An analytical formulation of Bergman–Milton conductivity bounds is used in a different way to obtain rigorous bounds on the real thermal conductivity of a fluid-saturated porous material. These bounds do not depend explicitly on the porosity, but rather on two formation factors—one associated with the pore space and the other with the solid frame.
REFERENCES
1.
2.
G. W.
Milton
, The Theory of Composites
(Cambridge University Press
, Cambridge, UK, 2002
).3.
S.
Torquato
, Random Heterogeneous Materials: Microstructure and Macroscopic Properties
(Springer
, New York, 2002
).4.
D. J.
Bergman
, Phys. Rep.
43
, 378
(1978
).5.
D. J.
Bergman
, Phys. Rev. Lett.
44
, 1285
(1980
).6.
G. W.
Milton
, Appl. Phys. Lett.
37
, 300
(1980
).7.
D. J.
Bergman
, Ann. Phys. (N.Y.)
138
, 78
(1982
).8.
J.
Korringa
and G. A.
LaTorraca
, J. Appl. Phys.
60
, 2966
(1986
).9.
D.
Stroud
, G. W.
Milton
, and B. R.
De
, Phys. Rev. B
34
, 5145
(1986
).10.
G. W.
Milton
, J. Appl. Phys.
52
, 5286
(1981
).11.
12.
13.
G. A.
Baker
, Jr., Essentials of Padé Approximants
(Academic
, San Diego, California, 1975
).14.
D. L.
Johnson
, J.
Koplik
, and L. M.
Schwartz
, Phys. Rev. Lett.
57
, 2564
(1986
).15.
D.
Wildenschild
, J. J.
Roberts
, and E. D.
Carlberg
, Geophys. Res. Lett.
27
, 3065
(2000
).16.
D. J.
Bergman
, Phys. Rev. B
14
, 1531
(1976
).17.
Y.
Asaad
, Ph.D. thesis, University of California—Berkeley
, Berkeley, CA, 1955
.18.
19.
© 2005 American Institute of Physics.
2005
American Institute of Physics
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