Top

Engineering with Computers

Published in:

03-03-2024 | Original Article

A novel identification method for the non-equilibrium heat transfer problem in porous material

Authors: Hua-Yu Liu, Bao-Qi Zhang, Kai Yang, Xiao-Wei Gao

Published in: Engineering with Computers | Issue 5/2024

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this study, a novel method is proposed to effectively identify the thermal properties of porous composite materials, which are challenging to determine directly through experiments due to non-equilibrium heat transfer between the porous matrix and fluids. To solve the non-equilibrium heat transfer in saturated porous media and calculate temperature sensitivities to unknown properties, a complex-variables-based spectral element collocation method is developed. The proposed collocation method achieves high accuracy and employs an explicit time-marching approach to avoid repetitively solving of large-scale linear systems. Additionally, a normalization conjugate gradient method is introduced to overcome the slow convergence issue of the original conjugate gradient method caused by stiffness problems. Numerical cases demonstrate that this proposed method significantly improves efficiency in solving inverse non-equilibrium heat conservation problems, making it valuable for identifying complex systems with numerous unknown parameters.

previous article A smooth single-variable-based interpolation function for multi-material topology optimization

next article Modified strain gradient analysis of the functionally graded triply periodic minimal surface microplate using isogeometric approach

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Chen J, Fu Y, Qian N, Jiang H, Ching CY, Ewing D, Dai C (2021) Investigation on cooling behavior of axially rotating heat pipe in profile grinding of turbine blade slots. Appl Thermal Eng 182:116031. https://doi.org/10.1016/j.applthermaleng.2020.116031CrossRef

Laraia M, Manna M, Cinque G, Di Martino P (2013) A combustor liner cooling system design methodology based on a fluid/structure approach. Appl Thermal Eng 60(1):105–121. https://doi.org/10.1016/j.applthermaleng.2013.06.012CrossRef

Huang Z, Zhu Y-H, Xiong Y-B, Jiang P-X (2014) Investigation of transpiration cooling for sintered metal porous struts in supersonic flow. Appl Thermal Eng 70(1):240–249. https://doi.org/10.1016/j.applthermaleng.2014.02.076CrossRef

Buahom P (2023) Theoretical modeling and optimization of thermal transport in thermal insulation foams. PhD thesis

Lin X-C, Li S-L, Li W-X, Wang Z-H, Zhang J-Y, Liu B-W, Fu T, Zhao H-B, Wang Y-Z (2023) Thermo-responsive self-ceramifiable robust aerogel with exceptional strengthening and thermal insulating performance at ultrahigh temperatures. Adv Funct Mater 33(27):2214913. https://doi.org/10.1002/adfm.202214913CrossRef

Cao B-Y, Zhang Z-T (2022) Thermal smart materials and their applications in space thermal control system. Acta Physica Sinica 71(1), 014401–1 (2022 - 2021-10-11)

Prasanth N, Sharma M, Yadav RN, Jain P (2020) Designing of latent heat thermal energy storage systems using metal porous structures for storing solar energy. J Energy Storage 32:101990. https://doi.org/10.1016/j.est.2020.101990CrossRef

Rahmanian S, Moein-Jahromi M, Rahmanian-Koushkaki H, Sopian K (2021) Performance investigation of inclined CPV system with composites of PCM, metal foam and nanoparticles. Solar Energy 230:883–901. https://doi.org/10.1016/j.solener.2021.10.088CrossRef

Yang X, Feng S, Zhang Q, Chai Y, Jin L, Lu TJ (2017) The role of porous metal foam on the unidirectional solidification of saturating fluid for cold storage. Appl Energy 194:508–521. https://doi.org/10.1016/j.apenergy.2016.09.050CrossRef

10.

Nield DA (1991) Estimation of the stagnant thermal conductivity of saturated porous media. Int J Heat Mass Transfer 34(6):1575–1576. https://doi.org/10.1016/0017-9310(91)90300-4CrossRef

11.

Nield DA, Bejan A (2013) Convection in porous media. Springer, New York. https://doi.org/10.1007/978-1-4614-5541-7CrossRef

12.

Yang XH, Bai JX, Yan HB, Kuang JJ, Lu TJ, Kim T (2014) An analytical unit cell model for the effective thermal conductivity of high porosity open-cell metal foams. Transport Porous Media 102(3):403–426. https://doi.org/10.1007/s11242-014-0281-zCrossRef

13.

Buahom P, Thongmongkol K, Alshrah M, Gong P, Park CB (2023) Effects of cell anisotropy on conductive and radiative thermal transport in polymeric foam insulation. Energy 275:127473. https://doi.org/10.1016/j.energy.2023.127473CrossRef

14.

