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Variational estimates of the effective thermal conductivities of transversely isotropic composites

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Abstract

A study is made of a type of composite material that is widely used in practical applications — a composite with fibers of constant cross section arranged parallel to one another in the matrix. The effective thermal conductivities of transversely Isotropie composites is estimated on the basis of dual variational principles from thermostatics. Certain geometric models that are of practical interest are examined and refined estimates of their effective conductivities are obtained. Due to mathematical equivalence, the results obtained can also be used for effective electrical conductivity, the effective diffusion coefficient, effective permittivity, and effective permeability.

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Literature cited

  1. 1.

    D. K. Hale, J. Mater. Sci.,11, 2105 (1976).

  2. 2.

    R. Christensen, Introduction to the Mechanics of Composites [Russian translation], Moscow (1982).

  3. 3.

    Z. Hashin, Theory of Fiber-Reinforced Materials, NASA CR-1974 (1972).

  4. 4.

    V. L. Berdichevskii, Variational Principles of Continuum Mechanics [in Russian], Moscow (1983).

  5. 5.

    S. D. Volkov and V. P. Stavrov, Statistical Mechanics of Composite Materials [in Russian], Minsk (1978).

  6. 6.

    Fo Fy Van, Theory of Reinforced Materials with Coatings [in Russian], Kiev (1971).

  7. 7.

    T. D. Shermergor, Theory of Elasticity of Micro-Inhomogeneous Media [in Russian], Moscow (1977).

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Additional information

Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 59, No. 10, pp. 562–568, October, 1990.

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Chau, L.H., Tin, F.D. Variational estimates of the effective thermal conductivities of transversely isotropic composites. Journal of Engineering Physics 59, 1245–1250 (1990). https://doi.org/10.1007/BF00878052

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Keywords

  • Permeability
  • Thermal Conductivity
  • Electrical Conductivity
  • Statistical Physic
  • Diffusion Coefficient