References
Becker, R.. Ann. Physik. 32, 128 (1938). Becker, R.. Dnring, Lf-., Zbid.. 24, 719 (1935). Bobalek, E. G.. Off.Digest 34, 1293 (1962). Bradley, R . S.,Quart. Xer.. (London) 5 , 315 (1951). Cheever. G. D., Bobalek. E. G.. Of. Dicest 35, 759 [1963), Cheever, G. D.. Parker. M. T., Rohileky E. G:. Ibtd’, 34, 1047 ’1962). (7)’ Chekick. J. J., J . Phys. Chem. 66, 762 (1962). (8) Cook, H. D.. Ries. H. E., Jr.. J . Phys. Chem. 63, 226 (1959). (9) Criegee. R . . Ann. 522, 75 (1936). (10) Dintenfass, L., Kolloid-Z. 161, 60, 70 (1958). (111 Dralev. J . E.. ArPonne ,Vatl. Lab. News-Bull. 3. 3 (1962). (l2j Epstein. H . T., j . Phyr. ColloidChem. 54, 1053(1950). ’ (13) Fieser. I,. F., Fieser, .M., “Organic Chemistry.” p. 61, Heath, Boston, 1950. (14) Frenkel, ,J., “Kinetic Theory of Liquids,” pp. 366-426, Dover Publications, New York, 1955. (15) Gebhardt, J.: Herrington, K., J . Phys. Chem. 62,120 (1958). (16) Gray! T. J., McCain. C. C.. Masse, N. G., Zbid., 63, 472 (19-lO~. \-.--,.
McCormick, J. L., Baer. E.. J . ColloidSci. 18, 208 (1963). Mathieson, R. T., ’Vature 183, 1803 (1959). Moroney, IM. J.. “Facts from Figures,” pp. 96-107, Penguin Books: Baltimore, 1962. (22 Porter, K. R., Kallman, F., Exptl. Cell Res. 4, 127 (1953). (231 R eyerson. L. H.: Honig, J. M.: J . Am. Chem. Soc. 75, 3917, ~
3020 (1057).
(24) R i & H.’E., Jr., Kimball, W.A . , J . Phys. Chem. 59, 94 (1955); Nature 181, 901 (1958). (25) Sandler. Y . L.,J . Phvs. Chem. 58. 54. 58 (1954). (26) Tammann, Y., “ThLStates of Aggregatidn,” Van Nostrand, New York. 1925 (Engl. transl.). P. A., 2’. Elektrochem. 48, 675 (1942). olmer, M., Ibid., 35, 555 (1929). (29 Volmer, M.. Weber, A., Z . Phyrik. Chem. 119, 277 (1926). (301 W ade, W. H., Hackerman, N.. J . Phys. Chem. 6 5 , 1681 (1961). RECEIVED for review July 22, 1963 ACCEPTED November 5, 1963 30th Annual Chemical Engineering Symposium. ACS Division of Industrial and Engineering Chemistry. University of Maryland. November 1963. Based on Ph.D. thesis of G. D. Cheever.
(17) Gulbransen. E. A , : McMillan, W. R., Andrew, K. F., Trans. AZME 200, 1027 (1954). (18) Harkins. \V. D.: Gam, D. &f.>J . Piiys. Chcm. 36, 86 (1932).
MECHANISM OF HEAT TRANSFER T O A
FIXED SURFACE IN A FLUIDIZED BED EDWARD N .
