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Heat Conduction in Two-Phase Composite Materials with Three-Dimensional Microstructures and Interfacial Thermal Resistance

  • Carlos Frederico MattEmail author
  • Manuel Ernani Cruz
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 2)

Abstract

The goals envisioned for the current chapter are threefold. First, it gives a general overview of heat conduction in two-phase composite materials with three dimensional microstructures and interfacial thermal resistance. Second, it describes the application of homogenization theory to the multiscale heat conduction problem in the composite medium in order to derive the boundary-value problem defined on a representative volume element of the composite microstructure (the cell problem) and an expression for the composite effective thermal conductivity. Third, it describes a finite-element-based computational scheme to calculate the effective thermal conductivity of composite materials with general 3-D microstructures and interfacial thermal resistance. Numerical results for the effective conductivity are presented and, when possible, compared with available analytical predictions. The numerical results reported here confirm that computational approaches are a helpful tool for understanding the complex macroscopic thermal behavior of composite materials.

Keywords

Representative Volume Element Effective Thermal Conductivity Biot Number Effective Conductivity Interfacial Thermal Resistance 
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.

Notes

Acknowledgement

M.E. Cruz would like to thank the Brazilian Council for Development of Science and Technology (CNPq) for Grants PQ-306592/2006-1 and APQ-471801/2004-6. The authors also thank Dr. Joachim Schöberl, from Johannes Kepler Universität Linz, Austria, for the free academic license of NETGEN 4.4.

