Skip to main content
Log in

A model for predicting thermal conductivity of porous composite materials

  • Original Article
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

An effective model of thermal conductivity (TC) can provide opportunity to design thermal insulation materials with specific insulation properties and contribute to the insulation industry by decreasing costs and saving time for laboratory testing. At present, there are five basic structural models, series, parallel, maxwell–eucken (ME) 1 and 2, and effective medium theory (EMT), which could be utilized to determine the TC of a material. In this study, these five basic models were selected to check which model is most suitable for estimating TC of porous composite materials. Two different types of materials (fiber composite and 3D-printed) were also selected as porous insulation materials, and their TC was determined experimentally. After that, experimental data were compared with the estimated data obtained from five basic models. It was found that among the five basic models, ME2 and EMT models give comparatively better predictions with average percentage differences (between experimental and estimated data) of 11.10% and 9.90%, respectively. However, the prediction of these existing models is not satisfactory enough to be used for commercial purposes. Hence, a model was developed combining ME1 and ME2 models. Tested results revealed that the proposed model provides better prediction of TC of porous composite materials. The average percentage differences between proposed models and experimental data are 3.12% and 0.92% for fibrous composite and printed insulation, respectively. This indicates that the accuracy of the proposed model is sufficient to be used in industrial sectors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

Data will be available upon request.

References

  1. Carson JK (2002) Prediction of the thermal conductivity of porous foods: a thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Food Engineering, Massey University, Palmerston North, New Zealand, 2002. Massey University

  2. Islam S, Bhat G (2019) Environmentally-friendly thermal and acoustic insulation materials from recycled textiles. J Environ Manage 251:109536 (1–21). https://doi.org/10.1016/j.jenvman.2019.109536

  3. Thermtest Instrument (2021) In: Mater Therm Prop database. https://thermtest.com/materials-database. Accessed 7 Jun 2021

  4. NCFS (2021) In: Therm Prop databases online interfaces. https://ncfs.ucf.edu/burn_db/Thermal_Properties/material_thermal.html. Accessed 7 Jun 2021

  5. Kuvandykova D (2010) A model for predicting thermal properties of asphalt mixtures from their constituents. University of New Brunswick (Canada)

  6. Islam S, Bhat G, Sikdar P (2023) Thermal and acoustic performance evaluation of 3D-Printable PLA materials. J Build Eng 67:105979. https://doi.org/10.1016/j.jobe.2023.105979

  7. Headley AJ, Hileman MB, Robbins AS et al (2019) Thermal conductivity measurements and modeling of ceramic fiber insulation materials. Int J Heat Mass Transf 129:1287–1294. https://doi.org/10.1016/j.ijheatmasstransfer.2018.10.060

    Article  Google Scholar 

  8. Carson JK (2006) Review of effective thermal conductivity models for foods. Int J Refrig 29:958–967. https://doi.org/10.1016/j.ijrefrig.2006.03.016

    Article  Google Scholar 

  9. Gong L, Wang Y, Cheng X et al (2014) A novel effective medium theory for modelling the thermal conductivity of porous materials. Int J Heat Mass Transf 68:295–298. https://doi.org/10.1016/j.ijheatmasstransfer.2013.09.043

    Article  Google Scholar 

  10. Miettinen L, Kekäläinen P, Turpeinen T et al (2012) Dependence of thermal conductivity on structural parameters in porous samples. AIP Adv 2:1–15. https://doi.org/10.1063/1.3676435

    Article  Google Scholar 

  11. Bolot R, Antou G, Montavon G, Coddet C (2005) A two-dimensional heat transfer model for thermal barrier coating average thermal conductivity computation. Numer Heat Transf Part A Appl 47:875–898. https://doi.org/10.1080/10407780590921953

    Article  Google Scholar 

  12. Rocha RPA, Cruz MAE (2001) Computation of the effective conductivity of unidirectional fibrous composites with an interfacial thermal resistance. Numer Heat Transf Part A Appl 39:179–203. https://doi.org/10.1080/10407780118981

    Article  Google Scholar 

  13. Divo E, Kassab A, Rodriguez F (2000) Characterization of space dependent thermal conductivity with a BEM-based genetic algorithm. Numer Heat Transf Part A Appl 37:845–875. https://doi.org/10.1080/10407780050045865

    Article  Google Scholar 

  14. Wang J, Carson JK, North MF, Cleland DJ (2008) A new structural model of effective thermal conductivity for heterogeneous materials with co-continuous phases. Int J Heat Mass Transf 51:2389–2397. https://doi.org/10.1016/j.ijheatmasstransfer.2007.08.028

