ENGINEERING, DESIGN, AND EQUIPMENT about a maximum in separation at about 1-inch plate spacing in t h e present column (Figure 4).
-0
I 2 HORIZONTAL PLATES PER INCH
Figure
4.
Separation as function of plate spacing
24-hour separation with horizontal barriers
appreciable separations. Considering not only separation but also the number of batch runs that could be made, columns with compound barriers are 70 time8 more effective than columns with no barriers. The enhanced separation rates allow flow operation to be used. The cclumn without barriers gave only one indication of separation, and that indication was hardly beyond t h e limit of experimental precision. With barriers, appreciable flows could be accomodated, and separations greater than those from batch operations were attained. It is difficult even to conceive of long columns with close clearances acting BS other than fluid flow devices under flow operation. With further work t o evaluate the effect of diverse barrier parameters, thermal diffusion utilizing “waste” heat may yet become a more common industrial operation. Summary
Systems of barriers introduced between hot and cold surfaces of a Clusius-Dickel column have been found to b e effective in
The data taken under flow conditions substantiate the fcregoing hypothesis. T h e 10-fold ratio of outer to inner annulus area for flow of gas necessitates a flow of gas across the column in a horizontal direction if the pressure drop is to be constant. T h e addition of feed gas at the outer wall augments the downflowing outer stream and reduces cross-plate flow to a pcint where the turbulence involved in introducing the stream counterbalances t h e reduction in cross-plate flow. Thus, flow separations increase and are almost double those that can be achieved under static conditions at 30 cr. per minute and then fall off rapidly to zero. No doubt annulus areas are important parameters t,hat determine the shape and position of curves, as shown in Figure 2. The-e parameters are a t present being investigated. Even more striking than improvement in separation efficiency is the increase in rate of separation. Only after 0.5 hour did the open rolumn shorn any separation a t all, whereas after only 4 to 5 minutes (the minimum that could be used to feed column, take samples, etc. ), columns with barriers had already produced very
increasing efficiency of batch separation, rate of separation, and separation under flow conditions. Barrier systems enable columns with wide spacing between hot and cold surfaces to be used, with attendant reduction in power requirements and construction cost. Compound hcrizontal-vertical barriers were most effective, increasing separation Pfficiency sixfold over open column separation and increasing separation rate tenfold. Only metal barriers were found to be effective. literature cited (1)
Brewer, A. K., and Bramley, A , U. S. Patent 2,258,594 (Oct. 14, 1942).
(2) Chapman, S., and Cowling, T. G., “Mathematical Theory of
Nonuniform Gases,” pp. 223, 254, Cambridge Univ. Press, Cambridge, Eng., 1939. (3) Donaldson, J., and Watson, W. W.,Phys. Rev., 82, 909-13 (1951).
(4) Drickamer, H. G., O’Brien, V. J., Breese, J. C . , and Ockert, C. E., J . Chem. Phvs., 16, 122 (1948). RECEIVED for review March 3, 1964.
ACCEPTED March 1 1 , 1955.
Natural Convection to Cold Cylinders ROBERT LEMLICH
AND
CHARLES SHARN’
Department o f Chemical Engineering, University o f Cincinnati, Cincinnati 2 I , Ohio
N
URIEROUS studies involving heat transfer by natural convection from a single long hot horizontal cylinder to a large
expanse of surrounding fluid have been made. The results of most of these investigations have been successfully correlated in dimensionless form b y McAdams ( 2 ) . However, a search of the literature revealed no information for natural convection occurring in the reverse direction-that is, from a large expanse of ssrrounding fluid to a colder cylinder. Accordingly, the purpose of this investigation was t o examine the effect of such an “inverse” temperature and velocity profile on the coefficient of natural convective heat transfer. Four cold cylinders, each of a different diameter, were subjected to unsteady-state natural convection with room air. Control runs for warm cylinders were also conducted. The results for the two opposite directions of heat transfer were compared with each other and with the correlation of McAdams. 1
Present address, 1735 North 26th St., East St. Louis, Ill.
