Heat transfer to horizontal cylinders immersed in fluidized beds has been extensively studied, but mainly in the context of heat transfer to boiler tubes in coal-fired beds. As a result, most correlations in the literature have been derived for cylinders of $25-50mm$ diameter in vigorously fluidizing beds. In recent years, fluidized bed heat treating furnaces fired by natural gas have become increasingly popular, particularly in the steel wire manufacturing industry. These fluidized beds typically operate at relatively low fluidizing rates $(G∕Gmf<5)$ and with small diameter wires $(1-6mm)$. Nusselt number correlations developed based on boiler tube studies do not extrapolate down to these small size ranges and low fluidizing rates. In order to obtain reliable Nusselt number data for these size ranges, an experimental investigation has been undertaken using two heat treating fluidized beds; one a pilot-scale industrial unit and the other a lab-scale ($300mm$ diameter) unit. Heat transfer measurements were obtained using resistively heated cylindrical samples ranging from 1.3 to $9.5mm$ in diameter at fluidizing rates ranging from approximately $0.5×Gmf$ (packed bed condition) to over $10×Gmf$ using aluminum oxide sand particles ranging from $dp=145-330μm$ (50–90 grit). It has been found that for all cylinder sizes tested, the Nusselt number reaches a maximum near $2×Gmf$, then remains relatively steady $(±5-10%)$ to the maximum fluidizing rate tested, typically $8-12×Gmf$. A correlation for maximum Nusselt number is developed.

1.
Saxena
,
S. C.
, 1989, “
Heat Transfer between Immersed Surfaces and Gas-Fluidized Beds
,”
0065-2717,
19
, pp.
97
190
.
2.
Li
,
H.-S
.,
Qian
,
R.-Z.
,
Huang
,
W.-D.
, and
Bi
,
K.-J.
, 1993, “
An Investigation on Instantaneous Local Heat Transfer Coefficients in High Temperature Fluidized Beds—I. Experimental Results
,”
Int. J. Heat Mass Transfer
0017-9310,
36
(
18
), pp.
4389
4395
.
3.
Khan
,
T.
, and
Turton
,
R.
, 1992, “
The Measurement of Instantaneous Heat Transfer Coefficients Around the Circumference of a Tube Immersed in a High Temperature Fluidized Bed
,”
Int. J. Heat Mass Transfer
0017-9310
35
(
12
), pp.
3397
3406
.
4.
Karamavruc
,
A. I.
, and
Clark
,
N. N.
, 1996, “
A Correction Factor for One-Dimensional Heat Transfer Coefficients Around a Horizontal Tube in a Fluidized Bed
,”
Powder Technol.
0032-5910,
86
, pp.
209
217
.
5.
Crowle
,
W.
, 1987, “
Annealing Wire in Fluidised Beds
,”
Wire Ind.
0043-6011,
54
(
644
), pp.
455
457
.
6.
Ergun
,
S.
, 1952, “
Fluid Flow Through Packed Columns
,”
Chem. Eng. Prog.
0360-7275,
48
, pp.
89
94
.
7.
Sathiyamoorthy
,
D.
,
Sridhar Rao
,
Ch.
, and
Raja Rao
,
M.
, 1988, “
Effect of Distributors on Heat Transfer from Immersed Surfaces in Gas Fluidised Beds
,”
Chem. Eng. J.
0300-9467,
37
, pp.
149
163
.
8.
Grewal
,
N. S.
,
Saxena
,
S. C.
,
Dolidovich
,
A. F.
, and
Zabrodsky
,
S. S.
, 1979, “
Effect of Distributor Design on Heat Transfer From an Immersed Horizontal Tube in a Fluidized Bed
,”
Chem. Eng. J.
0300-9467,
18
, pp.
197
201
.
9.
Grewal
,
N. S.
, and
Saxena
,
S. C.
, 1980, “
Heat Transfer Between a Horizontal Tube and a Gas-Solid Fluidized Bed
,”
Int. J. Heat Mass Transfer
0017-9310,
23
, pp.
1505
1519
.
10.
Vreedenberg
,
H. A.
, 1958, “
Heat Transfer Between a Fluidized Bed and a Horizontal Tube
,”
Chem. Eng. Sci.
0009-2509
9
, pp.
52
60
.
11.
Andeen
,
B. R.
, and
Glicksman
,
L. R.
, 1976, “
Heat Transfer to Horizontal Tubes in Shallow Fluidized Beds
,” ASME Paper 76-HT-67.
12.
Petrie
,
J. C.
,
Freeby
,
W. A.
, and
Buckham
,
J. A.
, 1968, “
In-bed Heat Exchangers
,”
Chem. Eng. Prog.
0360-7275
64
(
7
), pp.
45
51
.
13.
Ainshtein
,
V. G.
, and
Gel’Perin
, 1966, “
O Teploobmene Mezhdu Psevdoozhizhennym Sloem i Poverkhnost’yu
,”
Int. Chem. Eng.
0020-6318,
6
(
1
), pp.
67
74
.
14.
Molerus
,
O.
, and
Writh
,
K. E.
, 1997,
Heat Transfer in Fluidized Beds
,
Chapman and Hall
, London.