HEAT TRANSFER IN FLUIDIZED BEDS
by
.Anthony Bright
Kenneth A. Smith
FINAL REPORT
October, 1970
Prepared under Contract No. CPA-22-&3-44 for
National Air Pollution Control Administration
Division of Process Control Engineering
Chi... .-u . ~; .,.;-v.;
Department of Chemical Engineering
Massachusetts Institute of Technology
Cambridge, Massachusetts
-------
-------
Synopsis
This report contains: *.
(a) A summary of the state of the art for heat transfer to surfaces in
contact with fluidized beds, including a compilation of published
investigations; with a listing and discussion of the various theo-
retical, empirical/ and semi-empirical expressions for predicting
heat transfer coefficients in fluidized beds.
(b) A summary of the study carried out here, with a discussion relat-
ing these investigations to the general picture proposed above.
(c) A general discussion of the important factors to be considered in
the design of fluidized-bed heat transfer units with recommenda-
tions for future research.
I. THE STATE OF THE ART
Appendix IIIA presents a compilation, in tabular form, of the major ex-
perimental investigations carried out in the field of heat transfer to surfaces
in contact with fluidized beds. It has been found helpful to separate them
into two groups; heat transfer in the dense phase region i.e., up to the point
where there is a net movement of the. solids bed relative to the walls of the
confining vessel (low bed voidage of the order of magnitude 50-70 percent);
heat transfer in the dilute phase region (bed voidage usually in excess of 90
percent). Although many investigations overlap into both regions, the various
studies have been divided according to the region containing the majority of
the data points. The reason for the division is that no one particular dense-
phase heat-transfer correlation can be extended into the dilute zone, and vice
versa. The first group has been further divided into heat transfer to the con-
fining wall, and heat transfer to bodies immersed in the fluidized bed.
i
-------
r
From the extensive amount of experimental data that have been collected
;
by various investigators, a number of theoretical, empirical and semi-empiric.
correlations have been advanced. These are listed in Appendix IIIB. Each co.
relation is valid only within the limits of the experimental data used by the
author.
Appendix IIIC lists the two generalized empirical correlations for heat
transfer in fluidized beds, the Wen-Leva (38) and the Wender-Cooper (3^) cor-
relations. These two correlations are held to be the most useful in predictir
heat transfer coefficients at surfaces in fluidized beds, and cover a wide
range of conditions. Zenz (40), Kunii and Levenspiel (4_1J , and Zabrodsky (4_2^
all cite these generalized correlations in their books; Zabrodsky also con-
siders the correlation of Vreedenburg (28) for horizontal tubes to be generall
applicable .
Appendix HID shows by means of a power function equation, the predicted
effect of the many parameters which could affect the heat transfer in fluidize
beds. The values in the columns under each parameter are the exponents in a
standard power function equation of the type:
a*
C etc.
g
g s
etc., are the exponents listed, and the power equation is
had o C
p
where ai , aj, aj, an
derived from the empirical or theoretical correlation of the investigator. Th
value of such an analysis is questionable, since many of the parameters are
interrelated, but it has been suggested (Mickley (21) ) that the effect of the
thermal properties of the bed k , k , C , C on heat transfer can be separated
from the effect of bed dynamics, which includes those properties related to th
state of fluidization of the bed e.g., d , p , u etc. Bearing in mind the
interrelationships of many of the parameters, it is possible to discuss the
general effect of significant properties on the heat transfer process.
-------
'.[ ected
^pirical
:ach cor-
by the
m
^r
T heat
) cor-
ndicting
*
j de
>.y (4_2)
con-
^
e^nerally
edicted
ftiidized
in a
*
t ion is
or. The
re
of the
parated
^ to the
the
the
3
Effect of Variables (Empirical Models)
(a) Particle Diameter d
P
The majority of investigations show an inverse relationship between
the heat transfer coefficient h and the particle diameter d , the most notable
exception being the correlation of Leva (6) . The latter investigator, however,
included a fluidization efficiency factor of which makes allowance for the
inverse effect of the particle diameter d on h. There is a wide variation in
P
the precise dependence of h on d , as can be seen from Appendix HID e.g.,
P
-0 23
Dow (5) had
- P
Miller (24) had ~ฐ'96
P
(b) Medium Thermal Conductivity k
9
All investigators showed a direct proportionality between h and k ,
ranging as follows:
0 33
Mickley (22) h a k
g
Leva (6.) h a k1'0
This variation in exponents is discussed later when the proposed mechanisms of
heat transfer in fluidized beds are considered.