Z I E G L E R ’ A N D W I L L I A M T. B R A Z E L T Q N
The Technological Institute, IVorthwestern Crniiersity, Ecanston, Ill. Simultaneous heat and mass transfer from the surface of a sphere was studied for comparable situations in a gas stream and a gas fluidized bed of solid particles. The systems were chosen so that the fluidized particles would have capacity for heat transport but not mass transport. Solid particles in the fluidized state increased heat transfer 10- to 20-fold, but increased mass transfer only 1 ‘/z to 2 times. On the basis of the particles’ unique property for heat transport, and assuming analogous heat and mass transfer in the gas phase, it was concluded that in any mechanism of heat transfer in the fluidized state, 80 to 95% of the transfer must be accounted for by particle transfer mode. The remainder may be accounted for in Q path solely in the gaseous phase. HE phenomenon of heat transport in fluidized beds has Tbeen the subject of numerous studies in recent years. Of particular interest is the heat transfer between the bed and an internal or external surface. T h e results of work on this topic have been summarized extensively by Zenz and Othmer (26). Another review by Botterill (7) includes all but the most receit literature. Several of the early investigators verified the improvement in heat transfer, and offcred accompanying rationales in the form of mechanisms of transport. For instance, Leva 70) and Docv and Jakob (3) suggested and coworkers (8--that the increase in heat transfer was probably a consequence of the scrubbing action of particles against the transfer surface. This action was thought to disturb the gas film and hence decrease its resistance to the flow of heat. I n later presentations. such as those of Van Heerden, Kobel, and Van Kreveltm (78: 7 9 ) : \\*icke and Hedden (251, Wicke and Fetting ( 2 4 ) ;Mickley and Fairbanks ( 7 7 , 717), and Ernst ( 4 ) . rnechanisms were developed that appear to be more credible in explaining heat transfer improvement of the magnitude experienced. Although there are some differences in these siiggested models, common factors may be summarized as follokzs. T h e fluidized particles are visualized as a packeti.e.. closely locked assemblage of particles-moving from the I
Presrnt addrrss. Esso Rpsearch and Engineering Co., Linden.
N. J . 94
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FUNDAMENTALS
core of the bed to the particular boundary surface, absorbing or giving u p heat, depending upon the relative temperature of the surface, and then returning to the core of the bed. The interstitial gas serves as a stirring agent and as a heat transfer medium between the particles and the surface. T h e presence of the particles probably improves heat transfer by a combination of the two aforementioned effects-. conveyance of heat from the packet to the surface on contact and disturbance of the gas film adjacent to the surface. The simultaneous occurrence of these two effects has not yet been demonstrated by experiment. I t was the intention of this experimental investigation to verify the presence of these two effects and to determine their relative importance. T h e experiments performed involve simultaneous heat and mass transfer from a solid object to a fluidized bed. T h e system was chosen to allow both the particles and the gas to take part in the transport of heat a t the solid surface. O n the other hand, the particles in this system have negligible absorptivity for the diffusing species and consequentlv have no capacity for mass transport. Therefore! the only mechanism of importance in mass transfer is the diffusion of mass through the surface gas film. In systems without fluidized particles a t constant surface temperature and composition. it is known that the mechanisms of heat and mass transfer from a surface are analogous for low mass transfkr ra.tes. Both types of transfer may be considered to take place through
L E A V I N G AIR TO BE A N A L Y Z E D B Y DEW POINT DEVICE THERMOCOUPLE READING OF CELITE SURFACE TEMPERATURE
I
I 1 LUCITE COLUMN 4 ” -DIAMETER
I
I FLUIDIZED P4RTlCLES
C E L I T E SPHERE -DIAMETER
i
--
in the nearl) saturated air a t the interface may be assumed equal to the vapor pressure a t the surface temperature. T h e heat transfer coefficients are calculated from a knowledge of the air temperature and surface temperature and the mass transfer rate as determined by dew point measurements. iZllowance is then made for radiant heat transfer. T h e transfer area is that of the sphere minus the area of the thermocouples. T h e d a t a for the single sphere with no particles present agree well with those of Ranz and Marshall (74) and Griffith ( 7 ) . Analysis
T h e heat and mass transfer under steady-state conditions may be defined by the following equations: For heat and mass transfer balance a t the interface
q
=
LYX
POROUS P L A T E
For mass transfer rate
ENTERING AIR AT CONSTANT HUMIDITY
Figure 1, Experimental apparatus for simultaneous heat and mass transfer from sphere to air with aid of fluidized particles a gas film near the solid surface. As a consequence of the analogoris mechanisms for these conditions, the ratio of heat to mass transfer coefficients remains approximately constant, and there exists a n equality of j factors (2) for both cases. L p o n the addition of fluidized particles to a system, the heat transfer coefficient can be improved significantly. ‘The improvement of the mass transfer coefficient is studied herein and is used in the determination of a mechanism of heat transfer. For example, if heat is not transferred via the particles. the mass transfer coefficient would no doubt increase by the same factor as the heat transfer coefficient. O n the other hand, if the particle does have a part to play in heat transfer and not in the mass transfer, the transfer factors for the tlvo cases ~vouldbe expected to be affected differently.
