Heat Exchange in a Contact Zone of Nanoinstrumentation with Elements of the Microsystem Technology | Journal of Engineering Sciences

Heat Exchange in a Contact Zone of Nanoinstrumentation with Elements of the Microsystem Technology

Author(s): Antonyuk V. S.1, Bondarenko I. Iu.2, Vislouh S. P.1, Voloshko O. V.1, Bondarenko M. O.3

1 National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, 37, Peremohy Ave., 03056 Kyiv, Ukraine;
2 State Scientific Research Institute of Armament and Military Equipment Testing and Certification, 164, Chornovil St., 18028 Cherkasy, Ukraine;
3 Cherkasy State Technological University, 460, T. Shevchenka Blvd, 18006 Cherkasy, Ukraine

*Corresponding Author’s Address: [email protected]

Issue: Volume 10, Issue 1 (2023)

Submitted: February 24, 2023
Received in revised form: May 8, 2023
Accepted for publication: May 18, 2023
Available online: May 23, 2023

Antonyuk V. S., Bondarenko I. Iu., Vislouh S. P., Voloshko O. V., Bondarenko M. O. (2023). Heat exchange in a contact zone of nanoinstrumentation with elements of the microsystem technology. Journal of Engineering Sciences, Vol. 10(1), pp. F1-F6, doi: 10.21272/jes.2023.10(1).f1

DOI: 10.21272/jes.2023.10(1).f1

Research Area:  CHEMICAL ENGINEERING: Processes in Machines and Devices

Abstract. Theoretical studies of physical processes and phenomena in the zone of physical interaction of nanoinstruments with the surfaces of elements of microsystem technology are carried out in work. Based on the conducted research, mathematical models of energy heat exchange in the zone of physical contact of nanometric dimensions were compiled, and their analytical solution was obtained using the Fourier method of separation of variables and Goodman’s integral method. Simultaneously, the energy components of the processes in the nanocontact zone were considered. The numerical solution of the mathematical model of energy heat exchange in the zone of physical nanocontact was carried out using a software application based on the finite element method. The results were checked according to the equivalent thermal scheme to confirm the adequacy and accuracy of the obtained models. As a result, the mechanisms of energetic interaction of the nanoinstrument with the surfaces of the elements of microsystem technology devices were clarified. It is shown that the use of the proposed method of equivalent thermal circuits for the evaluation of mathematical models of the energy interaction of nanoinstruments with the surfaces of microsystem technology device elements, as well as the further study of the distribution of thermal fields in the nanocontact zone, differs from other numerical and analytical methods in terms of sufficient accuracy and speed of calculations. At the same time, it was established that the discrepancy between the results of mathematical modeling and the results obtained according to the equivalent thermal scheme does not exceed 5-8 %.

Keywords: energy heat exchange, mathematical modeling, physical contact, thermal energy, process innovation, equivalent thermal circuit.