(c) Solids Heat Capacity C
Most investigators showed a direct proportionality between h and C
_ ,_. . _ 0 . 25
Dow (5) h a C
""" S
Wender (39) h a C ฐ'8
s
(d) Other Solid and Gas Properties
Because of the wide disparities between the various investigators as
to the precise effects of properties such as bed-porosity e,.; bed geometry D.
and H ; superficial gas velocity u; gas density and viscosity p and u ; caused
by the complex nature of the fluidized state of the bed, a more detailed dis-
cussion will have to await developments in the understanding of the physical
I '
-------
nature of the complex behaviour of f.luidized beds. However, for engineerir
design purposes, Mickley (21') suggested the use of a stirring factor S whic
accoun'ts for bed motion and geometry to include the effects of those proper
which modify bed dynamics. The present study attempted to relate these prc
ties with a simplified model of gas bubble behaviour in fluidized beds.
(e) Gas Velocity u
A qualitative understanding of the overall picture of heat trans
in fluidized systems can be obtained by considering the way in which the he
transfer coefficient h varies with gas velocity. Up to the point of initia
fluidization, the value of h is essentially the same as for heat transfer t
packed bed. At the point of minimum f luidization, gas velocity u _, the he
transfer coefficient increases abruptly and continues to increase with gas
velocity until a maximum value h is reached. At higher gas velocities,
fflclX
heat transfer coefficient decreases slowly as the bed becomes "diluted" of
solid particles. This general trend is borne out by all the investigations
covered. Baerg (13), Kharchenko (20) and Varygin (27) have attempted to co
relate their data to predict the value of h , the maximum heat transfer c
max
efficient to surfaces in contact with fluidized beds. Leva (ฃ3_) suggested
another reason for the variation in the predictions might be that individua
investigators have studied different portions of the heat transfer - veloci
0 8
curve. For example, Dow (5_) gives h a u * , whereas Van Heerden (11) gives
0 45
h a u which suggests that the latter author's data refer to a region cl
to the maximum on the h vs u curve.
Theoretical Models {
Of the various models which have been presented to suggest the physic-
mechanism of heat transfer between fluidized beds and contacting surfaces,
general classes can be distinguished:
-------
Bering
"which
I
i
>;-operties
;e proper-
transfer
>^e heat
nitial
fer to a
he heat
gas
ies, the
" of
i o cor-
f'er co-
|jฃed that
vidual
elocity
gives
on closer
(a) The resistance to heat transfer lies within a relatively thin region
at the wall [ง.ปง./I/ill
(b) The resistance to hea't transfer, lies within a relatively thick emul-
\
sion layer which is being frequently replaced by fresh emulsion from the main
core of the fluidized bed []JL'U.'I1'11'1P_'1ง.'1ZJ
Botterill (44) suggests that the thermal conductivity of the fluidizing
medium is the limiting factor in the heat transfer process. Mickley (2JJ , pro-
posing the contacting emulsion-packet mechanism of type (b) above, found that
the heat transfer coefficient should vary as the square-root of the quiescent
I
bed conductivity, i.e., the gas conductivity raised to the one-third power
since the relationship between gas conductivity and quiescent bed conductivity
2/3
has been found to be approximated by k a k
*
hysical
i
ces, two *
Alternatively, if a gas film
were controlling the heat transfer process, (type (a)} as proposed by Leva (ฃ),
the heat transfer .coefficient should vary as the first power of the gas con-
ductivity. As shown previously, the exponent power on the gas conductivity
varies from 0.33 to 1.0 in the various correlations proposed, giving an indica-
tion of the type of mechanism operating in each case.
II. THE PRESENT STUDY
The overall purpose of the study was to investigate the heat transfer
characteristics between fluidized beds and contacting surfaces in order to
develop heat-transfer correlations for use in large-scale fluidized bed design.
The general approach was to consider the basic mechanics of fluidized bed heat
transfer in order to provide a foundation for a better understanding of the
many different correlations proposed in this field. To do this, generalized
serai-empirical correlations were selected from the literature representing the
two major theoretical models, and ware tested using available data.
As previously mentioned, the physical picture of the heat transfer
-------
process has been debated by several groups of investigators, the outcome of
which has been the division of opinion into two broad categories, the extremes
of which are best represented by the theories of Leva (6_) and Mickley (21) .