August 1955
Expressions for heat transfer are presented
The rate of heat transfer by convection from a warm body to cooler air is given by
where Q is the heat transferred from the body, 7 is the time, h is the coefficient of heat transfer, A is the surface area, and At is the absolute value of the temperature difference driving force between the surface and the bulk fluid. Previous investigation ( 3 ) has shown that, for a warm cylinder of moderately large diameter in natural convection to room air under a moderate At, h = K(At)1’4
(2)
where K is a constant for the particular system. For a cylinder
INDUSTRIAL AND ENGINEERING CHEMISTRY
1547
ENGINEERING, DESIGN, AND EQUIPMENT 0.65
t
Simple experimental unsteady-state technique i s utilized to determine heat transfer to or from cylinders
.
COLD CYLINDER-
0 60
4 '5 0 . 5 5 p
z
0.50
Y
0.45 0 40
_p' 0
CWARM CYLINDER
I
I
20
40
I 60
I
80
I 100
with
l-inch-
T I M E , MINUTES Figure 1 .
Natural convection in air diameter cylinder
of smaller diameter, Equation 2 may be generalized somewhat to the form (3 1
h = K(At)n
where the value of n depends on the diameter, The temperature change of the body is related to the heat transferred by the expression
dQ = -mcdt
(4)
where m is the mass of the cylinder, t its temperature, and c its heat capacity ( a t constant pressure). Furthermore, for a constant room temperature, dt = d ( A t )
(5)
Four smooth shiny solid copper cylinders, 1, l / ~ I/&, , and l/* inch in diameter, were subjected in turn t o natural convection with room air. The particular cylinder to be used a t any time was either first heated in a trough of stirred hot distilled water or cooled in a trough of stirred cold water, depending on whether a cooling run or a heating run was to be conducted. (Distilled water was used when the cylinder was heated to eliminate surface staining.) The cylinder was then thoroughly dried and suspended horizontally near the center of a small closed unventilated interior room. The temperature of each cylinder was sensed with a calibrated 30-gage copper-constantan thermocouple. For each of the three larger cylinders a hole slightly larger than the thermocouple junction was drilled along a radius to a depth of half a radius. The junction was then inserted and the rest of the hole was filled with solder. Each thermocouple lead was diagonally spiraled once around the cylinder to take advantage of the isothermal zone available, and then connected to a potentiometer with a precision of better than 10.1' F. The cold junction was thus a t room temperature, so that the potentiometer reading gave At directly. For the cylinder of smallest diameter a modification was required. The hot junction was made by separately wrapping each thermocouple lead around the cylinder so as t o give a split junction with a separation of about I inch. It has been shown ( I ) that for natural convection between air and a metallic surface the error inherent in measuring surface temperature in this manner is small. After the cylinder was suspended, time was allowed for extraneous air currents t o die down. Potentiometer readings were recorded a t various time intervals. For the cold cylinders, the magnitude of At was limited by the necessity for avoiding the condensation of dew on the surface. For warm cylinders, At was limited by possible darkening of the smooth shiny surface due t o corrosion. In addition, it was deemed advisable not to all0~7At for any control run to exceed greatly At for the corre-
Combining Equations 1, 3, 3, and 5, d~( A t ) -_ " = -n_K A dr mc
For moderate changes in temperature the quanKA . tity, -, is also constant. Therefore, by integratme ing Equation 6 without limits,
(7)
0.8
0.6
1 1
Thus, with the proper value of n , plotting ( A t ) - n against T as the cylinder cools yields a straight line Measurement of this slope permits mc determination of K , from which h can then be computed for various values of At by Equation 3 . This derivation, of course, assumes a negligible temperature gradient within the body. This assumption is well justified for the case a t handthat of a solid copper cylinder of moderate or small diameter in natural convection with air. With due regard for sign, and by assuming that Equation 3 applies, a similar derivation can be employed to show that Equation 7 also applies t o the inverse situation where heat is transferred by natural convection from warm air to a cooler cylinder. That Equation 3 does, in fact, apply to this case is demonstrated by the experimental results presented in this article.