Experimental Techniques
T h e experimental equipment used is indicated in Figure 1. A half inch-diameter sphere is saturated with distilled water and then exposed to a metered stream of dry inlet air under various fluidized bed conditions. T h e sphere was formed from Johns-hlanville I’ype VI11 catalyst carrier, a claylike material which after baking has been shown experimentally to have a convenient constant-rate drying period (77). T h e solid sphere has a fine hole drilled through all but V 3 2 inch of its thickness. A thermocouple is inserted in this hole and held there by the addition of more clay and rebaking. T h e sphere is then saturated with water and suspended from the thermocouple. As a consequence of the short height of suspension and the relatively low gas velocities, the sphere remains stationary. Temperatures are recorded throughout each run. T h e inlet and outlet air hurnidities are recorded on a General Electric dew point recorder (6) which has been calibrated to 1’ F. Temperatures of the air a t inlet and outlet conditions are measured by thermocouples. When steady state has been achieved, the outlet humidity and sphere temperature remain constant until the falling rate period is reached. Copper, glass? and Alundum particles were used as the fluidized medium. T h e mass transfer coefficients are calculated from a knowledge of inlet and outlet dew points and the surface temperature of the sphere. T h e partial pressure of the water vapor
For heat transfer rate 9 = h t ( t , - tJ7n
(3)
T h e quantities pp and t u vary little during the run. I n addition, p, is a function of t , only. T h e coefficients k , and h l are independent variables and, depending 011 their values, a certain value of t,, and hence p , , will be reached a t steady state-i.e.. the final value of the temperature a t the surface is a function of only the heat and mass transfer coefficients when the dry bulb temperature and the partial pressure of the water vapor in the air have small variation. T h e coefficients /io and h , for most systems have been found to vary similarly. but they should not be thought of as mutually dependent. T h e transfer of heat and mass is interdependent? but the coefficients of heat and mass transfer are independent. Only under conditions a t which heat and mass are transported by a n analogous mechanism d o the k, and h l have similar variation. For a n air-water system, Ranz and Marshall (74) presented the following relation : Nu’
=
2
+ 0.60 Re1”%c1/3
(4)
Equation 4 was developed from boundary layer theory as per Froessling (5) and from dimensional analysis. It is applicable for mass transfer in the Reynolds number range 0 to 200. T h e analogous heat transfer equation with S u ’ and Sc replaced by Nu and Pr. respectively, is found to hold equally well in the same range. Results
Experiments were performed without fluidized particles and the results were checked with Equation 4. T h e equations
Nu’ = 2
+ 0.56 R ~ ’ ’ * S C ~ ’ ~
(Sa)
for mass transfer (1 1 .5y0standard deviation of data). and N u = 2 f 0 68 Re1’*Pr1/3
(jb)
for heat transfer (8.5% standard deviation) were used to represent the d a t a of this system over the range investigated. With the addition of fluidized particles to the system. however, a n entirely ne\\. mechanism for heat transfer. particle transport (convenient name for transport via a path or paths which include particles), is available which has no equivalent in mass transfer for the conditions of the experiment ThereVOL. 3
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fore, for the system with fluidized particles, it is conceivable, and in fact a reality, that the heat transfer coefficient can change significantly from that of the no particle case with no comparable change in mass transfer coefficient. Table I is a sampling of representative heat and mass transfer coefficients and their ratios for the fluidized systems and empty tubes. For all systems of fluidized particles. a large increase in heat transfer coefficient occurs with a comparably minor increase in mass transfer coefficient. The ratio h,/ku is approximately constant (0.249, 4% standard deviation) for nonfluidized systems. This is in agreement with the “Lewis relation” (after W . K. Lewis) which states that h,/k, is approximately equal to C, and is a consequence of the analogous mechanism of heat and mass transport. It has been shown that for the air-water system, the relation is applicable. For pure air, C, = 0.24. The ratio h,/kv is plotted in Figure 2 as a function of gas velocity over the entire experimental range. T h e variation in the ratio, thus represented, is slight. With fluidized particles present, however, the ratio varies considerably and is greater than 5.0 in some instances. I t is apparent that the mechanism of heat transfer is not analogous to that for mass transfer in fluidized beds. Also, Equation 5 does not apply for systems with fluidized particles. The values of heat and mass transfer coefficients are plotted as a function of reduced gas velocity in Figure 3.