Leva (6) assumes that the chief resistance to heat exchange is in the laminar
gas film at the boundary of the surface in contact with the fluidized bed.
Heat flow through the film is by conduction. Further he suggests that the ver
tical motion of the particles along the surface considerably lessens the ther-
mal resistance of the laminar layer, causing the high heat-transfer coeffi-
cients observed in fluidized beds. The theory depends upon an understanding o
the pattern of this particle motion and the velocities of the particles.
Mickley (21) assumes that the controlling mechanism may be considered to be an
unsteady-state diffusion of heat into mobile elements of quiescent bed materia
"emulsion packets", in contact with the surface, which are constantly being
renewed by fresh.emulsion from the main core of the bed.
Neither of the theories can be tested directly since quantitative values
'for parameters such as Leva's interparticle friction factor 6, or Mickley"s
emulsion packet contact frequency <}>, are not well known. However, it was de-
cided to represent the two theories by the generalized correlations of Wen and
Leva (38) for the "thin-film"model and Wender and Cooper (39) for the "emulsioi
market" model. The basis for this assumption came from the following observa-
tions:
(a) The Wen-Leva (38) correlation was developed directly from the Leva
(6_) 'thin-film1 model.
(b) The Wender-Cooper (39) correlation for heat transfer to immersed
surfaces was developed from the data of Mickley (21) and when tested indepen-
dently gave a close alignment to the data of Pratt and Richards (45) , Fairbanks
(46), and Hawthorn (47) which were the source data of Mickley's (2_2_) theoret-
ical correlation.
-------
ปof
y's
as de-
*
Jen and
2mulsion
Dserva-
3 Leva
Mod
2epen-
lirbanks
:o ret-
to) The Wen-Leva, (38) correlation is based largely on data pertaining to
heat-transfer between fluidized beds and the confining vessel wall [5,6,10,11] .
The Wender-Cooper (3_9_) correlation used was based entirely on data from inves-
tigations with surfaces immersed in the fluidized bed [K^, 1J3,21^ 2_3_, 3j>_] . Toomey
(10) reported simultaneous bed-exterior wall and bed-interior calrod heat-
transfer coefficients and found large differences between the coefficients at
the two surfaces although at high fluid mass velocities the coefficients ap-
proach each other. It was deduced that the differences might be due to dif-
ferent mechanisms operating and that the Wen-Leva correlation (bed-wall)%rep-
resents the 'thin-film1 mechanism and the Wender-Cooper correlation (bed-
internal surface) represents the 'emulsion-contact' mechanism. Further it
seems likely that in a bubbling bed, surfaces immersed in the bed will be con-
tacted frequently with rising bubbles which allow fresh emulsion packets to
sweep up to the surface, while the frequency of bubbles near the wall will be
much Tower with solids descending along the wall surface and the development of
a thin gas film layer at the wall.
In order to test the Wen-Leva and the Wender-Cooper correlations, and the
theoretical models that they were chosen to represent, the data of Van Heerden
(13J and Dow and Jacob (5) for heat transfer from the bed to external surfaces
and the data of Fairbanks (4jy , Hawthorn (47) and Baerg (13) for heat transfer
to surfaces immersed in the bed were employed. The comprehensive data of
Fairbanks and Hawthorn were available at M.I.T. The data of Van Heerden and
Baerg are generally considered to be the most systematic and representative
data on heat transfer between fluidized beds and contacting surfaces [cf Leva
(4J[) , Kunii and Levenspiel (41), Zenz (40)]. Of the other data sources listed
in Appendix IIIA only Dow and Jacob gave information on bed voidage at dif-
ferent fluidization conditions which was necessary for application to the gen-
i .
oralized correlations. An attempt to. predict bed voidage from the 'M-plot1 of
-------
8
Leva (4JO was made, but the results did not prove very satisfactory. Thus me
of the investigations in this study wore based on the five data sources men-
tioned above which gave sufficient details to apply to the Wen-Leva and Wendc
Cooper correlations.
Appendix IV, Graphs 1 and 2, shows the results of the data-testing. As
might be expected, the bed-to-external surface heat transfer data of VanH^erc'
(1^), and Dow and Jacob (5_) (which had been employed by Wen and Leva, along wi
other data, to develop their correlation) aligned closest to the Wen-Leva coi
relation for bed-to-external surface transfer; also, the vertical immersed sv
face transfer data of Fairbanks (ฃ6_) (used by Wender and Cooper to help develc
their relationship) and Hawthorn (47) aligned closest to the Wender-Cooper cc
relation for transfer to vertical immersed tubes. The data of Baerg (13), ho.
ever, showed a tendency under certain conditions to follow the Wen-Leva cor-
relation whereas it would be expected to be in line with Wender-Cooper for in
mersed heat transfer surfaces.