Šimonová P, Uhlířová T, Pabst W (2023) Computer modeling of Young’s modulus and thermal conductivity changes during sintering without shrinkage. J Eur Ceram Soc 43(11):4885–4895. https://doi.org/10.1016/j.jeurceramsoc.2023.04.018CrossRef

15.

Yazdanparast R, Rafiee R (2023) Determining in-plane material properties of square core cellular materials using computational homogenization technique. Eng Comput 39(1):373–386. https://doi.org/10.1007/s00366-021-01562-wCrossRef

16.

Sans M, Farges O, Schick V, Parent G (2022) Solving transient coupled conductive and radiative transfers in porous media with a monte carlo method: characterization of thermal conductivity of foams using a numerical Flash Method. Int J Thermal Sci 179:107656. https://doi.org/10.1016/j.ijthermalsci.2022.107656CrossRef

17.

Polyaev VM, Mozhaev AP, Galitseysky BM, Lozhkin AL (1996) A study of internal heat transfer in nonuniform porous structures. Exp Thermal Fluid Sci 12(4):426–432. https://doi.org/10.1016/0894-1777(95)00132-8CrossRef

18.

Dixon AG, Cresswell DL (1979) Theoretical prediction of effective heat transfer parameters in packed beds. AIChE J 25(4):663–676. https://doi.org/10.1002/aic.690250413CrossRef

19.

Wakao N, Kagei S (1982) Heat and mass transfer in packed beds.

20.

Grangeot G, Quintard M, Whitaker S (1994) Heat transfer in packed beds: interpretation of experiments in terms of one- and two-equation models. In: Heat Transf. vol. 5, pp. 291–296

21.

Yang J, Wang J, Bu S, Zeng M, Wang Q, Nakayama A (2012) Experimental analysis of forced convective heat transfer in novel structured packed beds of particles. Chem Eng Sci 71:126–137. https://doi.org/10.1016/j.ces.2011.12.005CrossRef

22.

Hu Y, Wang J, Yang J, Mudawar I, Wang Q (2019) Experimental study of forced convective heat transfer in grille-particle composite packed beds. Int J Heat Mass Transfer 129:103–112. https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.103CrossRef

23.

Singh SK, Yadav MK, Sonawane R, Khandekar S, Muralidhar K (2017) Estimation of time-dependent wall heat flux from single thermocouple data. Int J Thermal Sci 115:1–15. https://doi.org/10.1016/j.ijthermalsci.2017.01.010CrossRef

24.

Sajedi R, Faraji J, Kowsary F (2021) A new damping strategy of Levenberg–Marquardt algorithm with a fuzzy method for inverse heat transfer problem parameter estimation. Int Commun Heat Mass Transfer 126:105433. https://doi.org/10.1016/j.icheatmasstransfer.2021.105433CrossRef

25.

Zhang C, Li Y, Cui M, Sun C, Gao X-W (2023) A novel method for simultaneous determination of thermophysical properties and boundary conditions of phase change problems based on element differential method. Eng Anal Bound Elements 157:1–11. https://doi.org/10.1016/j.enganabound.2023.09.002MathSciNetCrossRef

26.

Cui M, Zhao Y, Xu B, Gao X.-W, (2017) A new approach for determining damping factors in Levenberg–Marquardt algorithm for solving an inverse heat conduction problem. Int J Heat Mass Transfer 107:747–754. https://doi.org/10.1016/j.ijheatmasstransfer.2016.11.101

27.

Zeng Y, Wang H, Zhang S, Cai Y, Li E (2019) A novel adaptive approximate Bayesian computation method for inverse heat conduction problem. Int J Heat Mass Transfer 134:185–197. https://doi.org/10.1016/j.ijheatmasstransfer.2019.01.002CrossRef

28.

Luo X, Yang Z (2017) A new approach for estimation of total heat exchange factor in reheating furnace by solving an inverse heat conduction problem. Int J Heat Mass Transfer 112:1062–1071. https://doi.org/10.1016/j.ijheatmasstransfer.2017.05.009CrossRef

29.

Pang H-Q, Shao X, Zhang Z-T, Xie X, Zhang L-M, Chen X, Liu T-Y, Gao Y-F (2023) Inverse analysis of monolithic silica aerogel’s thermophysical properties under limited measurement using differentiable learning. Int J Thermophys 44(11):163. https://doi.org/10.1007/s10765-023-03268-1CrossRef

30.

