K.V. Gubareva, A.V. Eremin

STUDYING THE HEAT TRANSFER PROCESS IN A POROUS MEDIUM WITH A FISCHER–KOCH S TPMS STRUCTURE

The paper reports a study of the process of heat transfer in a porous medium with internal heat sources. A model material is considered, which is a porous plate formed by Fischer–Koch S elementary cells, with a topology of triply periodic minimal surfaces. The results of solving the boundary value problem of thermal conductivity in a thin plate under symmetric boundary conditions of the first kind are presented. The developed numerical-analytical method is used to obtain a simple solution to the problem, taking into account the topological features of the material. Computational homogenization methods based on computer-aided engineering simulation in the Ansys software are used to determine the transfer coefficients and thermophysical properties of the area under study. The paper presents graphs of temperature distribution in a porous plate at different times and compares the obtained analytical solutions with numerical ones. The results of the study can be used in designing thermal protection of heat-generating equipment, heat and mass transfer paths in thermal and mechanical equipment, etc. The solutions are presented in a simple analytical form; this enables them to be used by a wide range of researchers and engineers and does not require using expensive software and hardware.

Acknowledgments: The study was supported by a grant from the Russian Science Foundation (RSF), No. 23-79-10044, https://rscf.ru/project/23-79-10044/. The use of Ansys in Samara State Technical University was licensed under agreement ЕП127/21 dated 04 October 2021.

References:

1. Murzakova, A.R., Shayakhmetov, U.Sh., Vasin, K.A., and Bakunov, V.S. Developing a technology for the production of an effective porous structural heat and sound insulator. Stroitelnye Materialy, 2011, 5, 65–67. (In Russian).
2. Omarov, A.O. Substantiation of efficiency criteria of materials for rational enclosing structures and description of technology of efficient structural and heat-insulating cellular concrete on porous aggregates. Vestnik Evraziyskoy Nauki, 2021, 1, Available at: https://esj.today/PDF/10SAVN121.pdf. (In Russian).
3. Prokhorchuk, Е.А., Leonov, А.А., Vlasova, К.А., Trapeznikov, А.V., Nikitin, V.I., and Nikitin, К.V. Prospects for the use of hot isostatic pressing in cast aluminum alloys (review). Trudy VIAM, 2021, 12 (106), 21–30. DOI: 10.18577/2307-6046-2021-0-12-21-30. (In Russian).
4. Izzheurov, E.A. and Uglanov, D.A. Obliteration’s problems in capillary-porous structures of aerospace hydro systems’ parts. Vestnik Samarskogo universiteta. Aerokosmicheskaya Tekhnika, Tekhnologii, Mashinostroenie, 2009, 3 (19), 143–146. (In Russian).
5. Alifanov, O.M., Salosina, M.O., Budnik, S.A., and Nenarokomov, A.V. Design of aerospace vehicles’ thermal protection based on heat-insulating materials with optimal structure. Aerospace, 2023, 10 (7), 629. DOI: 10.3390/aerospace10070629.
6. Rydalina, N. V., Aksenov, B. G., Stepanov, O. A., and Antonova, E. O. Application of porous materials in heat exchangers of heat supply system. Izvestiya Vysshykh Uchebnykh Zavedeniy. Problemy Energetiki, 2020, 22 (3), 3–13. (In Russian). DOI: 10.30724/1998-9903-2020-22-3-3-13.
7. Rydalina, N.V., Stepanov, O.A., and Antonova, E.O. Application of porous metals in the designs of heat exchangers. Vestnik Evraziyskoy Nauki, 2023, 15 (1). (In Russian). Available at: https://esj.today/PDF/24SAVN123.pdf
8. Son, E.E. Damper systems for the high voltage equipment protection by porous metals. Izvestiya RAN. Energetika, 2019, 6, 78–109. (In Russian). DOI: 10.1134/S0002331019060098.
9. Andrianov, I.V., Kalamkarov, A.L., and Starushenko, G.A. Analytical expressions for effective thermal conductivity of composite materials with inclusions of square cross-section. Composites. Part B: Engineering, 2013, 50, 44–53. DOI: 10.1016/j.compositesb.2013.01.023.
10. Bragin, D.M., Popov, A.I., Ivannikov, Yu.N., Eremin, A.V., Zinina, S.A., and Kechin, N.N. Experimental study of effective thermal conductivity of materials based on TPMS. In: The 5th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA), IEEE, Lipetsk, Russian Federation, 2023, pp. 983–985. DOI: 10.1109/SUMMA60232.2023.10349385.
11. Prosviryakov, E.Yu. Gravitational Principle of minimum pressure for incompressible flows. Diagnostics, Resource and Mechanics of materials and structures, 2021, 2, 22–29. DOI: 10.17804/2410-9908.2021.2.022-029. Available at: http://dream-journal.org/issues/content/article_315.html
12. Gorshkov, A.V. and Prosviryakov, E.Yu. Analytical study of the Ekman angle for the Benard–Marangoni convective flow of viscous incompressible fluid. Diagnostics, Resource and Mechanics of materials and structures, 2021, 4, 34–48. DOI: 10.17804/2410-9908.2021.4.34-49. Available at: http://dream-journal.org/issues/2021-4/2021-4_340.html
13. Fischer, W. and Koch, E. Spanning minimal surfaces. Philosophical Transactions of the Royal Society A, 1996, 354 (1715), 2105–2142. DOI: 10.1098/rsta.1996.0094.
14. Lykov, A.V. Teoriya teploprovodnosti [Theory of Thermal Conductivity]. Vysshaya Shkola Publ., Moscow, 1967, 600 p. (In Russian).
15. Bragin, D.М., Eremin, А.V., Popov, A.I., and Shulga А.S. Method to determine effective thermal conductivity coefficient of porous material based on minimum surface Schoen's I-WP(R) type Vestnik IGEU, 2023, 2, 61–68. (In Russian). DOI: 10.17588/2072-2672.2023.2.061-068.
16. Popov, A.I., Bragin, D.М., Zinina, S.A., Eremin, А.V., and Olatuyi O.J. Determination of the effective thermal conductivity of a porous material with an ordered structure based on I-WP TPMS. Mezhdunarodnyi Zhurnal Informatsionnykh Tekhnologiy i Energoeffektivnosti, 2022, 7, 3–1 (25), 61–67. (In Russian).
17. Eremin, A.V., Gubareva, K.V, Popov, A.I. Investigation of the temperature state of fuel elements with a given spatial distribution of heat sources. AIP Conf. Proc, 2022, 2456, 020015. DOI: 10.1063/5.0074727.
18. Kudinov, I.V., Kotova, E.V., and Kudinov, V.A. A method for obtaining analytical solutions to boundary value problems by defining additional boundary conditions and additional sought-for functions. Numerical Analysis and Applications, 2019, 12 (2), 126–136. DOI: 10.1134/S1995423919020034.
19. Kudinov, V.A., Eremin, A.V., and Stefanyuk, E.V. Analytical solutions of heat-conduction problems with time-varying heat-transfer coefficients. Journal of Engineering Physics and Thermophysics, 2015, 88 (3), 688–698. DOI: 10.1007/s10891-015-1238-y.
20. Kudinov, V.A., Kartashov, E.M., and Kalashnikov V.V. Analiticheskie resheniya zadach teplomassoperenosa i termouprugosti dlya mnogosloynykh konstruktsyi [Analytical Solutions of Problem of Heat and Mass Transfer and Thermoelasticity for Multilayered Structures: Educational Book]. Vysshaya Shkola Publ., Moscow, 2005, 430 p. (In Russian).

Article reference