Heat and Mass Transfer

, Volume 53, Issue 1, pp 277–290 | Cite as

Evaluation of effective thermal diffusivity and conductivity of fibrous materials through computational micromechanics

  • Isa Ahmadi


The aim of present study is to investigate the effective thermal properties of composite material via micromechanical modeling of the composite material as a heterogeneous material. These properties mainly include the thermal diffusivity and the thermal conductivity of composites. For this purpose, a definition is presented for effective thermal diffusivity for heterogeneous materials based on heat diffusion rate into the material in a transient heat transfer. A micromechanical model based on the Representative Volume Element (RVE) is presented for modeling the heat conduction in the fibrous composite materials. An appropriate heat transfer problem for the RVE is defined so that by the analogy of the numerical results the effective properties of the RVE can be estimated. A numerical method is employed to analyze the steady-state and transient heat flux and temperature in the RVE. To validate the model, the predictions of present model are compared with results of analytical method, FEM and some available experimental data in the open literature. The effective thermal conductivity and thermal diffusivity are then obtained for fibrous composites via the present micromechanical model. The SiC/Ti, SiC/Ti6%Al4%V and Glass/Epoxy composites with various fiber volume fractions are considered in this study.


Thermal Diffusivity Representative Volume Element Effective Thermal Conductivity Fiber Volume Fraction Micromechanical Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Springer GS, Tsai SW (1967) Thermal conductivities of unidirectional materials. J Compos Mater 1:166–173CrossRefGoogle Scholar
  2. 2.
    Gogo W, Furmanski P (1980) Some investigations of effective thermal conductivity of unidirectional fiber-reinforced composites. J Compos Mater 14:167–176CrossRefGoogle Scholar
  3. 3.
    Progelhof RC, Throne JL, Ruetsch RR (1976) Methods for prediction the thermal conductivity of composite systems. Polym Eng Sci 9(16):615–625CrossRefGoogle Scholar
  4. 4.
    Han LS, Cosner AA (1981) Effective thermal conductivities of fibrous composites. ASME Trans J Heat Transf 103:387–392CrossRefGoogle Scholar
  5. 5.
    Gordon FH, Turner SP, Taylor R, Clyne TW (1994) The effect of the interface on the thermal conductivity of titanium-based composites. Composites 25:583–592CrossRefGoogle Scholar
  6. 6.
    Ning QG, Chou TW (1995) Closed-form solutions of the in-plane effective thermal conductivities of woven-fabric composites. Compos Sci Technol 55(1):41–48CrossRefGoogle Scholar
  7. 7.
    Chen CH, Wang YC (1996) Effective thermal conductivity of misoriented short-fiber reinforced thermoplastics. Mech Mater 23:217–228CrossRefGoogle Scholar
  8. 8.
    Milton GW (2000) Mechanics of composites. Cambridge University Press, CambridgeGoogle Scholar
  9. 9.
    Sevostianov I, Kachanov M (2003) Connection between elastic moduli and thermal conductivities of anisotropic short fiber reinforced thermoplastics: theory and experimental verification. Mater Sci Eng, A 360:339–344CrossRefGoogle Scholar
  10. 10.
    Zhou H, Zhang S, Yang M (2007) The effect of heat-transfer passages on the effective thermal conductivity of high filler loading composite materials. Compos Sci Technol 67:1035–1040CrossRefGoogle Scholar
  11. 11.
    Rolfes R, Hammerschmidt U (1995) Transverse thermal conductivity of CFRP laminates: a numerical and experimental validation of approximation formulae. Compos Sci Technol 54:45–54CrossRefGoogle Scholar
  12. 12.
    Jones WF, Pascal F (1995) Numerical calculations of thermal conductivities of composites—a 3-D model. Geophysics 60(4):1038–1050CrossRefGoogle Scholar
  13. 13.
    Fiedler Th, Pesetskaya E, Öchsner A, Gracio J (2005) Numerical and analytical calculation of the orthotropic heat transfer properties of fibre reinforced materials, Mat.-wiss. u. Werkstofftech., 36, No. 10 F 2005 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimGoogle Scholar