Pang H-Q, Shao X, Zhang Z-T, Xie X, Dai M-Y, Guo J-F, Zhang Y-B, Liu T-Y, Gao Y-F (2023) Physics-informed learning for thermophysical field reconstruction and parameter measurement in a nano-porous insulator’s heat transfer problem. Int Commun Heat Mass Transfer 148:107045. https://doi.org/10.1016/j.icheatmasstransfer.2023.107045CrossRef

31.

Liu T, Liu S (2018) Identification of diffusion parameters in a non-linear convection–diffusion equation using adaptive homotopy perturbation method. Inverse Prob Sci Eng 26(4):464–478. https://doi.org/10.1080/17415977.2017.1316495MathSciNetCrossRef

32.

Liu T (2018) A nonlinear multigrid method for inverse problem in the multiphase porous media flow. Appl Math Comput 320:271–281. https://doi.org/10.1016/j.amc.2017.09.039MathSciNetCrossRef

33.

Liu T, Xue R, Liu C, Qi Y (2021) A regularization homotopy strategy for the constrained parameter inversion of partial differential equations. Entropy 23(11):1480. https://doi.org/10.3390/e23111480MathSciNetCrossRef

34.

Liu T (2022) Porosity reconstruction based on Biot elastic model of porous media by homotopy perturbation method. Chaos Solitons Fract 158:112007. https://doi.org/10.1016/j.chaos.2022.112007MathSciNetCrossRef

35.

Cui M, Yang K, Xu X.-L, Wang S.-D, Gao X.-W, (2016) A modified Levenberg–Marquardt algorithm for simultaneous estimation of multi-parameters of boundary heat flux by solving transient nonlinear inverse heat conduction problems. Int J Heat Mass Transfer 97:908–916. https://doi.org/10.1016/j.ijheatmasstransfer.2016.02.085

36.

Lyness JN, Moler CB (1967) Numerical differentiation of analytic functions. SIAM J Numer Anal 4(2):202–210. https://doi.org/10.1137/0704019MathSciNetCrossRef

37.

Cui M, Mei J, Zhang B-W, Xu B-B, Zhou L, Zhang Y (2018) Inverse identification of boundary conditions in a scramjet combustor with a regenerative cooling system. Appl Thermal Eng 134:555–563. https://doi.org/10.1016/j.applthermaleng.2018.02.038CrossRef

38.

Zhang B, Mei J, Cui M, Gao X-W, Zhang Y (2019) A general approach for solving three-dimensional transient nonlinear inverse heat conduction problems in irregular complex structures. Int J Heat Mass Transfer 140:909–917. https://doi.org/10.1016/j.ijheatmasstransfer.2019.06.049CrossRef

39.

Jiang G-H, Tan C-H, Jiang W-W, Yang K, Wang W-Z, Gao X-W (2022) Shape reconstruction in transient heat conduction problems based on radial integration boundary element method. Int J Heat Mass Transfer 191:122830. https://doi.org/10.1016/j.ijheatmasstransfer.2022.122830CrossRef

40.

Wang D, Wang J, Wu J (2020) Arbitrary order recursive formulation of meshfree gradients with application to superconvergent collocation analysis of Kirchhoff plates. Comput Mech 65(3):877–903. https://doi.org/10.1007/s00466-019-01799-9MathSciNetCrossRef

41.

Deng L, Wang D (2023) An accuracy analysis framework for meshfree collocation methods with particular emphasis on boundary effects. Comput Methods Appl Mech Eng 404:115782. https://doi.org/10.1016/j.cma.2022.115782MathSciNetCrossRef

42.

Wright K (1964) Chebyshev collocation methods for ordinary differential equations. Comput J 6(4):358–365. https://doi.org/10.1093/comjnl/6.4.358MathSciNetCrossRef

43.

Canuto C, Hussaini MY, Quarteroni A, Zang TA (1988) Spectral methods in fluid dynamics. Scientific Computation. Springer, Berlin, HeidelbergCrossRef

44.

Gu Z, Kong Y (2021) Spectral collocation method for nonlinear Riemann–Liouville fractional differential system. Calcolo 58(2):12. https://doi.org/10.1007/s10092-021-00403-yMathSciNetCrossRef

45.

Gao X-W, Li Z-Y, Yang K, Lv J, Peng HF, Cui M, Ruan B, Zhu Q-H (2018) Element differential method and its application in thermal-mechanical problems. Int J Numer Methods Eng 113(1):82–108. https://doi.org/10.1002/nme.5604MathSciNetCrossRef

46.

Xu B-B, Gao X-W, Cui M (2021) High precision simulation of thermal-mechanical problems in functionally graded materials by spectral element differential method. Compos Struct 270:114084. https://doi.org/10.1016/j.compstruct.2021.114084CrossRef

47.

