Thermal Diffusivity and Thermal Conductivity of Dispersed Glass Sphere Composites Over a Range of Volume Fractions

  • James K. CarsonEmail author


Glass spheres are often used as filler materials for composites. Comparatively few articles in the literature have been devoted to the measurement or modelling of thermal properties of composites containing glass spheres, and there does not appear to be any reported data on the measurement of thermal diffusivities over a range of filler volume fractions. In this study, the thermal diffusivities of guar-gel/glass sphere composites were measured using a transient comparative method. The addition of the glass beads to the gel increased the thermal diffusivity of the composite, more than doubling the thermal diffusivity of the composite relative to the diffusivity of the gel at the maximum glass volume fraction of approximately 0.57. Thermal conductivities of the composites were derived from the thermal diffusivity measurements, measured densities and estimated specific heat capacities of the composites. Two approaches to modelling the effective thermal diffusivity were considered.


Composites Glass spheres Thermal conductivity Thermal diffusivity 

List of symbols


Parameter defined by Eq. 14


Parameter defined by Eq. 15


Biot number defined by Eq. 5


Specific heat capacity (J·kg−1·K−1)


Intercept of linear portion of temperature history


Heat transfer coefficient (W·m−2·K−1)


Thermal conductivity (W·m−1·K−1)


Radius (m)


Slope of linear portion of temperature history (s−1)


Time (s)


Temperature (°C)


Volume fraction


Mass fraction


Thermal diffusivity (m2·s−1)