1
I
CYLINDER 0 I
INCHWARM INCHCOLD 1/2 INCH WARM 112 INCH COLD 1/4 INCH WARM 1/4 INCH COLD 1/8 INCH WARM 1/8 INCH COLD I
A A
V
v
of slope n K A
I
AMS
-a
1548
I
I
Figure 2.
I
Dimensionless correlation of heat transfer investigation
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 8
ENGINEERING. DESIGN, AND EQUIPMENT Agreement between the results for both types of runs and the correlation of McAdams (9)is K , B.t.u./(Hr.)(Sq. also evident; the average deCylinder Ft.)(O F.l+n) Difference C,old in K , Diain., Nusselt Grashof Hot viation is about f 5 % . For n Number Number cylinder Inch cylinder % further comparison, the Mc1 0.25 4.2-6.4 7100-34000 0.507 0.513 f1.2 Adams representation of two ‘/2 0.20 2.4-3.8 380-3200 0.732 0,735 +0.4 0.16 1 6-2.3 29-320 1.059 1.073 +1.3 1/4 other correlations is also shown. 1/8 0.14 1.3-1.8 3 4-30 1.805 1.727 -4.4 The slight difference relative - 0 . 4 (av.) to the McAdams curve between the results for the smallest cylinder and those for the other cylinders is probably due to the difference in type of thermocouple sponding run with a cold cylinder in order to secure as valid a junction. For each of the three larger cylinders the solder around comparison as possible between the two sets of results. For all the junction as well as the junction itself possess a lower thermal runs taken as a group, At ranged from 1.5’ to 32.5’ F., a 21-fold conductivity than the copper and, therefore, a lower diff usivity. variation. Among the dimensionless groups, the Grashof numThus the changing junction temperature tends to lag behind her, Gr, varied from 3.4 to 34,000 and the Nusselt number, Nu, the changing cylinder temperature, but only slightly, since the varied from 1.3 to 6.4. The Prandtl number, Pr, was, of course, mass of the junction with its solder is small. Thus the resulting virtually constant. For each rod the ratio of length to diameter was 60, which repnegative error in h is very slight. On the other hand, the split resents a sufficiently close approximation to an infinitely long thermocouple junction for the smallest cylinder is a t the surface of the cylinder and so acts as a very small extended surface or cylinder. The relative unimportance of end effects was further checked by comparing the results for the 1-inch-diameter cylfin. This, in turn, tends t o cool the surface at the junction a trifle and so may induce a slight positive error in h. inder (for which this ratio was 60) with results for another l-inchdiameter cylinder for which the ratio was 30. The decrease The unsteady-state analysis presented in this discussion for in length induced no appreciable change in K and, therefore, none the determination of convective h can readily be modified for a case where a plot of ( A t ) - . versus 7 is not straight. Such a situin h. ation might arise, for example, where the fluid under consideration suffers a marked change in fluid properties over the range of Change in direction of heat flow does not temperatures involved, thus precluding any choice of a constant appreciably affect rate of heat transfer n. Nevertheless, Equation 6 still applies since it can be derived just as well with a variable n. Only the integrated form, EquaPlots of ( A t ) - I J 4versus 7 for both a cooling run and a heating tion 7 , requires n to be constant for a particular diameter. Thus run are shown in Figure 1 for the 1-inch-diameter cylinder. all that is required is the drawing of the appropriate curve fitting Both curves of Figure 1 are straight, in agreement with Equation the points, measurement of its slope and calculation of K a t 3 and 7 (and for this diameter with Equation 2 as well). Furtherrepresentative values of At by means of Equation 6, determination more, they are nearly parallel. By utilizing the appropriate exof h by Equation 3, and then application of any radiation correcponent, n (in place of I/d), similar results were obtained from tion that might be necessary. The gentle curvature, as compared analogous plots for the three cylinders of smaller diameter. It to a direct plot of At against 7, would facilitate accurate detercan be readily demonstrated that n is very nearly the