It is of interest to determine the effect, if any, of the moving particles on the gas film mass transfer. T o compare coefficients in systems before and after the addition of particles. it is essential that the comparison be made at identical average gas velocities so that changes are not caused merely by a change in velocity. Therefore, the fluidized bed coefficient, k,, is compared with ku’, defined as the coefficient before fluidized particles are added but a t the same average gas velocity, G,, as is present in the fluidized bed. The coefficient ku’ may be determined from Equation 5, which represents the ”no particle” case for this experimental work using G, in the Reynolds number. In each case k , is greater than k,‘, The factor of improvement, kv/kv’, varies little in all systems studied, the highest value being about 2. Representative values are shown for each of the systems in Table 11. The heat transferred to the interface may be considered as
4
0 23 022
I20
130
I40
150
160
180
I70
190
200
G or GI
Figure 2.
Ratio h./ky vs. gas velocity
210
220
-
(hf/h,)
(8)
In the experiments with no fluidized particles present it was previously shown that the ratio h,/ku has little variation with change in gas velocity past the surface (see Figure 2). This is in accord with the heat and mass transfer analogy for the air-water system. For systems containing fluidized particles the ratio of hf/k, is assumed to vary similarly. since it represents the ratio of coefficients for the gas phase where the analogy continues to exist. In fact, this ratio should be the same as h,/ky in the “no particle” case evaluated at the same average gas velocity. Hence, hrniay be calculated from: h,
X A-ALUNDUM B 8-ALUNDUM
(7)
Neglecting radiation from the fluidized system surrounding the sphere, a reasonable assumption considering the temperatures of the experiments, h c becomes equal to h,. By combining Equations 3, 6, and 7, the fraction of the total heat transport which is attributed to particle transport may be represented as: 4P/Y = 1
020 0
2
(6)
YI = hf(t, - d m
0 2 7 c
2
+ Yr
where yp is the heat transferred via particle transport and q f is the heat transferred via the continuous gas phase. In terms of its coefficient
V.L.2
xz
= YP
(h,’,’k,’)k,
=
(9)
where h,’/kl‘ is obtained from Figure 2, using the average gas velocity in the fluidized bed, G,, for the gas velocity. In-
0 COPPER
A GLASS
I .o
c
X A-ALUNDUM 8 8-ALUNDUM
0 COPPER A GLASS
I-
5u -
IO
iuL .= 540W “
sS30-
q
.> 2- IO v)
---e
/A&--&
&* :Ezo-
A 4x
A
0’71 0.6
I
I
I
I
I
I
Table I.
D p f X 703,
Fluidized Particles
In. ...
None
2.3 2.3
Copper powder A!lundum (sharp)
5.8 5.8 3.5 4.5
A
13 Glass spheres
Representative Experimental Data
Lb. G’ Hr.-Sq. Ft.
h,,
G/GW
145.6 163.2 70.0 145.6
3.18 6.60
92.6 145.6 92.5 72.3 124.7
2.27 3.57 5.78 3.61 6.23
...
