. Basova, M.A. Shilov

Vestnik IGEU, 2026 issue 2, pp. 89—95

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Abstract in English: 

Background. Friction losses account for a significant portion of energy consumption in technological processes. Modern lubricants are multi-component systems, and carbon nanoparticles have recently been actively used as additives. This significantly improves the thermal conductivity of the lubricant and promotes more efficient heat dissipation from the friction zone.  However, the widespread use of such materials is hindered due to the lack of reliable methods to calculate the thermal state of the lubricant layer, taking into account the concentration of additives and the nonlinear nature of the processes occurring.

Materials and methods. The numerical solution of the heat conduction problem is based on the cell model of Markov chain theory.

Results. A model of thermal conductivity in a two-component lubricant has been proposed. Two heat flows have been considered for different components of the lubricant taking into account the mutual exchange of energies between them. As a result of the numerical experiment, the dependences of the lubricating layer temperature on the additive concentration have been obtained and studied. Temperature gradients within the lubricating layer have been calculated. The influence of the power and position of the heat source on the temperature distribution has been shown.

Conclusions. The developed thermal conductivity model and the obtained results allow us to predict the temperature distribution in the lubricant layer and select the concentration of additives for the required friction pair operating parameters.

References in English: 

1. Shilov, M.A., Smirnova, A.I., Kupreenko, S.Yu., Gvozdev, A.A., Rozhkova, N.N., Dyachkova, T.P., Stolbov, D.N., Savilov, S.V., Usol’tseva, N.V. Mechanism of Lubricating Action of Model Systems with Additives of Carbon Nanostructures under Hard Friction Conditions. Journal of Friction and Wear, 2024, vol. 45, no. 6, pp. 337–343.

2. Garkunov, D.N. Tribotekhnika [Tribology]. Moscow: Izdatel′stvo MSKHA, 2001. 616 p.

3. Tolochko, N.K., Krauklis, A.V., Stanovoy, P.G., Shienok, Yu.A. Tribotekhnicheskie kharakteristiki motornogo masla, modifitsirovannogo uglerodnymi nanochastitsami [Tribological characteristics of motor oil modified with carbon nanoparticles]. Doklady Mezhdunarodnoy nauchno-prakticheskoy konferentsii «Opyt, problemy i perspektivy razvitiya tekhnicheskogo servisa v APK», posvyashchennoy 55-letiyu so dnya obrazovaniya BGATU i 100-letiyu so dnya rozhdeniya doktora tekhnicheskikh nauk, professora Suslova V.P., Minsk, 15–18 aprelya 2009 g.: v 2 ch. Ch. 1 [Proceedings of the International scientific and practical conference “Experience, Problems, and Prospects of the Development of Technical Services in the Agro-Industrial Complex” dedicated to the 55th Anniversary of the founding of the Belarusian State Agrarian University and the 100th anniversary of Doctor of Engineering Sciences, Professor V.P. Suslov, Minsk, April 15–18, 2009. In 2 parts. Part 1]. Minsk: BGATU, 2009, pp. 379–383.

4. Gvozdev, A.A., Smirnova, A.I., Berezina, E.V., Dunaev, A.V., Tkachev, A.G., Usol′tseva, N.V. Issledovanie tribotekhnicheskikh kharakteristik perspektivnykh smazochnykh materialov s uglerodnymi nanochastitsami [Study of tribotechnical characteristics of promising lubricants with carbon nanoparticles]. Zhidkie kristally i ikh prakticheskoe ispol'zovanie, 2018, vol. 18, no. 1, pp. 66–72. DOI: 10.18083/LCAppl.2018.1.66.

5. Tokhmetova, A.B. Povyshenie tribologicheskikh svoystv smazochnogo masla legirovaniem mikro-/nanodobavkami. Diss. … kand. tekhn. nauk [Improving the tribological properties of lubricating oil by alloying with micro-/nanoadditives. Cand. tech. sci. diss.]. Moscow, 2023. 113 p.