slope of the mination of slope. The inherent experimental simplicity in the correlation of McAdams. However, a t least for the present work, meth’od also permits its adaptation to bodies of other geometrical the choice of n is not critical in preparing plots of ( A t ) - ” versus 7 . configuration. Curves that were nearly straight and parallel were even obtainable (4)using a value of n = ‘/4 for the smaller diameters. Furthermore, values of Nusselt number based on an n of ’/* for all Conclusions diameters were not greatly different from those shown in the diWithin the limits of the dimensionless groups and experimental mensionless plot presented in Figure 2. precision of this investigation, and providing At is not too large, A summary is presented in Table I of the range of dimensionless the results for natural convection to cold horizontal cylinders groups (with fluid properties evaluated at the arithmetic mean agree with those for natural convection from warm horizontal film temperatures). Corresponding values of n and K are also cylinders. The inversion in temperature and velocity profiles shown. Differences between the two K values for each cylinder is without effect, and the same generalized correlation, such as are small, and the average difference is insignificant. that of McAdams, applies to either. For a given small At and a given diameter, the small radiation correction applied to the copper surfaces is virtually the same for cooling or heating. Thus, near agreement between correAcknowledgment sponding values of K implies near agreement between the coeffiThe authors wish to express their appreciation to William Licht cients of natural convective heat transfer for a given A t . I n and LeRoy A. Bromley for reviewing the manuscript and to other words, the results indicate that over the range of dimenthe McGraw-Hill Book Co. for permission t o include the repsionless groups considered, and within the precision of the exresentation shown in Figure 2. perimental work, inversion in the temperature and velocity profiles is without effect on the rate of heat transfer. This conclusion, however, may not apply where a very large At exists Nomenclature which, in turn, might produce large changes in fluid properties. A = surface area, sq. f t . Such is frequently the case with liquids, and additional work is c = heat capacity, B.t.u./(lb.)( F.) planned in order to investigate this aspect of the problem. Gr = Grashof number, dimensionless This agreement between the results for natural convection h = coefficient of heat transfer, B.t.u./(hr.)(sq. ft.)(’ F.) K = constant, B.t.u./(hr.)(sq. ft.)( ’ F.lf”) from a warm cylinder and natural convection to a cold cylinder m = mass, lb. is further illustrated in Figure 2. Log Nu, calculated from K n = exponent in Equation 3, dimensionless a t four representative values of At for each diameter and corrected Nu = Nusselt number, dimensionless for radiation, is plotted in the usual way against log (Gr X Pr). P r = Prandtl number, dimensionless Table I.
-
Summary of Experimental Results
O
August 1955
INDUSTRIAL AND ENGINEERING CHEMISTRY
1549
ENGINEERING, DESIGN, AND EQUIPMENT
Q
=
t At
=
7
= =
heat, B.t.u. temperature, F. absolute value of temperature difference driving force, F. time, hr. (or min.)
(3) Ibid., p. 177. (4) Sharn, C. F.,
O
M.S.thesis, University of Cincinnati, August 1954.
O
RECEIVEDfor review November 22, 1954. ACCEPTED March 4, 1955Material supplementary to this article has been deposited a s Document N o . 4506 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D. C. A copy m a y be secured b y citing the document number a n d b y remitting $1.25 for photoprints o r $1.25 for 35-mm. miciofilm. Advance payment is required. M a k e checks or money orders payable to Chief, Photoduplication Service, Library of Congress.
literature cited (1) Lemlich, R., Ph.D. dissertation, University of Cincinnati, June 1954. (2) McAdams, W.H., “Heat Transmission,” 3rd ed., p. 176,LIcGrawHill, New York, 1954.
Process Design Data..
..
Rate of Mass Transfer from Gas Stream to
Porous Solid in Fluidized Beds C. T. HSU’
AND
M. C. MOLSTAD
University of Pennsylvania, Philadelphia, Pa.
