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International Journal of Thermophysics

, Volume 7, Issue 3, pp 609–620 | Cite as

The effective thermal conductivity of a composite material with spherical inclusions

  • R. H. Davis
Article

Abstract

A new method is presented for calculating the effective thermal conductivity of a composite material containing spherical inclusions. The surface of a large body is assumed kept at a uniform temperature. This body is in contact with a composite material of infinite extent having a lower temperature far from the heated body. Green's theorem is then used to calculate the rate of heat transfer from the heated body to the composite material, yielding
$$k_e /k = 1 + \frac{{3(\alpha - 1)}}{{[\alpha + 2 - (\alpha - 1)\phi ]}}\{ \phi + f(\alpha )\phi ^2 + 0(\phi ^3 )\} $$
where ke is the effective thermal conductivity, k is the thermal conductivity of the continuous phase, α is the ratio of the thermal conductivity of the spherical inclusions to k, and φ is the volume fraction occupied by the dispersed phase. The function f(α) is presented in this work. Although a similar result has been found previously by renormalization techniques, the method presented in this paper has merit in that a decaying temperature field is used. As a result, only convergent integrals are encountered, and a renormalization factor is not needed. This method is more straightforward than its predecessors and sheds additional light on the basic properties of two-phase materials.

Key words

composite materials dispersions effective properties heat conduction thermal conductivity 

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References

  1. 1.
    G. K. Batchelor, J. Fluid Mech. 52:245 (1972).Google Scholar
  2. 2.
    G. K. Batchelor and J. T. Green, J. Fluid Mech. 56:461 (1972).Google Scholar
  3. 3.
    D. J. Jeffrey, Proc. R. Soc. 335:355 (1973).Google Scholar
  4. 4.
    H. S. Chen and A. Acrivos, Int. J. Solids Struct. 14:349 (1978).Google Scholar
  5. 5.
    E. J. Hinch, J. Fluid Mech. 83:695 (1977).Google Scholar
  6. 6.
    R. W. O'Brien, J. Fluid Mech. 91:17 (1979).Google Scholar
  7. 7.
    Z. Hashin and S. Shtrikman, J. Appl. Phys. 33:10, 3125 (1962).Google Scholar
  8. 8.
    J. C. Maxwell, Electricity and Magnetism (Clarendon Press, London, 1873).Google Scholar
  9. 9.
    A. S. Sangani and A. Acrivos, Proc. R. Soc. Lond. A386:263 (1983).Google Scholar
  10. 10.
    G. K. Batchelor and R. W. O'Brien, Proc. R. Soc. Lond. A355:313 (1977).Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • R. H. Davis
    • 1
  1. 1.Department of Chemical EngineeringUniversity of ColoradoBoulderUSA

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