In order to explain the anomalous results of Baerg, it was thought that
not only the location of the heat transfer surface (external wall or internal
immersed) but the geometry and size of that surface might be a governing fad
as to which correlation, and which corresponding mechanism, might be valid ii
any circumstance. Baerg"s internally heated tube was much larger than the
internal cylindrical heaters of Fairbanks and Hawthorn, and the following hy-
pothesis was therefore proposed:
1) Heat transfer coefficients to the containing walls of the fluid
ized bed can be predicted by the Wen-Leva (thin-film) correlation.
2) For surfaces immersed in the fluidized bed:
(a) If the dimensions of the surface (tube diameter) are smalL
than some characteristic dimension for the fluidized system, then the Wender
Cooper (emulsiom-contact) correlation should predict the heat-exchange rates
-------
?h.us mos-
(b) If the dimensions of the surface are large compared to this
men- Characteristic dimension then the Wen-Leva (thin-film) correlation will apply.
1 Wender- For the characteristic dimension, the b,ubble diameter was chosen based on
the physical picture that only when the bubbles are of sufficient size, in cora-
As parison with the size of the immersed surface, to be able to sweep packets of
nemulsion to the immersed surface will the conditions for the 'contacting emul-
long with sion packet1 mechanism be favorable. Estimations of the bubble diameter for
^a cor- 'different fluidizing gas rates were'attempted "in order to deduce values of
rsed sur-Hawthorn's emulsion-packet contact frequency, ,. Assuming that the unsteady
develop state behaviour of the emulsion packets is caused by the passage of the low
Doer cor-density bubbles, it was proposed that the contact frequency of the emulsion
91 I
13), how-packets can be equated to the frequency of bubbles past the surface. Values of
a cor- 'bubble frequency were determined theoretically from Davidson's (43) simplified
for im- model. It was found that these values were from two to ten times higher than
ht that
nternal
the emulsion contact frequencies measured by Hawthorn, which implies that the
theoretically derived values of bubble diameter over-estimated the actual bub-
hie size. Nonetheless, it was hoped that these estimates would serve as a corn-
factorparative guide for assessing the characteristic dimension proposed above.
a lid in
the
Graphs 3 and 4 in Appendix IV show the results of Baerg (13) and
H/reedenburg (28) in the form of a plot of h
.
/h , versus the ratio of pseudo
C 61 -L C
Ing hy- "bubble diameter to internal tube diameter d, /d . It was hoped to observe a
transition from the 'thin-film' mechanism to the "emulsion-contact1 mechanism
fluid- 'as d,/d increased. The general scatter of the data points do not show a clear
.transition; although the data of Vreedenburg indicate an agreement with the
above hypothesis i.e. at a certain d /d ratio (approx. 1.5) and greater the
smaller wender-Cooper correlation gave a better fit to the experimental results, whilst
Kender- pelow this value, the Wen-Leva correlation gave the closer fit. Vreedenburg
rates. himself found it necessary to propose two correlations of his own to represent
-------
ir
his experimental results, noticing a transition at a Reynolds Group No. ( p "c
~V(>"
of 2050, evidence of a change in nature of the fluidized bed and the
mechanism controlling heat transfer.
For large-scale systems, the data of Highley (18) for transfer to im-
mersed horizontal tubes in a 3-ft. diameter bed were applied to the correla-
tions. Appendix V shows the coefficients predicted by the correlations com-
pared with an average observed value of the heat-transfer coefficient from
individual horizontal tubes in a multiple bank of tubes. The Wender-Cooper
correlation gives the closer approximation, although neither of the correla-
tions takes account of factors such as tube position in the bundle or the
change in heat transfer coefficient around the circumference of the tube.
