Based on a lumped-parameter method, algebraic expressions for the stagnant thermal conductivity of some two-dimensional and three-dimensional spatially periodic media are obtained. The geometries under consideration include arrays of touching and non-touching in-line square and circular cylinders (two-dimensional), as well as touching and nontouching in-line cubes (three-dimensional). A comparison of results based on these algebraic expressions with existing numerical solutions and experimental data shows that they are in excellent agreement.

Issue Section:
Heat Conduction
Keywords:
Packed and Fluidized Beds
Topics:
Porous materials, Thermal conductivity, Algebra, Circular cylinders, Fluidized beds
1.
Chan
 
C. K.
, and
Tien
 
C. L.
,
1973
, “
Conductance of Packed Spheres in Vacuum
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
95
, pp.
302
–
308
.
2.
Deisser
 
R. G.
, and
Boegli
 
J. S.
,
1958
, “
An Investigation of Effective Thermal Conductivities of Powders in Various Gases
,”
ASME Transactions
, Vol.
80
, pp.
1417
–
1425
.
3.
Hall
 
R. O. A.
, and
Martin
 
D. G.
,
1981
, “
The Thermal Conductivity of Power Beds. A Model, Some Measurements on UO2, Vibro-Compacted Microspheres, and Their Correlation
,”
J. of Nuclear Materials
, Vol.
101
, pp.
172
–
183
.
4.
Kaviany, M., 1991, Principles of Heat Transfer in Porous Media, Springer-Verlag, New York.
5.
Kunii
 
D.
, and
Smith
 
J. M.
,
1960
, “
Heat Transfer Characteristics of Porous Rocks
,”
AIChE J.
, Vol.
6
, pp.
71
–
78
.
6.
Nozad
 
S.
,
Carbonell
 
R. G.
, and
Whitaker
 
S.
,
1985
, “
Heat Conduction in Multiphase Systems. I: Theory and Experiments for Two-Phase Systems
,”
Chem. Engg. Sci.
, Vol.
40
, pp.
843
–
855
.
7.
Ogniewicz, Y., and Yovanovich, M. M., 1978, “Effective Conductivity of Regularly Packed Spheres: Basic Cell Model With Constriction, Heat Transfer and Thermal Control Systems,” Progress in Astronautics and Aeronautics, L. S. Fletcher, ed., Vol. 60, pp. 209–228.
8.
Prasad
 
V.
,
Kladias
 
B. A.
, and
Tian
 
Q.
,
1989
, “
Evaluation of Correlations for Stagnant Thermal Conductivity of Liquid-Saturated Porous Beds of Spheres
,”
Int. J. Heat Mass Transfer
, Vol.
32
, pp.
1793
–
1796
.
9.
Sabraoui
 
M.
, and
Kaviany
 
M.
,
1993
, “
Slip and No-Slip Temperature Boundary Conditions at Interface of Porous, Plain Media: Conduction
,”
Int. J. Heat Mass Transfer
, Vol.
36
, pp.
1019
–
1033
.
10.
Saez
 
A. E.
,
Perfetto
 
J. C.
, and
Rusinek
 
I.
,
1991
, “
Prediction of Effective Diffusivities in Porous Media Using Spatially Periodic Models
,”
Transp. Porous Media
, Vol.
6
, pp.
143
–
157
.
11.
Shonnard
 
D. R.
, and
Whitaker
 
S.
,
1989
, “
The Effective Thermal Conductivity for a Point-Contact Porous Medium: An Experimental Study
,”
Int. J. Heat Mass Transfer
, Vol.
32
, pp.
503
–
512
.
12.
Zehner
 
P.
, and
Schlunder
 
E. U.
,
1970
, “
Thermal Conductivity of Granular Materials at Moderate Temperatures
,” [in German],
Chemie. Ingr. Tech.
, Vol.
42
, pp.
933
–
941
.
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