Heat transfer in a two-dimensional moving packed bed consisting of pellets surrounded by a gaseous atmosphere is numerically investigated. The governing equations are formulated based on the volume averaging method. A two-equation model, representing the solid and gas phases separately, and a one-equation model, representing both the solid and gas phases, are considered. The models take the form of partial differential equations with a set of boundary conditions, some of which were determined experimentally, and design parameters in addition to the operating conditions. We examine and discuss the parameters in order to reduce temperature differences from pellet to pellet. The calculation results show that by adopting a constant temperature along the preheater outer wall and decreasing the velocity of the pellets in the preheater, the difference in temperature from pellet to pellet is reduced from 120°C to 55°C, and the thermal efficiency of the preheater is tremendously improved.

1.
Tien
,
C. L.
, and
Vafai
,
K.
, 1989, “
Convective and Radiative Heat Transfer in Porous Media
,”
Adv. Appl. Mech.
0065-2156,
27
, pp.
225
281
.
2.
Kuzay
,
T. M.
,
Collins
,
J. T.
,
Khounasry
,
A. M.
, and
Morales
,
G.
, 1991, “
Enhanced Heat Transfer with Metal-Wood-Filled Tubes
,”
Proc. of ASME/JSEM Thermal Engineering Conference
, Reno, NV, ASME, New York, pp.
145
151
.
3.
Kuzay
,
T. M.
, 1992, “
Cryogenic Cooling of X-ray Crystals Using a Porous Matrix
,”
Rev. Sci. Instrum.
0034-6748,
63
(
1
), pp.
468
472
.
4.
Rosenfled
,
J. H.
, and
North
,
M. T.
, 1995, “
Porous Media Heat Exchangers for Cooling of High-Power Optical Components
,”
Opt. Eng.
0091-3286,
34
, pp.
335
341
.
5.
Khaled
,
A.-R. A.
, and
Vafai
,
K.
, 2003, “
The Role of Porous Media in Modeling Flow and Heat Transfer in Biological Tissue
,”
Int. J. Heat Mass Transfer
0017-9310,
46
, pp.
4989
5003
.
6.
Schumann
,
T. E. W.
, 1929, “
Heat Transfer: Liquid Flowing Through a Porous Prizm
,”
J. Franklin Inst.
0016-0032,
208
, pp.
405
416
.
7.
Burch
,
D. M.
,
Allen
,
R. W.
, and
Peavy
,
B. A.
, 1976, “
Transient Temperature Distribution within Porous Slabs Subjected to Sudden Transpiration Heating
,”
ASME J. Heat Transfer
0022-1481,
98
, pp.
221
225
.
8.
Whitaker
,
S.
, 1977, “
Simultaneous Heat, Mass, and Momentum Transfer in Porous Media: A Theory of Drying
,”
Adv. Heat Transfer
0065-2717,
13
, pp.
119
203
.
9.
Vafai
,
K.
and
Sözen
,
M.
, 1990, “
Analysis of Energy and Momentum Transport for Fluid Flow Through a Porous Bed
,”
ASME J. Heat Transfer
0022-1481,
112
, pp.
690
699
.
10.
Amiri
,
A.
, and
Vafai
,
K.
, 1999, “
Transient Analysis of Incompressible Flow through a Packed Bed
,”
Int. J. Heat Mass Transfer
0017-9310,
41
, pp.
4259
4279
.
11.
Vortmeyer
,
J.
, and
Schaefer
,
R. J.
, 1974, “
Equivalence of One- and Two-Phase Models for Heat Tarnsfer Processes in Packed Beds: One Dimensional Theory
,”
Chem. Eng. Sci.
0009-2509,
29
, pp.
485
491
.
12.
Riaz
,
M.
, 1977, “
Analytical Solutions for Single- and Two-Phase Models of Packed-Bed Thermal Storage Systems
,”
ASME J. Heat Transfer
0022-1481,
99
, pp.
489
492
.
13.
Whitaker
,
S.
