The problem of evaluating the effective thermal conductivity of random packed beds is of great interest to a wide-range of engineers and scientists. This study presents a boundary element model (BEM) for the prediction of the effective thermal conductivity of a two-dimensional packed bed. The model accounts for four heat transfer mechanisms: (1) conduction through the solid; (2) conduction through the contact area between particles; (3) radiation between solid surfaces; and (4) conduction through the fluid phase. The radiation heat exchange between solid surfaces is simulated by the net-radiation method. Two regular packing configurations, square array and hexagonal array, are chosen as illustrative examples. The comparison between the results obtained by the present model and the existing predictions are made and the agreement is very good. The proposed BEM model provides a new tool for evaluating the effective thermal conductivity of the packed beds.
Issue Section:
Porous Media
1.
Fogler
, H. S.
, 1999, Elements of Chemical Reaction Engineering
, 3rd ed., Prentice-Hall
, Englewood Cliffs, NJ.2.
Whitaker
, S.
, 1980, “Heat and Mass Transfer in Granular Porous Media
,” Advances in Drying
, Vol. 1
, Hemisphere
, New York, pp. 23
–61
.3.
Cho
, H. H.
, and Eckert
, E. R. G.
, 1994, “Transition from Transpiration to Film Cooling
,” Int. J. Heat Mass Transfer
0017-9310, 37
, pp. 3
–8
.4.
Tien
, C. L.
, and Cunnington
, G. R.
, 1973, “Cryogenic Insulation Heat Transfer
,” Advances in Heat Transfer
, Vol. 9
, Hemisphere
, New York, pp. 349
–417
.5.
Yagi
, S.
, and Kunni
, D.
, 1957, “Studies on Effective Thermal Conductivities in Packed Beds
,” AIChE J.
0001-1541, 3
(3
), pp. 373
–381
.6.
Zehner
, P.
, and Schlunder
, E. U.
, 1970, “Thermal Conductivity of Granular Materials at Moderate Temperatures (in German)
,” Chem.-Ing.-Tech.
0009-286X, 42
, pp. 933
–941
.7.
Argo
, W. B.
, and Smith
, J. M.
, 1953, “Heat Transfer in Packed Beds
,” Chem. Eng. Prog.
0360-7275, 49
(8
), pp. 443
–451
.8.
Schotte
, W.
, 1960, “Thermal Conductivity of Packed Beds
,” AIChE J.
0001-1541, 6
(1
), pp. 63
–67
.9.
Kunni
, D.
, and Smith
, J. M.
, 1960, “Heat Transfer Characteristic of Porous Rocks
,” AIChE J.
0001-1541, 6
(1
), pp. 71
–78
.10.
Krupiczka
, R.
, 1967, “Analysis of Thermal Conductivity in Granular Materials
,” Int. Chem. Eng.
0020-6318, 7
(1
), pp. 122
–144
.11.
Wakao
, N.
, and Kato
, K.
, 1969, “Effective Thermal Conductivity of Packed Beds
,” J. Chem. Eng. Jpn.
0021-9592, 2
(1
), pp. 24
–33
.12.
Nozad
, I.
, Carbonell
, R. G.
, and Whitaker
, S.
, 1985, “Heat Conduction in Multiphase Systems—I: Theory and Experiment for Two-Phase Systems
,” Chem. Eng. Sci.
0009-2509, 40
(5
), pp. 843
–855
.13.
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
0017-9310, 32
(3
), pp. 503
–512
.14.
Sahraoui
, M.
, and Kaviany
, M.
, 1993, “Slip and No-slip Temperature Boundary Conditions at Interface of Porous, Plain Media: Conduction
,” Int. J. Heat Mass Transfer
0017-9310, 36
(4
), pp. 1019
–1033
.15.
Hsu
, C. T.
, Cheng
, P.
, and Wong
, K. W.
, 1995, “A Lumped-Parameter Model for Stagnant Thermal Conductivity of Spatially Periodic Porous Media
,” ASME J. Heat Transfer
0022-1481, 117
, pp. 264
–269
.16.
Buonanno
, G.
, Carotenuto
, A.
, Giovinco
, G.
, and Massarotti
, N.
, 2003, “Experimental and Theoretical Modeling of the Effective Thermal Conductivity of Rough Steel Spheroid Packed Beds
,” ASME J. Heat Transfer
0022-1481, 125
, pp. 693
–702
.17.
Crane
, R. A.
, and Vachon
, R. I.