A large part of the investigation was centred on gaining physical insii
as to the internal workings of a bubbling fluidized bed by investigating pro
posed mechanisms for gas-particle motion and endeavouring to build a simplif
model relating fluidized bed dynamics with easily measured physical properti*
of the system. Davidson's (48) bubbling-bed model has already been mentione
in connection with bubble diameter and bubble frequency calculations. Howev
the complex nature of the gas-particle interactions in most of the experimen
systems studies make it unlikely that Davidson's simplifying assumptions appli
in these cases. The Davidson model, therefore, is of limited quantitative u
although it serves as an order-of-magnitude analytical tool for most fluidiz
situations, and is readily amenable to design work since only well-known phy
ical properties of the system under study are required for its application.
other physically-based model has been found which combines simplicity in dat
requirements with quantitative accuracy. This scarcity of viable theoretica
models for the purely mechanical behaviour of fluidized beds is the largest
obstacle to useful advance in understanding their heat transfer properties.
-------
10
,d Go
( P ฃ
i im-
ela
; com
: rom
rtela-
L insight
ig pro-
i-nplif ie
flerties
itioned
However
applied
^ive use
1 uidized
.in phys-
tion. Nc
in data
rcitical
rgest
ties .
11
Overall Conclusions ,
The lack of theoretical understanding of mechanism and of general correla-
tion work has left open the problem of predicting heat transfer coefficients
between fluidized beds and the surfaces in contact with them. The reported
empirical correlations of various individual investigators are valid only
within the limits of their own experiment and do not appear to be able to en-
compass the data of other investigators.
Two generalized correlations, Wen-Leva (38) and Wender-Cooper (3JU cover
more extensive ranges of conditions and data and may be expected to be extended
for use in large-scale design work after modification by the effect of such
factors as:
(i) Tube spacing and arrangement in multiple tube banks
(ii) Position around tube circumference
(iii) Bed diameter (changing the flow properties of the fluidized
solids)
(iv) Particle size distribution
(v) Gas entry configuration (distributor)
(vi) Baffles
However, it is important to note that even these correlations.ordinarily
require estimates of the void fraction; and in this regard, our present pre-
dictive abilities are very poor.
It is suggested, albeit very tentatively, that the choice of correlation
is based on the hypothesis outlined previously which proposes that for surfaces
immersed in a fluidized bed, the heat exchange rates will depend upon the phys-
ical state of the fluidized bed, either vigorously bubbling with the surfaces
often swept clean of emulsion ('emulsion-packet model") or fairly smooth fluid-
ซ
ization with particles descending near the surface "scouring" the gas film
formed there ("thin-film model"). That there mi^ht be a transition from one
-------
mechanism to the other with change in fluidization conditions is at least th
retically possible. Furthermore, transition would be -expected to depend on
relative sizes of the immersed element 'and a characteristic dimension of the
bubbling bed (e.g., bubble diameter), and the choice of design correlation
would depend on the physical mechanism operating i.e., Wen-Leva (38) for the
'thin-film' model and Wender-Cooper (390 for the 'emulsion-packet' model.
III. FUTURE RESEARCH REQUIRED
It is to be expected that future research in this field will be concer
trated mainly on bridging the gap between laboratory and industrial fluidizc
bed design with the emphasis on gaining information about the effects of pa:
meters such as those outlined in the conclusions.
Until the mechanics of gas-particle motion in a fluidized bed and its
relation to the physical properties of the bed is better understood, no the'
retical equation describing the heat transfer properties of fluidized beds
suitable for use as a design correlation can be formulated. For example, p
diction of bed voidage at any fluidized conditions with any degree of accur
is difficult with existing correlations, yet knowledge of this important pa
meter is essential for specifying the state of fluidization of a bed.
The problem of scaling-up laboratory experimentation into full-scale
units is to maintain the quality of fluidization. As more data are made a\
able from large-scale units, general design trends will become apparent. F
example, Volk (49) used vertical surfaces in the form of tubes to modify tf
'equivalent1 diameter of his large-scale bed to conform with the diameter c
his small-scale unit and Petrie (31) found that finned surfaces on the flu.
ized bed side of heat exchanger tubes increased heat transfer rates twofoli
Nonetheless, a sound interpretation of heat transfer in fluidized beds mus'
await future developments in our understanding of bed mechanics.
-------
12 :
13
the o-l
3 on th;- nomenclature
f the
ion
C
APPENDIX I
T the
1.
ft
oncen-
i dized
j" para-
[ its
> theo-
||ds and
.o, pre-
i::curacy
it para-
d *p p g
JE__1_3_ฃ.