References

  1. 1.
    Auriault, J.L., Ene, H.I.: Macroscopic modelling of heat transfer in composites with inter-facial thermal barrier. Int. J. Heat Mass Transf. 37, 2885–2892 (1994)CrossRefGoogle Scholar
  2. 2.
    Batchelor, G.K., O’Brien, R.W.: Thermal or electrical conduction through a granular material. Proc. R. Soc. Lond. A 355, 313–333 (1977)CrossRefGoogle Scholar
  3. 3.
    Bathe, K.J.: Finite Element Procedures in Engineering Analysis, 1st edn. Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1982). Chaps. 1, 3, 7Google Scholar
  4. 4.
    Bensoussan, A., Lions, J.L., Papanicolaou, G.C.: Asymptotic Analysis for Periodic Structures, 1st edn. North-Holland Publishing Co., Amsterdam (1978). Chaps. 1–2Google Scholar
  5. 5.
    Benveniste, Y.: Effective thermal conductivity of composites with a thermal contact resistance between the constituents: Nondilute case. J. Appl. Phys. 61, 2840–2843 (1987)CrossRefGoogle Scholar
  6. 6.
    Cheng, H., Torquato, S.: Effective conductivity of periodic arrays of spheres with interfacial resistance. Proc. R. Soc. Lond. A 453, 145–161 (1997)CrossRefGoogle Scholar
  7. 7.
    Cruz, M.E.: Computational approaches for heat conduction in composite materials. In: Esteve, Y.V., Carlomagno, G.M., Brebbia, C.A. (eds.) Computational Methods and Experimental Measurements X, pp. 657–668. WIT Press, Southampton, UK (2001)Google Scholar
  8. 8.
    Dunn, M.L., Taya, M., Hatta, H., Takei, T., Nakajima, Y.: Thermal conductivity of hybrid short fiber composites. J. Compos. Mater. 27, 1493–1519 (1993)CrossRefGoogle Scholar
  9. 9.
    Duschlbauer, D., Böhm, H.J., Pettermann, H.E.: Numerical simulation of thermal conductivity of MMCs: effect of thermal interface resistance. Mater. Sci. Technol. 19, 1107–1114 (2003)CrossRefGoogle Scholar
  10. 10.
    Duschlbauer, D., Pettermann, H.E., Böhm, H.J.: Heat conduction of a spheroidal inhomo-geneity with imperfectly bonded interface. J. Appl. Phys. 94(3), 1539–1549 (2003)CrossRefGoogle Scholar
  11. 11.
    Every, A.G., Tzou, Y., Hasselman, D.P.H., Raj, R.: The effect of particle size on the thermal conductivity of ZnS/diamond composites. Acta Metallica Mater. 40, 123–129 (1992)CrossRefGoogle Scholar
  12. 12.
    Furmañski, P.: Influence of different parameters on the effective thermal conductivity of short-fiber composites. J. Compos. Mater. 4, 349–362 (1991)Google Scholar
  13. 13.
    Furmañski, P.: Heat conduction in composites: homogenization and macroscopic behavior. Appl. Mech. Rev. 50, 327–356 (1997)CrossRefGoogle Scholar
  14. 14.
    Garnier, B., Dupuis, T., Gilles, J., Bardon, J.P., Danes, F.: Thermal contact resistance between matrix and particle in composite materials measured by a thermal microscopic method using a semi-intrinsic thermocouple. In: Proceedings of the 12th International Heat Transfer Conference, Grenoble, France, pp. 9–14 (2002)Google Scholar
  15. 15.
    Hasselman, D.P.H., Johnson, L.F.: Effective thermal conductivity of composites with inter-facial thermal barrier resistance. J. Compos. Mater. 21, 508–515 (1987)CrossRefGoogle Scholar
  16. 16.
    Hasselman, D.P.H., Johnson, L.F., Syed, R., Taylor, M.P., Chyung, K.: Heat conduction characteristics of a carbon-fibre-reinforced lithia-alumino-silicate glass-ceramic. J. Mater. Sci. 22, 701–709 (1987)CrossRefGoogle Scholar
  17. 17.
    Hatta, H., Taya, M.: Equivalent inclusion method for steady state heat conduction in composites. Int. J. Eng. Sci. 24, 1159–1172 (1986)CrossRefGoogle Scholar
  18. 18.
    Jiajun, W., Su, Y.X.: Effects of interfacial thermal barrier resistance and particle shape and size on the thermal conductivity of AIN/PI composites. Compos. Sci. Technol. 64, 1623–1628 (2004)CrossRefGoogle Scholar
  19. 19.
    Kumar, S., Murthy, J.Y.: A numerical technique for computing effective thermal conductivity of fluid-particle mixtures. Numer. Heat Transf. B Fund. 47, 555–572 (2005)CrossRefGoogle Scholar
  20. 20.
    Matt, C.F., Cruz, M.E.: Calculation of the effective conductivity of ordered short-fiber composites. In: Proceedings of the 35th AIAA Thermophysics Conference, Anaheim, California, Paper AIAA 2001–2968 (2001)Google Scholar
  21. 21.
    Matt, C.F., Cruz, M.E.: Application of a multiscale finite-element approach to calculate the effective conductivity of particulate media. Comput. Appl. Math. 21(2), 429–460 (2002)Google Scholar
  22. 22.
    Matt, C.F., Cruz, M.E.: Enhancement of the thermal conductivity of composites reinforced with anisotropic short fibers. J. Enhanced Heat Transf. 13, 1–22 (2006)CrossRefGoogle Scholar
  23. 23.
    Matt, C.F., Cruz, M.E.: Numerical prediction of the effective thermal conductivity of composite materials. In: Proceedings of the 9th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, San Francisco, California, Paper AIAA 2006–54155 (2006)Google Scholar
  24. 24.
    Matt, C.F., Cruz, M.E.: Effective thermal conductivity of composite materials with 3-d microstructures and interfacial thermal resistance. Numer. Heat Transf. Appl. A 53, 577–604 (2008)CrossRefGoogle Scholar
  25. 25.
    McKenzie, D.R., McPhedran, R.C., Derrick, G.H.: The conductivity of lattices of spheres II. The body centred and face centred cubic lattices. Proc. R. Soc. Lond. A 362, 211–232 (1978)CrossRefGoogle Scholar
  26. 26.
    McPhedran, R.C., McKenzie, D.R.: The conductivity of lattices of spheres I. The simple cubic lattice. Proc. R. Soc. Lond. A 359, 45–63 (1978)CrossRefGoogle Scholar
  27. 27.
    Milton, G.W.: The Theory of Composites, 1st edn. Cambridge University Press, Cambridge (2002). Chaps. 2, 7CrossRefGoogle Scholar
  28. 28.
    Mirmira, S.R., Fletcher, L.S.: Comparative study of thermal conductivity of graphite fiber organic matrix composites. In: Proceedings of the 5th ASME/JSME Joint Thermal Engineering Conference, San Diego, California, Paper AJTE99-6439 (1999)Google Scholar
  29. 29.
    Nomura, S., Chou, T.W.: Bounds of effective thermal conductivity of short-fiber composites. J. Compos. Mater. 14, 120–129 (1980)CrossRefGoogle Scholar
  30. 30.
    Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12, 617–629 (1975)CrossRefGoogle Scholar
  31. 31.
    Reddy, J.N., Gartling, D.K.: The Finite Element Method in Heat Transfer and Fluid Dynamics, 2nd edn. CRC Press LLC, Boca Raton (2001). Chaps. 1–3Google Scholar
  32. 32.
    Rocha, R.P.A., Cruz, M.E.: Computation of the effective conductivity of unidirectional fibrous composites with an interfacial thermal resistance. Numer. Heat Transf. A Appl. 39, 179–203 (2001)CrossRefGoogle Scholar
  33. 33.
    Rolfes, R., Hammerschmidt, U.: Transverse thermal conductivity of CFRP laminates: a numerical and experimental validation of approximation formulae. Compos. Sci. Technol. 54, 45–54 (1995)CrossRefGoogle Scholar
  34. 34.
    Sangani, A.S., Acrivos, A.: The effective conductivity of a periodic array of spheres. Proc. R. Soc. Lond. A 386, 263–275 (1983)CrossRefGoogle Scholar
  35. 35.
    Schöberl, J.: NETGEN – 4.4, User’s Manual. Numerical and Symbolic Scientific Computing, Institute of Mathematics, Johannes Kepler Universität Linz, Austria (2001)Google Scholar
  36. 36.
    Takei, T., Hatta, H., Taya, M.: Thermal expansion behavior of particulate filled composites II: multi-reinforcing phases (hybrid composites). Mater. Sci. Eng. A 131, 145–152 (1991)CrossRefGoogle Scholar
  37. 37.
    Torquato, S.: Random Heterogeneous Materials, Microstructure and Macroscopic Properties, 1st edn. Springer, New York (2002). Chaps. 1, 2, 5–7Google Scholar
  38. 38.
    Yoshida, K., Morigami, H.: Thermal properties of diamond/copper composite material. Microelectron. Reliab. 44, 303–308 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Electric Power Research CenterRio de JaneiroBrazil
  2. 2.Federal University of Rio de Janeiro, Politécnica/COPPE/UFRJRio de JaneiroBrazil

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