Modeling of the heat conduction process in a porous medium with time-varying boundary conditions


Аuthors

Gubareva K. V.*, Eremin A. V.

Samara State Technical University,

*e-mail: r.kristina2017@mail.ru

Abstract

The present study is devoted to solving the non-stationary heat transfer problem for porous materials structured on the basis of triply periodic minimal surfaces (TPMS). These surfaces, such as gyroids, Schwarz and Neovius surfaces, find application in biomedical implants, filtration systems and aerospace thermal protection due to their unique topology combining high strength with minimal density. However, their complex geometry, including tortuous channels and non-uniform pore distribution, makes traditional heat transfer analysis methods, such as Fourier analytical solutions or standard finite element modeling, of little use. To overcome these limitations, an approximate analytical approach based on a modified integral heat balance method is proposed. The key innovation is the introduction of a special function approximating the heat flux in a porous medium and additional boundary conditions taking into account the topology of the unit cell of the material. This made it possible to reduce the original system of partial differential equations to a system of ordinary differential equations, which significantly simplified the calculations without losing the physical reliability of the model. The main objective of the work was to develop an approximate analytical solution for a Neovius plate, one of the basic classes of TPMP structures characterized by high symmetry and minimal surface energy. Particular attention is paid to taking into account the microstructural features of the material, including the pore distribution, the thickness of the partitions and their effect on the effective thermal conductivity. To verify the method, CAE modeling in ANSYS was used, where a three-dimensional parametric model of the unit cell with an adaptive grid was created, ensuring the resolution of local temperature gradients. Comparison of the results demonstrated high consistency: the maximum deviation of the analytical solution from the numerical one did not exceed 4 % over the entire range of time and space variables. The practical significance of the study is due to the possibility of using the obtained solutions in the design of energy-efficient heat exchangers, thermal protection systems for aerospace vehicles, and porous catalytic reactors. In addition, the developed approach provides flexibility: it allows adaptation to other types of TPMS structures by adjusting the unit cell parameters.

Keywords:

non-stationary thermal conductivity, triply periodic minimal Neovius surface, integral method of heat balance, exact analytical solution, effective thermal conductivity, ordered porous structures.

References

  1. Karnachev IP, Nikolaev VG, Biryukov VV et al. Thermal regime of large-span workings during the construction of nuclear energy facilities. Izvestiya Tul'skogo gosudarstvennogo universiteta. Nauki o Zemle. 2020;(2): 289–301. (In Russ.). EDN: QBBTPF
  2. Piksaykina AA, Konin MA, Babenkova YuV. Porous pavements as a modern concept of green construction. Effektivnye stroitel'nye konstruktsii: teoriya i praktika: sbornik statei XIX Mezhdunarodnoi nauchno-tekh-nicheskoi konferentsii, Penza, 28–29 marta 2019 goda / Penzenskii gosudarstvennyi universitet arkhitektury i stroitel'stva. – Penza: Avtonomnaya nekommercheskaya nauchno-obrazovatel'naya organizatsiya «Privolzhskii Dom znanii», 2019. pp. 107–111. (In Russ.). EDN: XCHFLT
  3. Ogunsola AW, Oyedotun MF. Effects of nonlinear thermal radiation on magnetized Al2O3-Blood nanofluid flow through an inclined microporous channel: An investigation of second law analysis. Electrophoresis. 2023. DOI: 10.1002/elps.202300157. 
  4. Jing L, Huo J, You X et al. Numerical investigation of an aerospace thruster with ADN-based liquid propellant. Qinghua Daxue Xuebao (Ziran Kexue Ban). 2016; 56(10):1085–1090. DOI: 10.16511/j.cnki.qhdxxb2016. 22.043
  5. Huabkhuntod T, Sinjapo S, Luampon R et al. Study on heat transfer in two-layer porous media with heat generation in porous media. Energy Reports. 2022;8:1565–1576. DOI: 10.1016/j.egyr.2022.11.062
  6. Zhang Zh, Xu T, Li Sh et al. Comprehensive effects of heat and flow on the methane hydrate dissociation in porous media. Energy. 2023;265. DOI: 10.1016/j.energy. 2022.126425
  7. Kartashov EM, Krylov SS. Analytical solutions of boundary value heat conduction problems with a free boundary. Thermal processes in engineering. 2023; 15(10):456–467. (In Russ.). EDN: QVYUOZ
  8. Kartashov EM. Boundary value problems for parabolic equations in non-cylindrical domains. Teplofizika vysokikh temperatur. 2022;60(5):725–739. (In Russ.). DOI: 10.31 857/S004036442204007X
  9. Kartashov EM, Krylov SS. Modification of generalized Tikhonov-Samarskii heat potentials in the analytical theory of unsteady heat transfer for non-cylindrical domains // Thermal processes in engineering. 2022; 14(11):482–494. (In Russ.). DOI: 10.34759/tpt-2022-14-11-482-494
  10. Kudinov IV. Obtaining exact analytical solutions of heat conduction problems with time-varying boundary conditions. Vestnik Samarskogo gosudarstvennogo tekhniche-skogo universiteta. Seriya: Tekhnicheskie nauki. 2016; (4(52)):108–117. (In Russ.). EDN: XWZDFB
  11. Popov AI, Zinina SA, Eremin AV. Determination of permeability of porous media based on triply periodic Neovius minimal surfaces. Inzhenerskii vestnik Dona. 2024; (6(114)):648–655. (In Russ.). EDN: NDUZMT
  12. Al-Ketan O, Abu Al-Rub RK. Multifunctional Mechanical Metamaterials Based on Triply Periodic Minimal Surface Lattices. Advanced Engineering Materials. 2019;21(10). DOI: 10.1002/adem.201900524
  13. Gunaydin K. Energy absorption ability of crush boxes filled with strut based and ТПМП lattice structures. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2024;46(11). DOI: 10.1007/s40430-024-05207-z
  14. Ren ZY, Zheng QS. A Quantitative study of minimum sizes of representative volume elements of cubic polycrystals-numerical experiments. Journal of the Mecha-nics and Physics of Solids. 2002;50(4):881–893. EDN: AUAFDL
  15. Bragin DM, Eremin AV, Popov AI et al.  Method for determining the effective thermal conductivity of a porous material based on Schoen's I-WP(R) minimal surface. Vestnik Ivanovskogo gosudarstvennogo energeticheskogo universiteta. 2023;(2):61–68. (In Russ.). DOI: 10.17588/ 2072-2672.2023.2.061-068
  16. Gubareva KV, Popov AI, Zinina SA et al. Modeling of heat exchange in a plate with variable thermophysical properties. Nauchnoe obozrenie. Tekhnicheskie nauki. 2020(6):52–57. (In Russ.). EDN: CNFSBP

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