:ale
3e avail
?. For
fy the
ter of
ftfluid-
cfold.
must
Avogadro No.
heat capacity of fluidizing gas
heat capacity of solid particles
correlation factor for non-axial location of internal tube
particle diameter
bubble diameter
external diameter of immersed object (tube, sphere)
diameter of containing vessel
superficial mass velocity of fluidizing gas
superficial mass velocity of fluidizing gas at minimum fluidization
heat transfer coefficient
heat transfer coefficient measured by investigator
i .. heat transfer coefficient calculated according to one of the generalized
ca Xc
correlations
height of heat transfer surface exposed to fluidized bed
emulsion thermal conductivity
thermal conductivity of fluidizing gas
thermal conductivity of solid particles
length of immersed tube
height of bubbling fluidized bed
mf
h
exp
mf
bed height at minimum fluidizing conditions
hd
* ซ
>r
Nusselt No.
Prandtl No. r-
g
-------
R
Re
T
B
mf
lmf
u
pc
oฃ
Pn
*.:
expansion ratio, Lf/L
Gd
Reynolds No. *-
mf
bed temperature
superficial velocity of fluidizing gas
superficial velocity of fluidizing gas at minimum fluidizing conditions
void fraction in fluidized bed
void fraction in fluidized bed at minimum fluidizing conditions
fluidization efficiency (defined by Leva (6_) )
viscosity of fluidizing gas
density of fluidizing gas
density of solid particles
bulk density of fluidized bed at minimum fluidization
emulsion-packet contact frequency (Mickley (21))
kinematic viscosity
-------
15
renditions
ป
APPENDIX II
Reference^
1. Agarwal, O.P., and J.A. Storrow, "Heat Tr-ansfer in Fluidized Beds," Chem.
{. Ind., 321 (1951) .
2. Ciborowski, J., and J. Roszak, "An Investigation of Heat Transfer Between
a Heated Surface and a Fluidized Bed," in "Hydrodynamics and Heat Trans-
fer in Fluidized Beds," S.S. Zabrodsky, loc. cit. pp 268-270.
3. Ibid., pp 242-243.
4. Drinkenburg, A.A.M., N.J.J. Huige, and K. Rietama, Proc. 3rd Internation-
al Heat Transfer Conf., 4_, 271, Chicago (1966).
5. Dow, W.M., and M. Jakob, "Heat Transfer Between a Vertical Tube and a
Fluidized Air-Solid Flow," Chem. Eng. Progr., 47, 637 (1951).
6. Leva., M. , M. Weintraub and M. Grummer, "Heat Transmission through Fluid-
ized Beds of Fine Particles," Chem. Eng. Progr., 4_5_, 563 (1949).
7. Levenspiel, O., and J. S. Walton, "Bed Wall Heat Transfer in Fluidized
Systems," Chem. Eng. Progr. Symp. Ser., 50, No. 9, 1, (1954).
8. Matsuyama, T, Kagaku Kogaku, 18, 406 (1954), in "Fluidization Engineer-
ing," D. Kunii and O. Levenspiel, loc. cit. p 269.
9. Massimilla, L., S. Bracale and A. Cabella, "Solido-Gas Fluidizzati," in
"Hydrodynamics and Heat Transfer in Fluidized Beds," S. S. Zabrodsky,
loc. cit. p 261.
10. Toomey, R., and Johnstone H., "Heat Transfer Between Beds of Fluidized
Solids and the Walls of the Container," Chem. Eng. Progr. Symp. Ser. 49 ,
No. 5, 51 (1953).
11. Van Heerden, C., A.P. Nobel, and D. Van Krevelen, "Mechanism of Heat
Transfer in Fluidized Beds," Ind. Eng. Chem., 45, 1237 (1953).
-------
(' I
16 ;
12. Ainshtein, V.G., "An Investigation, of Heat Transfer Processes Between
Fluidized Beds and Single Tubes Submerged in the Beds," in "Hydrodynamic
and Heat Transfer in Fluidized Beds," S.S. Zabrodsky, Ic5c_. cit. pp 270-
272. i"
13. Baerg, A., J. Klassen, and P.E. Gishler, "Heat Transfer in a Fluidized
\
Solids Bed," CajT^^J^Re^earch^^ F2_8, 287 (1950). |
14. Bondareva, A.K., "Measurement of the Thermal Conductivity of Suspended *
Beds," from S.S. Zabrodsky, loc. cit. p 267.