, 1977, “A Prediction of the Bounds on the Effective Thermal Conductivity of Granular Materials
,” Int. J. Heat Mass Transfer
0017-9310, 20
(7
), pp. 711
–723
.18.
Prasad
, V.
, Kladias
, N.
, Bandyopadhaya
, A.
, and Tian
, Q.
, 1989, “Evaluation of Correlations for Stagnant Thermal Conductivity of Liquid-Saturated Porous Beds of Spheres
,” Int. J. Heat Mass Transfer
0017-9310, 32
(9
), pp. 1793
–1796
.19.
Argento
, C.
, and Bouvard
, D.
, 1996, “Modeling the Effective Thermal Conductivity of Random Packing of Spheres through Densification
,” Int. J. Heat Mass Transfer
0017-9310, 39
(7
), pp. 1343
–1350
.20.
Cheng
, G. J.
, Yu
, A. B.
, and Zulli
, P.
, 1999, “Evaluation of Effective Thermal Conductivity from the Structure of a Packed Bed
,” Chem. Eng. Sci.
0009-2509, 54
, pp. 4199
–4209
.21.
Vargas
, W. L.
, and McCarthy
, J. J.
, 2001, “Heat Conduction in Granular Materials
,” AIChE J.
0001-1541, 47
(5
), pp. 1052
–1059
.22.
Deissler
, R. G.
, and Boegli
, J. S.
, 1958, “An Investigation of Effective Thermal Conductivities of Powders in Various Gases
,” Trans. ASME
0097-6822, 80
, pp. 1417
–1425
.23.
Brebbia
, C. A.
, 1978, The Boundary Element Method for Engineers
, Wiley
, New York.24.
Brebbia
, C. A.
, Telles
, J. C. F.
, and Wrobel
, L. C.
, 1984, Boundary Element Techniques
, Springer
, Berlin, Germany.25.
Beer
, G.
, and Watson
, J. O.
, 1992, Introduction to Finite and Boundary Element Methods for Engineers
, Wiley
, New York.26.
Banerjee
, P. K.
, 1994, Boundary Element Methods in Engineering
, 2nd ed., McGraw-Hill
, London.27.
Wrobel
, L. C.
, 2002, Boundary Element Method
(Vol. 1
, Applications in Thermo-Fluids and Acoustics), Wiley
, New York.28.
Johnson
, K. L.
, 1985, Contact Mechanics
, Cambridge University Press
, Cambridge, MA.29.
Vortmeyer
, D.
, 1978, “Radiation in Packed Solids
,” Proceedings of the 6th International Heat Transfer Conference
, Vol. 6
, U.
Grigul
et al., eds., Toronto August 7–11, Hemisphere
, Washington, DC
, pp. 525
–539
.30.
Siegel
, R.
, and Howell
, J. R.
, 2002, Thermal Radiation Heat Transfer
, 4th ed., Hemisphere
, Washington, DC.31.
Siu
, W. W. M.
, and Lee
, S. H.-K.
, 2000, “Effective Conductivity Computation of a Packed Bed Using Constriction Resistance and Contact Angle Effects
,” Int. J. Heat Mass Transfer
0017-9310, 43
, pp. 3917
–3924
.32.
Larkin
, B. K.
, and Churchill
, S. W.
, 1959, “Heat Transfer by Radiation through Porous Insulations
,” AIChE J.
0001-1541, 5
(4
), pp. 467
–474
.33.
Chen
, J. C.
, and Churchill
, S. W.
, 1963, “Radiant Heat Transfer in Packed Beds
,” AIChE J.
0001-1541, 9
(1
), pp. 35
–41
.34.
Yang
, Y. S.
, Howell
, J. R.
, and Klein
, D. E.
, 1983, “Radiative Heat Transfer through a Randomly Packed Bed of Spheres by the Monte Carlo Method
,” ASME J. Heat Transfer
0022-1481, 105
, pp. 325
–332
.35.
Argento
, C.
, and Bouvard
, D.
, 1996, “A Ray Tracing Method for Evaluating the Radiative Heat Transfer in Porous Media
,” Int. J. Heat Mass Transfer
0017-9310, 39
(15
), pp. 3175
–3180
.36.
Godbee
, H. W.
, and Ziegler
, T. W.
, 1966, “Thermal Conductivities of MgO, Al2O3, and ZrO2 Powders to 850°C. II. Theoretical
,” J. Appl. Phys.
0021-8979, 37
(1
), pp. 56
–65
.Copyright © 2007
by American Society of Mechanical Engineers
You do not currently have access to this content.
