H e a t Transfer Coefficients in
AGITATED VESSELS E. I. DU PONT DE NEMOURS & COMPANY, INC., WILMINGTON, DEL.
%
7
A n extension of the general method for correlating forcedconvection heat transfer data i s proposed for the case of a coil and the inside surface of a vessel w i t h the fluid agitated by a flat paddle. The method of correlation for conduits and for plane surfaces proposed by Colburn ( 2 ) and later modified by Sieder and Tate (9) has been found applicable to agitated vessels. The correlation i s found suitable for the turbulent region of agitation, u p to the point two oils, where gas i s drawn into the liquid. Four liquids-water, and glycerol-were used, and the temperature difference across the the heat transFer surface was varied over a w i d e range. The correlations obtained approximate the data of several investigators for agitated systems considerably different from those used in this study.
VER-ALL heat transfer coefficients in agitated vessels have been reported for a particular arrangement of vessel, agitator. and coil or jacket. Pierce and Terry (7) and Rhodes (8) have reported over-all coefficients for special tank and coil arrangements with liquids agitated by a flat paddle and by a draft tube with a propeller agitator, respectively. King and Howard (6) reported high film heat transfer coefficients (5000-6000) when heating water and sugar solutions with a fine wire and using a cylinder for an agitator. More recently Hixson and Baum (6) reported film heat transfer coefficients for melting solids in liquids of the same material. Gordon (4) determined film heat transfer coefficients for the inside metal surface of a tank when heating batches of water and oil. None of the above workers, however, attempted to present a general correlation which could be used to predict heat transfer coefficients for vessels stirred by the common, flat, paddle agitator. An experimental program was undertaken here in which a 1-foot diameter steel vessel was used to determine the effect of the physical properties of the liquid and the speed of the agitator upon the film heat transfer coefficient for both a coil and the inside surface of a vessel. Tests were made by heating and cooling water, glycerol, and oils under steadystate and batch conditions. From the results it was possible to obtain a general correlation involving the usual dimensionless ratios employed for presenting heat transfer data for forced convection inside tubes.
0-
jacket could be cooled with water or heated by steam at pressure* up to 100 pounds per square inch gage. Inside the vessel a coil of llrinch 0.d. copper tubing wound 7.7 turns on 0.8-foot meani diameter could be readily installed. This coil had an over-all height of 5.75 inches and an outside area of 2.42 square feet The lower edge of the coil was held on the same level as the lower edge of the straight side of the vessel. A flat paddle, 0.6 foot long and 0.1 foot wide, of No. 14 gage metal was used for agitrttion. The lower edge of the paddle and the coil were spaced ab the same level, at the top of the curved portion of the dished bottom. Agitation speeds from 50 to 1000 r.p.m. were available with the drive provided. Eight thermocouples were placed as shown in Fi ure 1. Three were used to measure the surface temperature of &e coil (0, 10, and 9), one read the surface temperature of the jacket (7 or 8) and four read the temperature of the fluid ( 5 , 4, 3, and 2). The readings used in the temperature difference values were the arithmetic mean of those obtained for each group, Thermocouples in the steel vessel were placed in a l/srinch hole, drilled approximately 1/4 inch deep, parallel to the surface of the vessel where the dished head protruded inside the side walls of the vessel
EQUIPMENT
A standard arrangement of equipment (Figure 1) was used in all tests. A jacketed, 1-foot diameter, steel dish-bottomed vessel was made up of 12-and 14inch, Schedule 40 steel pipe. The
Figure 1.
510
Semiworks Equipment
lune, 1944
511
The thermocouples placed in the llrinch copper tubing in the top, center, and bottom turns were embedded in a '/rpinch groove under solder. The leads were wrapped around the pipe in a shdlow groove. Thermometers were used to read the temperature of the cooling water to and from the equipment, and the temperature of the steam and condensate. The thermometers and thermocouples were calibrated against one another in water et room temperature and a t 60" C. After the thermocouples
Figure 9.