15. Campbell, J.R., and F. Rumford, "The Influence of Solid Properties on
Heat Transfer from a Fluidized Solid Medium," J. Soc. Chem. Ind. ^ 6_9_, 37ซ
I
(1950). |
s
16. Chechetkin, A.V., "High Temperature and Heat Transfer Agents," from
0
S.S. Zabrodsky, loc. cit. p 262. ]
<
17. Ernst, R. , "Heat Transfer Mechanism in Fluidized Beds," Chem. Ing. Tcchr.,
3_1, No. 3, 166 (1959) . j
18. Highley, J., 'Heat Transfer Between Horizontal Tubes and a Fluidized Bed
of Ash," National Coal Board, Coal Researcji Establishment, Fluidized '
Combustion Section Report No. _20^ (1969) .
19. Jacob, A., G.L. Osberg, "Effect of Gas Thermal Conductivity on Local Heat
Transfer in Fluidized Bed," Can. J. Chem. Eng., 3J[, 5 (1957).
20. Kharchenko, N.V., and K.E. Makhorin, "The Rate of Heat Transfer Between
a Fluidized Bed and an Immersed Body at High Temperatures," Intern. Chem.
Eng., 4_, 650 (1364) .
21. Mickley, H.S., and D.F. Fairbanks, "Mechanism of Heat Transfer to Fluid-
ized Beds,1' A.I.Ch.E. J., I, 374 (1955). '
22. Mickley, H.S., D.F. Fairbanks, and R.D. Hawthorn, "Heat Transfer Coef-
ficients in Fluidized Beds," Chem. Eng. P rog r. Symp ^ งe_r_ie_s_ 57 , 32, 51
(1961). ,
-------
.
Dynamic;'
P 270-
ended
r> on
6_9, 37]
om
5_._jrechn_
Lzed Bed
L zed
Deal Heal
Eetween
rn_._ Chem
o Fluid-
Coef-
32, 51
I
17
23. Olin, H.L., and O.C. Dean, Petrol. Eng. 25, C-23 (1953) in "Fluidization
Engineering," D. Kunii and O. Levenspiel, loc_. cit. p 268.
24. Miller, C.O., and A.K. Logwinuk, "Fluidization Studies of Solid Particles1,'
Ind. Eng. Chem. , 4_3, No. 5, 1220 (1951).
25. Sarkits, V.B., "Heat Transfer from Suspended Beds of Granular Materials
and Walls," from S.S. Zabrodsky, log, c it. p 275.
26. Shirai, T., and H. Yoshitome, "Heat and Mass Transfer on the Surface of
Solid Spheres Fixed within Fluidized Beds," Kagaku Kogaku (English
edition) ฃ, 162 (1966) .
27. Varygin, N.N., and I.G. Martyushin, "Calculation of Heat Transfer Area in
Fluidized Bed Equipment," from S.S. Zabrodsky, loc. cit_. p 272.
28. Vreedenburg, H., "Heat Transfer Between a Fluidized Bed and a Horizontal
Tube," Chem. Eng. Sci. , 9, 52 (1958).
29. Vreedenburg, H". , "Heat Transfer Between a Fluidized Bed and a Vertical
Tube," Chem. Eng. Sci.,11, 274 (1960).
30. Ziegler, F.N., and W.T. Brazelton, "Mechanism of Heat Transfer to a Fixed
Surface in a Fluidized Bed," Ind. Eng. Chem. Fundamentals, 3_, 94 (1964).
31. Petrie, J.C., W.A. Freeby and J.A. Buckham, "In-Bed Heat Exchangers,"
Chem. Eng. Prog., 64, 45 (1968).
32. Bartholomew, R.N., and D.L. Katz, "Heat Transfer from the Wall of a Tube
to a Fluidized Bed," Chem. Eng. Progr. Symp. Ser. 48, No. 4, 3 (1952).
33. Brazelton, W.T., Ph.D. Thesis Northwestern University (1951) in "Fluid-
ization," M. Leva, loc. cit. p 218.
34. Trense, R.V., "Heat Transfer in Gas-Solid Fluidized Beds," Piss. Abstrs.,
15_, 1814 (1955) .
35. Mickley, U.S., and C. Trilling, "Heat Transfer Characteristics of Fluid-
ized Beds," Ind. Eng. Chem., 4_1^, 1135 (1949).
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(1948).