    Article  Google Scholar 

  15. Leach AG (1993) The thermal conductivity of foams. I. Models for heat conduction. J Phys D Appl Phys 26:733–739. https://doi.org/10.1088/0022-3727/26/5/003

    Article  Google Scholar 

  16. Hashin Z, Shtrikman S (1962) A variational approach to the theory of the effective magnetic permeability of multiphase materials. J Appl Phys 33:3125–3131. https://doi.org/10.1063/1.1728579

    Article  MATH  Google Scholar 

  17. Landauer R (1952) The electrical resistance of binary metallic mixtures. J Appl Phys 23:779–784. https://doi.org/10.1063/1.1702301

    Article  Google Scholar 

  18. Hochstein DP (2013) Thermal Conductivity of Fiber-Reinforced Lightweight Cement Composites. Columbia University

  19. Wang J, Carson JK, North MF, Cleland DJ (2006) A new approach to modelling the effective thermal conductivity of heterogeneous materials. Int J Heat Mass Transf 49:3075–3083. https://doi.org/10.1016/j.ijheatmasstransfer.2006.02.007

    Article  MATH  Google Scholar 

  20. Wei S, Yiqiang C, Yunsheng Z, Jones MR (2013) Characterization and simulation of microstructure and thermal properties of foamed concrete. Constr Build Mater 47:1278–1291. https://doi.org/10.1016/j.conbuildmat.2013.06.027

    Article  Google Scholar 

  21. Islam S, El Messiry M, Sikdar PP et al (2020) Microstructure and performance characteristics of acoustic insulation materials from post-consumer recycled denim fabrics. J Ind Text. https://doi.org/10.1177/1528083720940746

  22. Levenspiel O (2014) The three mechanisms of heat transfer: conduction, convection, and radiation. In: Levenspiel O (ed) Engineering Flow and Heat Exchange. Springer, New York, pp 179–210

    Chapter  Google Scholar 

  23. Dempsey BJ, Thompson MR (1970) A heat transfer model for evaluating frost action and temperature-related effects in multilayered pavement systems. Highw Res Rec 39–56

  24. Adkins DF, Merkley GP (1990) Mathematical model of temperature changes in concrete pavements. J Transp Eng 116:349–358. https://doi.org/10.1061/(ASCE)0733-947X(1990)116:3(349)

    Article  Google Scholar 

  25. Jiji LM (2009) Heat Conduction, 3rd edn. Springer, Berlin, Heidelberg

    Book  MATH  Google Scholar 

  26. Bergman TL, Incropera FP, DeWitt DP, Lavine AS (2011) Fundamentals of heat and mass transfer. John Wiley & Sons, Hoboken, NJ

    Google Scholar 

  27. Skochdopole RE (1961) The thermal conductivity of foamed plastics. Chem Eng Prog 57:55–59

    Google Scholar 

  28. Pietrak K, Wisniewski TS (2015) A review of models for effective thermal conductivity of composite materials. J Power Technol 95:14–24

    Google Scholar 

  29. Xu G (2013) Direct measurement of through-plane thermal conductivity of partially saturated fuel cell diffusion media. University of Tennessee, Knoxville

    Google Scholar 

  30. Carson JK, Lovatt SJ, Tanner DJ, Cleland AC (2005) Thermal conductivity bounds for isotropic, porous materials. Int J Heat Mass Transf 48:2150–2158. https://doi.org/10.1016/j.ijheatmasstransfer.2004.12.032

    Article  MATH  Google Scholar 

  31. Sadeghi E, Bahrami M, Djilali N (2008) Analytic determination of the effective thermal conductivity of PEM fuel cell gas diffusion layers. J Power Sources 179:200–208. https://doi.org/10.1016/j.jpowsour.2007.12.058

    Article  Google Scholar 

  32. Maxwell JC (1904) A treatise on electricity and magnetism. Oxford University Press, Oxford, UK

    MATH  Google Scholar 

  33. McCartney LN, Kelly A (2008) Maxwell’s far-field methodology applied to the prediction of properties of multi-phase isotropic particulate composites. Proc R Soc A Math Phys Eng Sci 464:423–446. https://doi.org/10.1098/rspa.2007.0071

    Article  MathSciNet  MATH  Google Scholar 

  34. Bird RB, Stewart WE, Lightfoot EN (2006) Transport phenomena. John Wiley & Sons, Hoboken, NJ

    Google Scholar 

  35. Eucken A (1932) W armeleitf ahigkeit keramischer feuerfester Stoffe-Berechnung aus der W armeleitf ahigkeit der Bestandteile. Forsch auf dem Gebiet des Ingenieurwesens 3:16

