Determination of the Effective Thermal Conductivity Tensor of Heterogeneous Media Using a Self-Consistent Finite Element Method: Application to the Pseudo-percolation Thresholds of Mixtures Containing Nonspherical Inclusions

[+] Author and Article Information
A. Decarlis, M. Jaeger, R. Martin

IUSTI, CNRS UMR 6595, 5 rue E. Fermi, 13453 Marseille Cedex 13, France

J. Heat Transfer 122(1), 171-175 (Sep 09, 1999) (5 pages) doi:10.1115/1.521451 History: Received November 20, 1998; Revised September 09, 1999
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.


Lord  Rayleigh, 1892, “On the Influence of the Obstacles in Rectangular Order Upon the Properties of a Medium,” Philos. Mag., 134, pp. 481–502.
Wiener,  O., 1912, Abh. Sächs. Ges. (ahad) Wiss., 32, p. 509.
Buyevich,  Y. A., 1974, “On the Thermal Conductivity of Granular Material,” Chem. Eng. Sci., 29, pp. 37–48.
Buyevich,  Y. A., 1992, “Heat Mass Transfer in Disperse Media-I, II,” Int. J. Heat Mass Transf., 35, pp. 2445–62.
Furmañski,  P., 1997, “Heat Conduction in Composites: Homogenization and Macroscopic Behavior,” Appl. Mech. Rev., 50, p. 327.
Bruggeman,  D. A. G., 1935, “Berechnung Verschiedener Physikalischer Konstanten Von Heterogenen Substanzen,” Ann. Phys. (Paris), 24, p. 636.
Landauer,  R., 1952, “The Electrical Resistance of Binary Metallic Mixtures,” J. Appl. Phys., 23, p. 779.
Kerner,  E. H., 1956, “The Electrical Conductivity of Composite Media,” Proc. Phys. Soc. B, 69, p. 802.
Hashin,  Z., and Shtrikman,  S., 1962, “A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials,” J. Appl. Phys., 33l, p. 3125.
Hashin,  Z., 1968, “Assessment of the Self Consistent Scheme Approximation: Conductivity of Particulate Composites,” J. Comp. Mat., 2, pp. 284–300.
Yang,  Q. S., Tang,  L., and Chen,  H., 1994, “Self-Consistent Finite Element Method: A New Method of Predicting Effective Properties of Inclusion Media,” Finite Elem. Anal. Design, 17, pp. 247–257.
Batchelor,  G. K., 1974, “Transport Properties of Two-Phase Materials With Random Structure,” Annu. Rev. Fluid Mech., 6, p. 227.
Miloh,  T., and Benveniste,  Y., 1988, “A Generalized Self-Consistent Method for the Effective Conductivity of Composites With Ellipsoidal Inclusions and Cracked Body,” J. Appl. Phys., 63, pp. 789–796.
Landauer, R., 1978, “Electrical Conductivity in Inhomogeneous Media,” Electrical, Transport and Optical Properties of Inhomogeneous Media, Garland & Tanner, eds., American Institute of Physics, New York, Vol. 99.
Clerc,  J. P., , 1983, “La Percolation: Modèles, Simulations Analogiques et Numériques,” Ann. Phys. , 8, pp. 1–108.
Banhegyi,  G., 1986, “Comparison of Electrical Mixture Rules for Composites,” Colloid Polym. Sci., 264, pp. 1030–1050.
Hatta,  H., and Taya,  M., 1985, “Effective Thermal Conductivity of Misoriented Short Fiber Composite,” J. Appl. Phys., 58, pp. 2478–2486.
Polder,  D., and Van Santen,  J. H., 1946, “The Effective Permeability of Mixtures of Solids,” Physica XII, 5, p. 257.


Grahic Jump Location
Influence of the group orientation of a mixture of cylinders on the effective normalized thermal conductivity in the three principal directions (β=105,v(2)=15 percent, γ=2)
Grahic Jump Location
Influence of the elongation ratio on the effective normalized thermal conductivity of mixtures of cylinders or capsules aligned with the applied flux (β=105,v(2)=15 percent)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In