, 1998,
The Method of Volume Averaging
, “
Theory and Applications of Transport
” in
Porous Media Series
,
Kluwer Academic Publishers
, Dordrecht, The Netherlands, Vol.
13
.
14.
Lee
,
D.-Y.
, and
Vafai
,
K.
, 1999, “
Analytical Characterization and Conceptual Assessment of Solid and Fluid Temperature Differentials in Porous Media
,”
Int. J. Heat Mass Transfer
0017-9310,
42
, pp.
423
435
.
15.
Wiseman
,
L. G.
,
Bale
,
R. A.
,
Chapman
,
E. T.
, and
Martin
,
B.
, 1988, “
Inco’s Copper Cliff Nickel Refinery
,”
Proc. Symposium on Metallurgy of Nickel and Cobalt
, edited by
G. P.
Tyroler
and
C. A.
Landolt
,
The Metallurgical Society
, Warrendale, PA, pp.
373
390
.
16.
Tonneau
,
D.
,
Auvert
,
G.
, and
Pauleau
,
Y.
, 1989, “
Deposition of Nickel Microstructures by CO2 Laser-Assisted Decomposition of Nickel Tetracarbonyl
,”
J. Appl. Phys.
0021-8979,
66
(
1
), pp.
165
168
.
17.
Dullien
,
F. A. L.
, 1979,
Porous Media Fluid Transport and Pore Structure
,
Academic Press
, NY.
18.
Crawshaw
,
J. P.
,
Paterson
,
W. R.
, and
Scott
,
D. M.
, 2000, “
Gas Channelling and Heat Transfer in Moving Beds of Spherical Particles
,”
Trans. Inst. Chem. Eng., Part A
0263-8762,
78
, pp.
465
472
.
19.
Crawshaw
,
J. P.
,
Paterson
,
W. R.
, and
Scott
,
D. M.
, 1993, “
Gas Residence Time Distribution Studies of Fixed, Moving and Frozen Beds of Spheres
.”
Trans. Inst. Chem. Eng., Part A
0263-8762,
71
, pp.
643
648
.
20.
Wakao
,
N.
,
Kaguei
,
S.
, and
Funazkri
,
T.
, 1979, “
Effect of Fluid Dispersion Coefficients on Particle-to-Fluid Heat Transfer Coefficients in Packed Beds
,”
Chem. Eng. Sci.
0009-2509,
34
, pp.
325
336
.
21.
Dixon
,
A. G.
, and
Cresswell
,
D. L.
, 1979, “
Theoretical Predictions of Effective Heat Transfer Parameters in Packed Beds
,”
AIChE J.
0001-1541,
25
, pp.
663
676
.
22.
Femlab 2.3, Comsol AB, Stockholm, Sweden, 2003.
23.
Whitaker
,
S.
, 1991, “
Improved Constraints for the Principle of Local Thermal Equilibrium
,”
Ind. Eng. Chem. Res.
0888-5885,
30
, pp.
983
997
.
24.
Thorpe
,
G. R.
, and
Whitaker
,
S.
, 1992, “
Local Mass and Thermal Equilibrium in Ventilated Grain Bulks I: The Development of Heat and Mass Conservation Equations
,”
J. Stored Prod. Res.
0022-474X,
28
, pp.
15
27
.
25.
Quintard
,
M.
, and
Whitaker
,
S.
, 1993,
One and Two-Equation Models for Transient Diffusion Processes, in Advances in Heat Transfer
, Vol.
23
,
Academic Press
, NY.
26.
Quintard
,
M.
, and
Whitaker
,
S.
, 1995, “
Local Thermal Equilibrium for Transient Heat Conduction: Theory and Comparison with Numerical Experiments
,”
Int. J. Heat Mass Transfer
0017-9310,
38
, pp.
2779
2796
.
27.
Sozen
,
M.
,
Vafai
,
K.
, and
Kennedy
,
L. A.
, 1991, ”
Analysis of Thermal Charging and Discharging for Sensible Heat and Latent Heat Storage Packed Beds
,”
J. Thermophys. Heat Transfer
0887-8722,
5
, pp.
623
625
.
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