    Google Scholar 

  36. Maxwell JC (1954) A Treatise on Electricity and Magnetism. Dover Publications Inc., New York, NY

    MATH  Google Scholar 

  37. Eucken A (1940) Allgemeine gesetzmäßigkeiten für das wärmeleitvermögen verschiedener stoffarten und aggregatzustände. Forsch auf dem Gebiet des Ingenieurwesens A 11:6–20. https://doi.org/10.1007/BF02584103

    Article  Google Scholar 

  38. Hamilton RL, Crosser OK (1962) Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Fundam 1:187–191. https://doi.org/10.1021/i160003a005

    Article  Google Scholar 

  39. Shin D-H, Cho H-K, Tak N-I, Park G-C (2014) Evaluation of Effective thermal conductivity models on the prismatic fuel block of a Very High Temperature Reactor by CFD analysis. https://inis.iaea.org/collection/NCLCollectionStore/_Public/48/076/48076893.pdf. Accessed 1 Apr 2021

  40. Bohorquez de Silva M (2010) Study of microstructure effect on the thermal properties of Yttria-stabilized-Zirconia thermal barrier coatings made by atmospheric plasma spray and pressing machine. Louisiana State University

  41. Sundén B, Yuan J (2013) Evaluation of models of the effective thermal conductivity of porous materials relevant to fuel cell electrodes. Int J Comput Methods Exp Meas 1:440–455. https://doi.org/10.2495/CMEM-V1-N4-440-455

    Article  Google Scholar 

  42. Yuan J (2009) Intumescent coating performance on steel structures under realistic fire conditions

  43. Di Blasi C, Branca C (2001) Mathematical model for the nonsteady decomposition of intumescent coatings. AIChE J 47:2359–2370. https://doi.org/10.1002/aic.690471020

    Article  Google Scholar 

  44. (2017) ASTM F1868 - 17. In: Stand. Test Method Therm. Evaporative Resist. Cloth. Mater. Using a Sweating Hot Plate. https://www.astm.org/Standards/F1868. Accessed 10 May 2022

  45. Keane P (2020) Thermally Conductive Polymer Materials for 3D Printing. https://3dprinting.com/3d-printing-use-cases/thermally-conductive-polymer-materials/#:~:text=PLA has a thermal conductivity of about 0.13,%28m%2AK%29%2C depending on the alloy and other factors

  46. Hearle JWS, Morton WE (2008) Physical properties of textile fibres. Woodhead Publishing, Cambridge

    Google Scholar 

  47. DuPont. In: DuPontTM Sorona® 3301 NC010 Renew. sourcedTM Thermoplast. Polym. https://www.gc.co.th/upload/datasheet/sorona_3301_nc_010.pdf. Accessed 7 Jun 2021

  48. ASTM F316–03 (2019) In: Stand. Test Methods Pore Size Charact. Membr. Filters by Bubble Point Mean Flow Pore Test. https://www.astm.org/Standards/F316.htm. Accessed 10 May 2022

  49. Fatima S, Mohanty AR (2011) Acoustical and fire-retardant properties of jute composite materials. Appl Acoust 72:108–114. https://doi.org/10.1016/j.apacoust.2010.10.005

    Article  Google Scholar 

  50. Grabowska B, Kasperski J (2020) The Thermal Conductivity of 3D Printed Plastic Insulation Materials—The Effect of Optimizing the Regular Structure of Closures. Materials (Basel) 13:1–15. https://doi.org/10.3390/ma13194400

    Article  Google Scholar 

  51. Touloukian YS, Liley PE, Saxena SC (1970) Thermophysical properties of matter-the tprc data series. volume 3. thermal conductivity-nonmetallic liquids and gases. Thermophysical and electronic properties information analysis center

Download references

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Author information

Authors and Affiliations

Authors

Contributions

Shafiqul Islam: Conception and design of study, acquisition of data, analysis and/or interpretation of data, draft and revise the manuscript, and approve the final manuscript. Gajanan Bhat: Conception and design of study, revise the manuscript, and approve the final manuscript.

Corresponding author

Correspondence to Shafiqul Islam.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Islam, S., Bhat, G. A model for predicting thermal conductivity of porous composite materials. Heat Mass Transfer 59, 2023–2034 (2023). https://doi.org/10.1007/s00231-023-03380-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-023-03380-w

Navigation