-------
18
37. Wicke, E., and F. Fetting, "Heat Transfer in Fluidized Beds," Che in. Ing.
Tech. , 26_, 301 (1954). ' ':
i-
38. Wen, C.Y., and M. Leva, "Fluidixed Bed Heat Transfer; A Generalized Dens
I
Correlation," A.I.Ch.E. J._, 2, 482 (1956). I
39. Wender, L., and G.T. Cooper, "Heat Transfer Between Fluidized Solids Bed;'
and Boundary Surfaces - Correlation of Data," A.I.Ch.E. J., 4_, 15 (1958).<
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(1969) .
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M.I.T. Press (1966).
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Thesis, M.I.T. (1951).
46. Fairbanks, D.F., "Heat Transfer to Fluidized Beds," Sc.D. Thesis, M.I.T.
(1953).
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(1956) .
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Quality of Fluidization," Chem. Eng. Prog., 58, 44 (1962).
-------
IS
19
ed Dense
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APPENDIX IIIA
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APPENDIX HID
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APPENDIX _1IIB>
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26
27
APPENDIX II1C
GENERALIZED CORRELATIONS FLUIDIZED BED HEAT TRANSFER TO SURFACE
.
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1 !
APPENDIX HID
EFFECT OF INDIVIDUAL BCD PROPERTIES ON HEAT TRANSFER COEFFICIENT
28
VALUES LISTED ARE EXPONENTS TO WHICH EACH PROPERTY IS RAISED
to
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Wender (39)
-------
29
" exp
BTU
hrftฐF
175
150
125
100
100
125 150
calc
BTU
hr ft2ฐF
175
FROM WEN-LEVA (38)
CORRELATION
a
c
0)
APPENDIX TSL GRAPH 1
COMPARISON OF MEASURED AND CALCULATED
HEAT -TRANSFER COEFFICIENTS .
-------
30
"exp
BTU
hr ft2ฐF
175
15O
125
100
75
50
25
0
9
DATA SOURCES
FAIRBANKS
a HAWTHORN
ฉ DOW and JACOB
A BAERG
X VAN HEERDEN
O 25 50
BTU
hcalc.
2 0
tt F
75 100 125 15O
FROM WENDER-COOPER(39)
175
CORRELATION
APPENDIX EZ1 GRAPH 2
COMPARISON OF MEASURED AND CALCULATED
HEAT TRANSFER COEFFICIENTS
-------
31
J.U
2r~
.5
2.O
hexp
M i~n\r i PC
t-UH- I.O
1 Pi
l.U
0.5
0
(
I I
HWEN-LEVA PREDICTIONS
ฉWENDER-COOPER PREDICTIONS
0
ซ ฉ
ฎ
ฎ
A ^ A
* Q w
O
ฉ 0 00ฎฉ 9
0 ซ ซ a 9 0
OO ซH O HWB
0 DP BV^ a a E ป
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^ ua B
B 0 *
B 0ฉ
^ 0 ฉ Q
ฉ
^ 0 I I
<^> 1 1
D 1 2 3 4 5 6-7
dt, bubble diameter
dt
internal tube diameter
APPENDIX W. GRAPH 3
DATA OF BAERG (13)
INTERNAL VERTICAL HEATED TUBE dt = 1.25'
-------
h
ex p.
hcalc.
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0
a WEN-LEVA CORRELATION.
0 WENDER-COOPER CORRELATION
>
/
3.5
0 0.5 1.0 1.5 2.0 2.5 3.O
db bubble diameter
dt internal tube diameter
APPENDIX IZ GRAPH 4
DATA OF VREEDENBURG (28)
SINGLE HORIZONTAL TUBES dt =0.66"and 1.35
-------
APPENDIX V
Calculation of Heat Transfer Coefficients in a Large Diameter Bed Compared ,.
the Data of Highley (18)
Vessel Diameter - 3 ft.
avg
w-c
w-1
u
Average value of heat transfer coefficient from measurements to ir-.-
2
vidual horizontal tubes in a multiple tube bank, Btu/hr-ft -ฐF.
Heat transfer coefficient calculated from the correlation of Wendซ:
2
and Cooper (3_9_) , Btu/hr-ft -ฐF.
- ' Heat transfer coefficient calculated from the correlation of Wen ar
2
Leva (3ฃ) , Btu/hr-ft -ฐF.
Superficial gas velocity, ft/sec.
U li 11
avg w-c
0
1
2
3
.98
.97
.95
.94
33
38
41
43
.4
.2
.8
.8
31
30
28
27
.9
.2
.9
.9
w-1
42
64
77
86
.3
.8
.6
.7
------- |