6. Vyavhare, K., Aswath, P.B. Tribological Properties of Novel Multi-Walled Carbon Nanotubes and Phosphorus Containing Ionic Liquid Hybrids in Grease. Front. Mech. Eng., 2019, vol. 5. DOI: 10.3389/fmech.2019.00015.

7. Shilov, M.A., Usol’tseva, N.V. Modelirovanie vliyaniya prisadok uglerodnykh nanostruktur na tribotekhnicheskie kharakteristiki smazochnykh materialov [Modeling of the effect of carbon nanostructure additives on tribotechnical properties of lubricants]. Zhidkie kristally i ikh prakticheskoe ispol′zovanie, 2025, vol. 25, no. 4, pp. 91–101.

8. Yuan, C., Tony, A., Yin, R., Wang, K., Zhang, W. Tactile and Thermal Sensors Built from Carbon–Polymer Nanocomposites – A Critical Review. Sensors, 2021, vol. 21, issue 4. https:// doi.org/10.3390/s21041234.

9. Barantseva, E.A., Mizonov, V.E. Vvedenie v teoriyu tsepey Markova i ee inzhenernye prilozheniya [Introduction to Markov Chain Theory and its engineering applications]. Ivanovo, 2010. 80 p.

10. Mizonov, V.E., Tikhonov, A.I., Basova, E.V., Mitrofanov, A.V. Modelirovanie teploprovodnosti v srede s fazovym perekhodom s podvizhnoy granitsey razdela faz [Modeling of thermal conductivity in a medium with a phase transition and a moving phase boundary]. Problemy regional'noy energetiki, 2021, no. 3(51), pp. 53–61. DOI: 10.52254/1857-0070.2021.3-51.05.

11. Mizonov, V.E., Mitrofanov, A.V., Basova, E.V., Shuina, E.A. Teoreticheskoe issledovanie nelineynoy teploprovodnosti v mnogosloynoy srede s fazovymi perekhodami v sloyakh [Theoretical study of nonlinear thermal conductivity in a multilayer medium with phase transitions in layers]. Vestnik IGEU, 2020, issue 1, pp. 53–59. DOI: 10.17588/2072-2672.2020.1.053-059.

12. Karpushenkova, L.S., Kabo, G.Ya., Blokhin, A.V. Mnogosloynye uglerodnye nanotrubki – komponent energoemkikh suspenzionnykh reaktivnykh goryuchikh [Multiwalled carbon nanotubes as a component of energy-intensive suspension reactive fuels]. Tonkie khimicheskie tekhnologii, 2020, vol. 15, no. 2, pp. 38–46.

13. Zolotukhin, I.V., Golev, I.M., Markova, A.E., Blinov, S.N., Grishin, D.A., Rakov, E. The effective density and transport properties of compacted carbon nanotubes and nanowhiskers. Technical Physics Letters, 2005, vol. 31, no. 2, pp. 159–160. DOI: 10.1134/1.1877634.

14. Tomishko, M.M., Demicheva, O.V., Alekseev, A.M., Tomishko, A.G., Klinova, L.L., Fetisova, O.E. Mnogosloynye uglerodnye nanotrubki i ikh primenenie [Multiwalled carbon nanotubes and their applications]. Rossiyskiy khimicheskiy zhurnal, 2008, vol. 52, no. 5, pp. 39–42.

15. Tokhmetova, A.B., Mikheev, A.V., Tananov, M.A. Issledovaniya tribologicheskikh svoystv motornogo masla s soderzhaniem fullerenov [Studies of the tribological properties of motor oil containing fullerenes]. Problemy mashinostroeniya i nadezhnosti mashin, 2022, no. 4, pp. 108–112. DOI: 10.31857/S0235711922040150.

Key words in Russian: 
теплопроводность, углеродные нанотрубки, цепь Маркова, смазочный материал, энергия трения, трибологические характеристики смазочных композиций
Key words in English: 
thermal conductivity, carbon nanotubes, Markov chain, lubricant, friction energy, tribological characteristics of lubricant compositions
The DOI index: 
10.17588/2072-2672.2026.2.089-095
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