F
adsorbs about 0.46 gram of carbon tetrachloride when the partial LUIDIZED solids, which offer a large surface area for the pressure of carbon tetrachloride is only 0.2 mm. of mercury transfer of mass and heat and assume within the mass a a t room temperature), the adsorbate content of charcoal may uniform distribution of temperature and composition by rapid be accurately determined by weighing. Moreover, because of mixing, have been successfully used since 1943 by the petroleum the low partial pressure of carbon tetrachloride which could be industry in the catalytic cracking of hydrocarbons (8, 26, 26). used, the heat of adsorption would have little effect on the temThis technique is expected to be useful for many other chemical perature of the bed in the course of adsorption. These two and physical processes involving the transfer of mass or heat, or properties of the carbon tetrachloridecharcoal system not only both (6, 9, 23, 28, 29, 52). simplify the apparatus and the analytical procedure to be used, Fluidized solids have been extensively studied in the past but also make the calculation simple and reliable because of the decade. The published results may be classified into three main essentially isothermal condition the bed assumes during adsorpcategories-mechanics of fluidization of solid particles by a liquid tion. It was expected that the results obtained might serve or a gas (4, 10, 18, 22, SI); heat and mass transfer across the as a bridge linking the external transfer process and the more fluid film around the solid particles in fluidized beds (5, 7 , 11, 16, complicated heterogeneous catalytic reactions. IS, 81, 24, 27); and heterogeneous chemical reactions involving a fluid and a eolid carried out in fluidized beds (16, 19, 20). isothermal adsorption of carbon tetrachloride The mass transfer coefficients reported were all controlled by on fluidized activated charcoal i s studied the fluid film around the solid, and a general correlation was Materials. The solid adsorbent used was gas-purification possible when the physical properties of the system and the turgrade activated charcoal (Columbia AC) supplied by Cnion bulent condition of the fluid were properly taken into consideraCarbide and Carbon Corp. It was ground in a laboratory ball tion. Empirical relations between the mass transfer factor, mill from the original granules of 6 to 14 mesh and the size cuts j , , and the modified Reynolds number, involving the fractional of 20 to 28, 28 to 35, 35 to 48, and 48 to 65 mesh were collected void of the fluidized beds, have been suggested. Heterogeneous and used in the present work. Before they were used, the chemical reactions in fluidized beds involve both heat and mass screened cuts were fluidized with silica-gel-dried air a t highest transfer in addition to the chemical change, so no single general possible rates t o remove the fines. I n Table I are summarized correlation is to be expected in view of the specific nature of the the physical characteristics of the charcoal particles (13, 14). individual chemical reactions. The expansion of fluidized beds of charcoal particles a t different The investigation described in this article was undertaken to air rates, plotted as fractional void versus superficial air velocity, study mam transfer in the adsorption of a vapor adsorbate by a is shown in Figure 1 and will be used in the correlation of the solid adsorbent in fluidized beds and to determine the relative mass transfer results. magnitude of comDonent mass transfer coefficients in the course of adsorption under different operating conditions. The solid adsorbent was activated charTable 1. Physical Characteristics of Activated Charcoal coal and the vapor adsorbate was carbon tetrachloride, carAv. Bulk Particle Fractional Fractional External Surface Particle Density, Density, Internal Void External Void Area (a) ried by nitrogen. As activated Mesh Diam. ( D p ) , PB, (PP), (e;), Co./Cc. ( e ) , Cc./Cc. Sq. Ft./Cu.’Ft. Bulk Vol. Size Ft. G./Cc. G./Cc. Solid Bulk Vol. charcoal can adsorb a large amount of carbon tetrachloride 1454 0.612 0.954 0.461 0.368 20-28 0.00232 2110 0.463 0.612 0,950 0.00160 0.367 28-35 (for instance, 1 gramof charcoal 2940 0.465 0.618 0.946 0.00113 0,362 35-48 1 Present address, Department of Chemical Engineering, Alabama Polytechnic Institute, Auburn, Ala.
1550
48-65
AV.
0.00082
0.358
0.950
0.463
0.620
...
0.364
0.950
0.463
0.615
4030
~~
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 8