Dimensionless temperature change


Roots of Eq. 4


Parameter defined by Eq. 14


Bulk condition


Referring to reference sample


Referring to test sample or effective property


Referring to the guar gel


Referring to the glass spheres


Initial value


Maximum value


  1. 1.
    D.M. Bigg, Polym. Compos. 7, 125 (1986)CrossRefGoogle Scholar
  2. 2.
    Y. Agari, T. Uno, J. Appl. Polym. Sci. 32, 5705 (1986)CrossRefGoogle Scholar
  3. 3.
    I.H. Tavman, J. Appl. Polym. Sci. 62, 2161 (1996)CrossRefGoogle Scholar
  4. 4.
    M. Rusu, N.M. Sofian, C. Ibanescu, D. Rusu, Polym. Polym. Compos. 8, 427 (2000)Google Scholar
  5. 5.
    N.M. Sofian, M. Rusu, R. Neagu, E. Neagu, J. Thermoplast. Compos. Mater. 14, 20 (2001)CrossRefGoogle Scholar
  6. 6.
    Y.P. Mamunya, V.V. Davydenko, P. Pissis, E.V. Lebedev, Eur. Polym. J. 38, 1887 (2002)CrossRefGoogle Scholar
  7. 7.
    D. Kumlutas, I.H. Tavman, J. Thermoplast. Compos. Mater. 19, 441 (2006)CrossRefGoogle Scholar
  8. 8.
    N.L.B. Hussain, H. Ismail, D.M. Mariatti, J. Thermoplast. Compos. Mater. 19, 413 (2006)CrossRefGoogle Scholar
  9. 9.
    A.S. Luyt, J.A. Molefi, H. Krump, Polym. Degrad. Stab. 91, 1629 (2006)CrossRefGoogle Scholar
  10. 10.
    H.S. Tekce, D. Kumlutas, I.H. Tavman, J. Reinf. Plast. Compos. 26, 113 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    S.R. Annapragada, D. Sun, S.V. Garimella, Comput. Mater. Sci. 40, 255 (2007)CrossRefGoogle Scholar
  12. 12.
    V. Chifor, R. Orban, Z. Tekiner, M. Turker, Mater. Sci. Forum 672, 191 (2011)CrossRefGoogle Scholar
  13. 13.
    J.K. Carson, M. Noureldin, Int. Commun. Heat Mass Transf. 36, 458 (2009)CrossRefGoogle Scholar
  14. 14.
    J.K. Carson, Int. Commun. Heat Mass Transf. 38, 1024 (2011)CrossRefGoogle Scholar
  15. 15.
    M. Nikzad, S.H. Masood, I. Sbarski, Mater. Des. 32, 3448 (2011)CrossRefGoogle Scholar
  16. 16.
    J.K. Carson, M. Alsowailem, Polym. Polym. Compos. 25, 447 (2017)Google Scholar
  17. 17.
    D. Senior, Why use high quality glass spheres in plastics resin systems? Technical Report, Potters Industries Pty LtdGoogle Scholar
  18. 18.
    J.Z. Liang, F.H. Li, Polym. Test. 25, 527 (2006)CrossRefGoogle Scholar
  19. 19.
    J.Z. Liang, F.H. Li, Polym. Test. 26, 419 (2007)CrossRefGoogle Scholar
  20. 20.
    D. Mishra, A. Satapathy, A. Patnaik, Adv. Mater. Res. 445, 526 (2012)CrossRefGoogle Scholar
  21. 21.
    L. Běhálek, P. Lenfeld, J. Habr, J. Dobránsky, M. Seidl, B. Jiří, Key Eng. Mater. 669, 3 (2012)CrossRefGoogle Scholar
  22. 22.
    A.S. Doumbia, D. Jouannet, T.E. Falher, L. Cauret, Key Eng. Mater. 611–612, 859 (2014)CrossRefGoogle Scholar
  23. 23.
    A.S. Doumbia, A. Bourmaud, D. Jouannet, T. Falher, F. Orange, R. Retoux, L. Le Pluart, L. Cauret, Polym. Degrad. Stab. 114, 146 (2015)CrossRefGoogle Scholar
  24. 24.
    Zwart J, M.M. Yovanovich, Effective thermal diffusivity of simple packed system of spheres, in Proceedings of the ASME National Heat transfer Conference, Denver, Co, USA (1985)Google Scholar
  25. 25.
    Y.A. Cengel, A.J. Ghajar, Heat and Mass Transfer Fundamentals and Applications, 4th edn. (McGraw-Hill, New York, 2011)Google Scholar
  26. 26.
    F.P. Incropera, D.P. DeWitt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat Transfer, 6th edn. (Wiley, Hoboken NJ, 2006)Google Scholar
  27. 27.
    J.P. Holman, Heat Transfer, 7th edn. (McGraw-Hill, Singapore, 1992)Google Scholar
  28. 28.
    J.K. Carson, S.J. Lovatt, D.J. Tanner, A.C. Cleland, Int. J. Heat Mass Transf. 48, 2150 (2005)CrossRefGoogle Scholar
  29. 29.
    D.F. Jaguaribe, D.E. Beasley, Int. J. Heat Mass Transf. 17, 399 (1984)CrossRefGoogle Scholar
  30. 30.
    X. Zhang, H. Gu, M. Fujii, Int. J. Thermophys. 27, 569 (2006)ADSCrossRefGoogle Scholar
  31. 31.
    J.K. Carson, J.F. Wang, M.F. North, D.J. Cleland, J. Food Eng. 175, 65 (2016)CrossRefGoogle Scholar
  32. 32.
    L.E. Nielsen, Ind. Eng. Chem. Fundam. 13, 17 (1974)CrossRefGoogle Scholar
  33. 33.
    L.E. Nielsen, J. Appl. Polym. Sci. 17, 3819 (1973)CrossRefGoogle Scholar
  34. 34.
    C. Vales-Pinzon, A. Vega-Flick, N.W. Pech-May, J.J. Alvarado-Gil, R.A. Medina-Esquivel, M.A. Zambrano-Arjona, J.A. Mendez-Gamboa, J. Appl. Phys. 120, 205109 (2016)ADSCrossRefGoogle Scholar
  35. 35.
    W.P. Schimmel, J.V. Beck, A.B. Donaldson, J. Heat Transf. 99, 466 (1977)CrossRefGoogle Scholar
  36. 36.
    I. Ahmadi, Heat Mass Transf. 53, 277 (2017)ADSCrossRefGoogle Scholar
  37. 37.
    Y. Choi, M.R. Okos, Effects of temperature and composition on the thermal properties of foods. Food Eng. Process Appl. 1, 93–101 (1986)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of WaikatoHamiltonNew Zealand

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