-
0.61 E
3
0.151
Z
were calibrated, each of the junctions was lightly touched by a heated soldering iron. An immediate response by the potentiometer indicated that the thermocou le junction was a t the deeired point and not too deeply embedled in the metal, and that a secondary junction was not registerin during the calibration. Cooling-water flow rates to the ja&et or coil were measured b collecting the water in a pail for periods of 1 or 2 minutes. 7% ensure dry steam, the steam flow was split before the reducin valve. Approximately 50 pounds per hour of steam W M ble2 down through a tee and carried condensate with it. The steam wed in the tests assed up through the tee and was relatively when it reac%ed the reducing valve. After the reducing v ve, the steam pressure and temperature were measured The steam temperature was controlled to give 3' or 4' C. superb a t after the reducin valve by adjusting the bleed valve athead of the reducing vafve. The steam condensate was weighed m a springless indicating scale graduated to 0.01 pound. A constant flow of excess steam was maintGned through the jacket by passing the condensate from the equipment through a variableorifice steam trap and allowing excess steam to pass off into the
1.
Physical Properties of Liquids
a,P.c.u./(hr.)(aq.ft.)(' C./ft.) 200 c. 1000 c. Y. lbJ(hr.1 (ft.) 200 c. 60' C. 1000 c. P , Ib./ou. ft. 200 c. 1000 c. e. P.c.u./(lb.)(' C . ) 200 c. 1000 c.
PHYSICAL PROPERTIES OF LIQUIDS
The physical properties of the liquids used are given in Table I. Density and viscosity, except for water, were determined in
Effect of Agitator Speed on Heat Transfer Coefficients L
Table
air. This practice helped to carry out air which might have been in the steam. The loss of condensate by flashing was considered negligible.
Water
92% Glycerol
L-M
A-12
0.346 0.415
0.17 0.175
0.076 0.065
0.078 0.075
2.42 1.14 0.64
740 21 76
270 39 12
3300 350 68
62.2 59.6
77.1 74.0
67.4 64.0
66.7 52.3
1.00 1.02
0.60 0.70
0.435 0.505
0.46 0.615
0 1 1
Oil
-
0.831 W = 0.1, D
-
1
the laboratory with a pycnometer and Saybolt viscometer, respectively. The thermal conductivity and specific heat of the oils were obtained from correlations given by Cragoe (3). The thermal conductivity of water and the specific heat of water and glycerol were obtained from Perry's Chemical Engineers' Handbook. The thermal conductivity of glycerol was obtained from data given by Bates (1). PROCEDURE
Initial tests were made under steady-state conditions; i.e., liquid in the vessel was heated by steam in the jacket while being cooled by water flowing in the coil. A blank heat loss value was obtained by measuring the heat required t o keep the jacket hot witE no liquid in the vessel. This heat loss, measured for the various steam pressures used, was subtracted from the heat quantity measured from the steam condensate. The amount of heat transferred was also obtained from the temperature rise and quantity of cooling water used: these values generally checked with each other within 5'%. When the amount of condensate collected per unit time had become constant, readings were taken of the liquid temperatures, metal surface temperatures, steam pressure, steam Condensate, cooling water temperatures, agitator speed, and height of liquid on the vessel wall. Heat transfer coefficients, both over-all and liquid-side surface film, were calculated for the coil and jacket. From the over-all coefficients i t was also possible to calculate the surface film coefficients as a check. Because of the general agreement between the surface film coefficients as obtained from the measured surface temperature and
512
Vole 36, No. 6
INDUSTRIAL AND ENGINEERING CHEMISTRY
Figure 3. Correlation of Jacket Date for a $-Foot Dish Bottomed Vessel and a Number 1 Coil, WhereL =0.6, = 0.1,5 = 0.1 5, and = 0.83
w
z
A.
Nusselt v5. Reynolds
B. (Revno _ N u r s eId%E)v I , Nusselt
6. (Prancltl) __-213 D,
srow.
Prendtl. vs. Reynolds.
Nusselt ________ (Reynolds)*/3
(Prandtl)'/j
P W
"" -;
those calculated from the over-all coefficients, the dirt-film coefficients are believed to h a w been negligible. Tests made Iyith water in the vessel over a period of 1.5 gears showed little change in the surface film 'coefficient*. provided the metal surfaces were reasonably clean but not poli,4~cd The steel equipment n-as initially given a n inhibited acid treatment on bot,h sides of the metal to remove, mill scale. After pack. shutdown of more than a n-n-eclr, both the inside of the coil and the steam side of t'hc jacket were given an acid treatment to remove rust and algae. The water used in the vessel dlwing tejts contained 20 p.p.m. of sodiulr. dichromate to prevent corrosion STEADY-STATE CONDlTlONS
Steady-stat>e tests were first made with water in the vesscl, heating by means of steam in the jacket, and cooling with water in the coil. The speed of the agitator w2s varied from 50 to 200 r.p.m. The results of these test? are given in Table 11, runs 1 t o 19. Tests were also made with 92% glycerol (runs 20 to 25)i light medium lubricating oil, L-M (runs 26 to 31), and a head, transfer oil, A-12 (runs 32 to 39). I n tests made with water, agitator speeds above 200 r.p.m. sucked air into the water. These results at high agitator speeds, (Figure 2, left-hand graph) did not, fall in line with those obtained with unaerated liquids. For evaluation of heat transfer coefficients, the agitator speeds were kept in the range between 75 r.p.m. and the speed that, aerated the liquid. At agitator speeds less than 75 r.p.m., pasticularly with a low-temperature difference between the wall and liquid, the temperature of the liquid was not uniform. The temperature of the liquids in the vessels, when measured at the points indicated in Figure I,
June, 1944
513
- II.