Lb. ku’ Hr.-Sq. Ft. H I . -OF.-Sq. Ft. Mole Fraction 3.12 12.3 3.79 15.6 34.0 21.4 34.0 26.4
B.t.u.
3.48 2.99 2.63 4.22 5.40
21.9 24.5 23.7 23.9 18.6
76.0 73.3 62.4 100.9 100.5
Relative Effect of Particles on Film (Representative Values) Lb. Lb. B.t.u./Hr.-Sq. Ft.-’F. Hr.-Sq. Ft. Mol. Fract. Ge’ Hr.-Sq. Ft. h, hc h/ kU k, ’ 131.7 34.0 3.25 5.29 21.4 13.1 172.2 42.8 3.62 5.76 23.0 14.5
hclku 0.253 0.244 1.59 1.29
Table II. Flutdtred Pmttcles
Copper Alundum A ..
13
Void Fraction,
0.532 0.632 0 784
n 706 0 722 0 751
Glass
0.570 0.618
t
159 . O 182 9 12s 0 144 6 126.9 150.0
73.3 73 3 62 4 57 9 100.9 81.1
3.51
6.15 6 11 5 90 5 30 5.92 4.51
3 71
3 22 3 37 3.22 3.43
terpolation between the discrete experimental values of gas velocity is necessary in using Figure 2, but an exact value of velocity is not necessary because very little change occurs in the ratio hc’/kv’. Using Equation 9 to compute h l and the experimental value of h,. the ratio q p / q may now be calculated from Equation 8. Figure 4 is a plot of this ratio us. reduced mass velocity of the gas. This indicates that 80 to 95% of heat transfer, neglecting radiation, is by the particle transport mechanism ; the actual percentage appears to depend on particle properties. Assuming that Equation 9 is correct, i t is apparent that the factor of improvement of heat transfer in the gas film, h1,’hc’, is exactly the same as the improvement factors for mass transfer, ky,’ky’, listed in Table 11. Also included in Table I1 is the per cent of the total heat transfer caused by the film disturbance ( h l - h,’)/h, X 1000/0 for these systems. These values are less than 8y0in all systems tested. The heat transfer coefficient is ‘dependent upon the kind of fluidized particles used, whereas mass transfer coefficients seem to have little dependence of this type in the range studied. If heat )transfer by particle transport is accepted as the dominant mechanism, it is understandable that a particle property such as spec:ific heat and a geometry factor such as particle diameter might be of considerable influence. In a number of articles ( 7 7 , 78, 200-2.3) it was concluded that h, increases with increasing density and specific heat of the solid particles. T h e exact relationship between h, and the solid properties varied among the different authors. T h e probable cause of this variation was the different conditions of gas flow rate and solid materials investigated. Likewise, an explicit depency of h , on particle diameter, valid for all conditions, could not be found because of the differences in experimental range and the effect of particle diameter on bed porosity. In the work of Sarkits, ‘Traber. and Mukhlenov (73> 75, 7 6 ) ) a correlation of experimental data is divided into two regions of f l o i v ithe laminar flow regime and the turbulent flow regime). T h e direct dependency of h, on solids density and
24.7 24 5 23 7 27 0 23.9 18.1
14.1 14.9 13 0 13 5 13.0 13.8
1.6 1.6
6.0 5.0
1.8 1.6 1.8 2.0 1.8 1.3
3.6 3.3 4.3 5.8 2.7 1.3
specific heat becomes weaker as the flow becomes more turbulent. Nevertheless, h, increases with increasing values of these properties in both regions. The particle diameter effect differs for the two regions, however. For laminar flow, h, varies inversely with particle diameter, and for turbulent flow, it has direct variation. Also, higher coefficients, h,, resulted for smooth particles than for coarse particles. A more detailed description of the conditions necessary for laminar and turbulent flow is given by Sarkits, Traber, and Mukhlenov (76). In the present investigation, the smooth glass spheres of highest specific heat gave the highest values of h, and the sharper copper powder of lowest specific heat, the lowest h, values. Two sizes of Alundum particles were used and gave little apparent variation in h,. T h e values of h, vary with the solid properties in a manner consistent with the previous articles cited. The depth of suspension of the sphere may be another variable of importance. For the region of gas velocities and particle properties studied, the predominant mechanism of heat transfer to a surface in a fluidized bed is that of particle transport. The other mechanism, additional disturbance of the gas film, improved heat and mass transfer, but the heat transferred in this manner is only a small portion of the total. Nomenclature
CYl
D, DPJ Do G G, h,
= heat capacity of gas, B.t.u./lb.-” F. = diameter of sphere, ft. = diameter of fluidized particles, in. =
gas diffusivity, sq. ft./hr.