Liu H-Y, Gao X-W, Zhang G-Y, Cui M (2023) Explicit spectral element collocation method for nonlinear transient heat transfer. Comput Math Appl 143:289–302. https://doi.org/10.1016/j.camwa.2023.05.018MathSciNetCrossRef

48.

Liu H-Y, Gao X-W, Zhang G-Y, Yang K (2023) Jacobian weighted element differential method for solid mechanics. J Comput Sci 71:102038. https://doi.org/10.1016/j.jocs.2023.102038CrossRef

49.

Wang D-D, Wang J-R, Wu J-C (2018) Superconvergent gradient smoothing meshfree collocation method. Comput Methods Appl Mech Eng 340:728–766. https://doi.org/10.1016/j.cma.2018.06.021MathSciNetCrossRef

50.

Wen PH, Cao P, Korakianitis T (2014) Finite Block Method in elasticity. Eng Anal Bound Element 46:116–125. https://doi.org/10.1016/j.enganabound.2014.05.006MathSciNetCrossRef

51.

Xu B-B, Gao X-W, Cui M (2021) High precision simulation and analysis of non-Fourier heat transfer during laser processing. Int J Heat Mass Transfer 178:121574. https://doi.org/10.1016/j.ijheatmasstransfer.2021.121574CrossRef

52.

Auricchio F, Beirão da Veiga L, Hughes TJR, Reali A, Sangalli G (2012) Isogeometric collocation for elastostatics and explicit dynamics. Comput Methods Appl Mech Eng 249–252:2–14. https://doi.org/10.1016/j.cma.2012.03.026MathSciNetCrossRef

53.

Gao X-W, Zheng Y-T, Fantuzzi N (2020) Local least-squares element differential method for solving heat conduction problems in composite structures. Numer Heat Transfer Part B Fund 77(6):441–460. https://doi.org/10.1080/10407790.2020.1746584CrossRef

54.

Khan FA, Fischer C, Straatman AG (2015) Numerical model for non-equilibrium heat and mass exchange in conjugate fluid/solid/porous domains with application to evaporative cooling and drying. Int J Heat Mass Transfer 80:513–528. https://doi.org/10.1016/j.ijheatmasstransfer.2014.09.051CrossRef

55.

Calmidi V (1998) Transport phenomena in high porosity fibrous metal foams. PhD thesis, University of Colorado, Boulder, Colorado

56.

Li Z, Zhang H, Liu Y, McDonough JM (2020) Implementation of compressible porous-fluid coupling method in an aerodynamics and aeroacoustics code part I: laminar flow. Appl Math Comput 364:124682. https://doi.org/10.1016/j.amc.2019.124682MathSciNetCrossRef

57.

Moukalled F, Mangani L, Darwish M (2016) The finite volume method in computational fluid dynamics: an advanced introduction with OpenFOAM® and Matlab. Springer, Heidelberg

58.

Zienkiewicz OC, Taylor RL (2013) The finite element method: its basis and fundamentals, 7th, edition. Butterworth-Heinemann, Oxford

Title: A novel identification method for the non-equilibrium heat transfer problem in porous material
Authors: Hua-Yu Liu
Bao-Qi Zhang
Kai Yang
Xiao-Wei Gao
Publication date: 03-03-2024
Publisher: Springer London
Published in: Engineering with Computers / Issue 5/2024
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI: https://doi.org/10.1007/s00366-024-01948-6

Element differential method for contact problems with non-conforming contact discretization

Original Article

A multiscale stabilized physics informed neural networks with weakly imposed boundary conditions transfer learning method for modeling advection dominated flow

Original Article

Unstructured mesh tools for magnetically confined fusion system simulations

Original Article

Coupling of bond-based peridynamics and continuous density-based topology optimization methods for effective design of three-dimensional structures with discontinuities

Open Access
Original Article

A rapidly trained DNN model for real-time flexible multibody dynamics simulations with a fixed-time increment

Original Article

NeuFENet: neural finite element solutions with theoretical bounds for parametric PDEs

Original Article

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Element differential method for contact problems with non-conforming contact discretization

A multiscale stabilized physics informed neural networks with weakly imposed boundary conditions transfer learning method for modeling advection dominated flow

Unstructured mesh tools for magnetically confined fusion system simulations

Coupling of bond-based peridynamics and continuous density-based topology optimization methods for effective design of three-dimensional structures with discontinuities

A rapidly trained DNN model for real-time flexible multibody dynamics simulations with a fixed-time increment

NeuFENet: neural finite element solutions with theoretical bounds for parametric PDEs