  14. 14.
    Al-Nassar YN (2006) Prediction of thermal conductivity of air voided-fiber-reinforced composite laminates part II: 3D simulation. Heat Mass Transf 43:117–122CrossRefGoogle Scholar
  15. 15.
    Al-Sulaiman FA, Mokheimer EMA, Al-Nassar YN (2006) Prediction of the thermal conductivity of the constituents of fiber reinforced composite laminates. Heat Mass Transf 42:370–377CrossRefGoogle Scholar
  16. 16.
    Al-Sulaiman FA, Al-Nassar YN, Mokheimer EMA (2006) Numerical prediction of the thermal conductivity of fibers. Heat Mass Transf 42:449–461CrossRefGoogle Scholar
  17. 17.
    Graham S, McDowell DL (2003) Numerical analysis of the transverse thermal conductivity of composites with imperfect interfaces. ASME J Heat Transf 125(3):389–393CrossRefGoogle Scholar
  18. 18.
    Marcos-Gَmez D, Ching-Lloyd J, Elizalde MR, Clegg WJ, Molina-Aldareguia JM (2010) Predicting the thermal conductivity of composite materials with imperfect interfaces. Composites Science and Technology 70:2276–2283CrossRefGoogle Scholar
  19. 19.
    Klett JW, Ervin VJ, Edie DD (1999) Finite-element modeling of heat transfer in carbon/carbon composites. Compos Sci Technol 59(4):593–607CrossRefGoogle Scholar
  20. 20.
    Ahmadi Isa, Aghdam MM (2011) Heat transfer in composite materials using a new truly local meshless method. Int J Numer Meth Heat Fluid Flow 21(3):293–309CrossRefGoogle Scholar
  21. 21.
    Sihn S, Roy AK (2011) Micromechanical analysis for transverse thermal conductivity of composites. J Compos Mater 45(11):1245–1255CrossRefGoogle Scholar
  22. 22.
    Abot JL, Bardin G, Spriegel C, Song Y, Raghavan V, Govindaraju N (2011) Thermal conductivity of carbon nanotube array laminated composite materials. J Compos Mater 45:321–340. doi: 10.1177/0021998310373512 CrossRefGoogle Scholar
  23. 23.
    Mulholland GP, Cobble MH (1972) Diffusion through composite media. Int J Heat Mass Transf 15:147–160CrossRefGoogle Scholar
  24. 24.
    Maewel A, Bache TC, Hegemier GA (1976) A continum model for diffusion in laminated composite media. ASME J Heat Transf 98:133–138CrossRefGoogle Scholar
  25. 25.
    Schimmel WP, Beck JV, Donaldson AB (1977) Effective thermal diffusivity for a multimaterial composite laminate. ASME J Heat Transf 99:466–470CrossRefGoogle Scholar
  26. 26.
    Kyaar KhA, Vares VA (1982) Calculation of the effective thermal diffusivity of heterogeneous layered material. J Eng Phys 43(1):768–773CrossRefGoogle Scholar
  27. 27.
    Antonopoulos KA, Tzivanidis C (1996) Analytical solution of boundary value problems of heat conduction in composite regions with arbitrary convection boundary conditions. Acta Mech 118:65–78CrossRefzbMATHGoogle Scholar
  28. 28.
    Sakiyama T, Akutsu M, Miyawaki O, Yano T (1999) Effective thermal diffusivity of food gels impregnated with air bubbles. J Food Eng 39(1999):323–328CrossRefGoogle Scholar
  29. 29.
    Sakamoto H, Kulacki FA (2008) Effective thermal diffusivity of porous media in the wall vicinity. J Heat Transfer. doi: 10.1115/1.2787022 Google Scholar
  30. 30.
    Huo Z, Mohamed M, Nicholas JR, Wang X, Chandrashekhara K (2015) Experimentation and simulation of moisture diffusion in foam-cored polyurethane sandwich structure. J Sandwich Struct Mater. doi: 10.1177/1099636215582218 Google Scholar
  31. 31.
    John H, Lienhard IV, John H (2003) Lienhard V (2003) A heat transfer text book, 3rd edn. Phlogiston Press, CambridgeGoogle Scholar
  32. 32.
    Furmanski P, Gogol W (1979) Investigation of steady-state heat conduction in two dimensional model of composite with symmetrically arranged circular fibers. Arch Thermodyn Combust 2 (Archiwum Termodynamiki i Spalania-in Polis)Google Scholar
  33. 33.
    Thornburg JD, Pears CD (1965) Prediction of the thermal conductivity of filled and reinforced plastics. ASME Paper 65-WA/HT-4, American Society of Mechanical EngineersGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Advanced Materials and Computational Mechanics Lab., Department of Mechanical EngineeringUniversity of ZanjanZanjanIran

Personalised recommendations