= superficial gas velocity, lb./hr.-sq. ft. = average gas velocity based on void area of bed:
lb. ’hr.-sq. ft. radiation heat transfer coefficient, B.t.u./hr.sq. f t . - O F. = total heat transfer coefficient, B.t.u.,/hr.-sq. ft.=
O
F. VOL. 3
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1964
97
- h , = experimental heat transfer coefficient of mechanisms other than radiation. B.t.u. ’hr,sq. f t . - O F. = heat transfer coefficient for film convection in presence of fluidized particles, B.t.u./hr.sa. ft.-’ F. = heat transfer coefficient for film convection in absence of fluidized particles, evaluated a t G, of fluidized bed, B.t.u./hr.-sq. ft.-O F. = mass transfer coefficient, 1b.-moles/hr.-sq. ft.atm. = experimental mass transfer coefficient, kuPaMu= lb./hr.-sq. ft. = mass transfer coefficient in absence of fluidized particles, evaluated from Equation 5 a t G, of fluidized bed, Ib./hr.-sq. ft. = molecular weight of air, lb./lb.-mole = h,Dp/o = k,D,/pD, = av. partial pressure of air, atm. = saturation partial pressure of water vapor, vapor pressure corresponding to t,, atm. = partial pressure of water vapor in the air, atm. = logarithmic mean partial pressure difference, atm. = ht
hc h!
= Cpp,’cy = rate of heat transfer a t interface, by particle
transport, via gas film, B. t.u.:’hr.-sq. ft. GD,/p, Reynolds No. based on superficial gas mass velocity = dpDr = bulk gas temperature, temperature a t surface of sph;ere, O F. = loearithmic mean temuerature difference. O F ” = mass transfer rate, 1b.-moles,’hr.-sq. ft. =
GREEK cy
= gas thermal conductivity, B.t.u./hr.-ft.-”
E
P
bed void fraction, dimensionless = gas viscosity, lb./hr.-ft. = gas density, Ib./cu. ft.