  1. Manz, A., Becker, H. (2003). Microsystem Technology in Chemistry and Life Sciences. Springer Science & Business Media, London, UK.
  2. Zhuoqing, Y. (2021). Advanced MEMS/NEMS Fabrication and Sensors. Springer, London, UK.
  3. Bembenek, M., Makoviichuk, M., Shatskyi, I., Ropyak, L., Pritula, I., Gryn, L., Belyakovskyi, V. (2022). Optical and mechanical properties of layered infrared interference filters. Sensors, Vol. 22(21), 8105. DOI: 10.3390/s22218105
  4. Hovorun, T.P., Pylypenko, O.V., Berladir, K.V., Dyadyura, K.O., Dunaeva, M.N., Vorobiov, S.I., Panda, A. (2019). Physical-mechanical properties and structural-phase state of nanostructured wear-resistant coatings based on nitrides of refractory metals Ti and Zr. Functional Materials, Vol. 26(3), pp. 548-555. DOI: 10.15407/fm26.03.548
  5. Krukovskyi, S.I., Arikov, V., Voronko, A.O., Antonyuk, V.S. (2022). Features of low-temperature GaAs formation for epitaxy device structures. Journal of Nano- and Electronic Physics, Vol. 14(2), 02016(5pp). DOI: 10.21272/jnep.14(2).02016
  6. Tatsiy, R.M., Pazen, O.Y., Vovk, S.Y., Ropyak, L.Y., Pryhorovska, T.O. (2019). Numerical study on heat transfer in multilayered structures of main geometric forms made of different materials. Journal of the Serbian Society for Computational Mechanics, Vol. 13(2), pp. 36-55. DOI: 10.24874/JSSCM.2019.13.02.04
  7. Vasudha, H., Yellampalli, S., Ravikumar, H. M. (2020). Simulation, mathematical modeling, fabrication and experimental analysis of piezoelectric acoustic sensor for energy harvesting applications. Microsyst. Technol., Vol. 26(5), pp. 1613-1623. DOI: 10.1007/s00542-019-04702-x
  8. Belmiloudi, A. (2011). Heat Transfer – Mathematical Modelling, Numerical Methods and Information Technology. Physical Chemistry. IntechOpen, London, UK. DOI: 10.5772/569
  9. Laurençot, P., Nik, K., Walker, C. (2021). Convergence of energy minimizers of a MEMS model in the reinforced limit. Acta Appl. Math., Vol. 173, 9. DOI: 10.1007/s10440-021-00416-3
  10. Krysko-Jr, V.A., Awrejcewicz, J., Yakovleva, T.V., Kirichenko, A.V., Jarzyna, O., Krysko, A.V. (2018). Mathematical modeling of MEMS elements subjected to external forces, temperature and noise, taking account of coupling of temperature and deformation fields as well as a nonhomogenous material structure. Communications in Nonlinear Science and Numerical Simulation, Vol. 72. DOI: 10.1016/j.cnsns.2018.12.001
  11. Ralchenko, S., Andriienko, V. (2019). Features of thermal control of components of electrical engineering devices and systems. In: Fourteenth International Scientific Conference “АVІА”. Kyiv 23-25.04.2019. Available online: http://conference.nau.edu.ua/index.php/AVIA/AVIA2019/paper/view/5951/4479
  12. Bondarenko, M.A., Bilokon, S.A., Antonyuk, V.S., Bondarenko, I.I. (2014). Mechanism of origin and neutralization of residual triboelectricity at scanning of dielectric surfaces by a silicon probe of the atomic-force microscope. Journal of Nano- and Electronic Physics, Vol. 6(2), 02018(5pp).
  13. Folland, G. B. (1995). Introduction to Partial Differential Equations. Princeton Univ. Press, Princeton, USA.
  14. Andriienko, О., Ralchenko, S. (2019). Energy heat exchange in the zone of contact of the probe of an atomic force microscope with the surface under study. Machines. Technologies. Materials, Vol. XIII(11), pp. 495-499.
  15. Parker, A. E. (2020). Solving linear first-order differential equations Bernoulli’s (almost) variation of parameters method. Differential Equations. Available online: https://digitalcommons.ursinus.edu/triumphs_differ/3
  16. Lipschutz, S. (2017). Schaum’s Outline of Mathematical Handbook of Formulas and Tables. McGraw Hill, London, UK.
  17. Vaschenko, V.A., Kotelnikov, D.I., Lega, Yu.G., Krasnov, D.M., Yatsenko, I.V., Kirichenko, O.V. (2006). Thermal Processes in the Electronic Processing of Optical Materials and Use of Products Based on Them. Naukova Dumka, Kyiv, Ukraine.
  18. Artale, P.H., Garra, R. (2001). Nonlinear heat conduction equations with memory: Physical meaning and analytical results. J. Math. Phys., Vol. 58, 063501. DOI: 10.1063/1.4984583
  19. Wood, A.S. (2001). A new look at the heat balance integral method. Applied Mathematical Modelling, Vol. 25(10), pp. 815-824. DOI: 10.1016/S0307-904X(01)00016-6
  20. Grafakos, L., Teschl, G. (2013). On Fourier transforms of radial functions and distributions. J. Fourier Anal. Appl., Vol. 19, pp. 167-179. DOI: 10.1007/s00041-012-9242-5
  21. Kutz, M. (2011). Plastics Design Library, Applied Plastics Engineering Handbook. William Andrew Publishing, London, UK. DOI: 10.1016/B978-1-4377-3514-7.10045-5
  22. Lewis, R.W., Nithiarasu, P., Seetharamu, K.N. (2004). Fundamentals of the Finite Element Method for Heat and Fluid Flow. John Wiley & Sons, Hoboken, USA.
  23. Kattan, P.I. (2003). The Linear Triangular Element. Springer, Berlin, Germany. DOI: 10.1007/978-3-662-05209-9_11
  24. Milosan, I. (2015). Mathematical modeling by using a C++ software. In: International Conference of Scientific Paper (AFASES 2015). Brasov 28-30.05.2015. Available online: www.afahc.ro/ro/afases/2015/afases_2015/math/Milosan%20Ioan%201.pdf
  25. Pulatov, A., Mamadaliev, B., Bekmurodov, J., Makhmudov, N. (2023). Application of the method of equivalent thermal circuits in the calculation of thermal modes of induction crucible furnaces in stationary and non-stationary modes. AIP Conference Proceedings, Vol. 2552, 040014. DOI: 10.1063/5.0111948

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