x
=
(1) Botterill, J. S. M., Brit. Chem. En!. 8, 21 (1963). (2) Chilton, T. H., Colburn, A. P., Ind. Eng. Chem. 26, 1183 (1934). (3) DO”, CV. M., Jakob, M., Chem. Eng. Progr. 47, 637 (1951). (4) Emst, R., Chem.-Ingr.-Tech. 31, 166 (1959). (5) Froessling, N., Geriunds Beitr. Geophyr. 52, 170 (1938). (6) General Electric Co., “Dew Point Recorder Pamphlet,” GEI-40444A. (7) Griffith, R. M . , Chem. Eng. Sci. 12, 198 (1960). (8) Leva, M., General Discussion of Heat Transfer, London, SeDtrmber 1951. . .~ (9) Leva, M., Grummer, M., Ind. Eng. Chem. 40, 415 (1948). (10) Leva, M., Ll’eintraub, M., Grummer, .M,, Chern. Eng. Ptogr. 4 5 , 563 (1949). i l l ) Micklev. H. S..Fairbanks. D. F.. i4.I.Ch.E. J . 1. 374 1195.5). (12) Mickley; H. S., Fairbanks, D. F., Hawthorn, k.D.: Chem Ene. P?OPY. .Cvmb. S c r . 32. 51 11961\. (13) uMukhenov, I. P.,- Traber, D. G., Sarkits, V. S.,Bondarchuck, T. P., Zh. Priklud. Khim.32, No. 6, 1291 (1959). (14) Ranz, W.E., Marshall, LV. R., Jr., Chem. Eng. Progr. 4 8 , 141, 173 (1952). (15) Sarkits; V. B., Traber, D. G., Mukhlenov, I. P., Zh. Ptiklad. Khim. 32, No. 10, 2218 (1959). (16) Z6id.,33, N o . 10, 2197, 2200 (1960). (17) Thodos, G., Northwestern University, Evanston, Ill., personal communication. (18) Van Heerden. C., Nobel, A. P. P., Van Krevelen, D. LV., Chem. Ene. Sci. 1. N o . 2. 51 11951). (19) Van keerdeh, C., ‘hobel, A: P. P., Van Krevelen, D. LV., Ind. Eng. Chem. 4 5 , 1237 (1953). (20) Vreedenberg, H. A , , Chem. Eng. Sci.11, 274 (1960). (21) Vreedenberg, H. A,, J. .4fipl. Chem. 2, Suppl. Issue No. 1. S26 11952). (22) Cqen, C.-Y.,Leva, Max, A.I.Ch.E. J . 2, 482 (1956). (23) Ll’endFr, L., Cooper, G. T., Ibid.,4 , 15 (1958). (24) b’icke, E., Fettins, F., Chem.-In,nr.-Tech. 26, 301 (1954). (25) bVicke, E., Hedden, K.: Ibid.,2 4 , 82 (1952). (26) Zcnz, F. A . , Othmer, D. F., “Fluidization and Fluid Particle Systems,” Reinhold, New York, 1960. ~~
~
2
’
-
\ - -
~
-
/
F.
=
iL
literature Cited
B.t.u. latent heat of vaporization of water, _ _ lb.-mole
RECEIVED for review July 25, 1963 ACCEPTED November 22, 1963 Lliork performed under the auspices of the I!. S. Atomic Energy Commisqion at the Argonne National Labordtorv, Argonnc, Ill.
CONCENTRATION AND MASS FLOW DISTRIBUTIONS IN A GAS-SOLID SUSPENSION S . L . S O O , G . J . T R E Z E K , R . C . D I M I C K , A N D G. F . H O H N S T R E I T E R University of Illinois, Crbana, Ill.
Distributions of concentration, mass flow, and velocity of solid particles were studied with a fiber-optic probe and an electrostatic probe. Concepts concerning these distributions and electrostatic charges on solid particles were furthered and substantiated. The relation between electrostatic charge on solid particles and diffusivity of solid particles, and the difference between static loading and mass flow ratio of phases were proved.
and correlation of momentum, heat, and mass transfer in a gas-solid suspension call for a knowledge of the concentration distribution of solid particles and the velocities of the phases. Earlier studies are applicable to given concentration distributions ( 7 7 . 79) or assume constant concentration in analysis (22) and data correlation from overall average concentration (3, 27). Measurements were made by impact counter system with the assumption of similar REDICTION
Present address, Lockheed Research Laboratory, Palo Alto, Calif. 98
I&EC
FUNDAMENTALS
velocity of phases ( 7 8 ) ; the differences between velocity of phases and between mass flow and concentration distribution of particles were later recognized and presented (73). These, together with studies on dense suspensions (15), measurement by point study probe ( 2 3 ) , and measurement by capacitance (24), show that more definitive measurements need to be made. Results of earlier studies (73, 78) are further generalized in the study of boundary layer theory of gas-solid suspensions ( 7 6 ) . Methods of measurement of concentration of the particulate phase in a suspension consist of electric measurement as