Table (Z
Liquid Water
Run No. 1 2 3 4 5 6 7 8 9 10 11
Glycerol
L-M oil
A-12 oil
Water
L-M oil
A-12 oil
4
12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
Speed, R.P.M. 50 75 75a 75" 100 100" 125 125a 1255 135 140 140n 180 199 200 200a 200a
2000 2000 75 75 125 125 300 300 75 75 125 125 300 300 75 75 100 125 128 200 300 300 125 300 75 125 175 225 300 125 175 225 300
Temperature, t!
to
63.0 62.0 65.1 64.7 62.0 65.8 65.0 65.2 64.0 63.0 61.0 64.5 04.2 61.0 61.5 01.5 64.8 64.0 67.4 65.5 91.7 65.5 92.5 66.4 92.0 66.9 117.3 67.6 116.4 70.3 116.6 63.1 107.6 64.1 108.7 65.9 66.1 66.2 111.0 99.9 100.7 83.5 83.0 83.0 83.0 82.5 85.6 85.8 86.3 85.8
31.0 35.0 42.3 51.9 37.0 47.0 52.7 49.7 52.4 41.0 39.0 54.4 53.8 42.5 44.0 43.0 52.1 49.0 52.0 18.3 23.7 20.5 27.5 26.3 36.7 14.4 19.7 16.9 23.5 19.3 30.9 11.7 15.7 23.7 16.5 12.0 25.2 14.8 22.7 102.6 96.8 102.4 102.2 102.2 97.4 91.5 100.4 100.2 99.6 95.4
-
Results of Steady-State Tests
0.83; L
0.6:
W
0.1; B
h
C. ti 96.0 92.0 90.2 90.9 88.0 89.7 87.6 88.0 87.8 84.5 84.0 86.0 86.2 80.0 80.5 80.0 85.8 84.5 85.4 98.6 131.6 96.5 130.0 93.0 123.2 100.4 153.8 98.8 154.2 97.6 147.4 101.2 156.5 103.6 156.8 100.5 103.0 99.7 153.2 81.4
...
34.2 36.8 40.5 42.6 44.5 28.8 31.8 33.2 35.4
hc
386 580 508 570 710 605 765 763 86 1 757 870 927 1177 1155 1160 1170 1030 1280 1060 68.1 83.2 113.0 108.0 171 224 30.2 43.7 41.5 68.5 73.5 103 20.1 27.0 30.8 40.4 26.0 37.0 37.5 61.4 560 2660 70.7 101.0 131.0 163.0 189.0 69.3 86.2 100.5 115.5
hi 288 422 408 400 558 515 592 617 592 720 600 641 781 781 746 840 752 848 642 69.5 99.6 103.0 136.5 174 280 34.2 77.5 47.9 121.7 92.5 174 19.3 35.7 24.0 55.5 28.1 32.0 39.5 84.8 5500 5850 23.1 29.7 53.0 59 7 71 0 15.3 20.6 23.0 32.0
-
s
k 1014 1520 1323 1485 1865 1580 1990 1988 2250 1988 2290 2420 3070 3040 3050 3080 2680 3340 2750 390 476 646 618 978 1280 428 643 585 1050 1050 1517 272 365 416 546 352 500 507 830 1350 6410 982 1403 1820 2265 2630 950 1180 1380 1582
0.12)
g
j
hjD, k 755 1,110 1,063 1,100 1.466 1,342 1,544 1,608 1,548 1,890 1,580 1,676 2,040 2,060 1,965 2,210 1,960 2,220 1,660 397 569 688 780 993 1,600 482 1,140 675 1,790 1,322 , 2,560 261 483 326 750 380 433 534 1,148 13,280 14,100 321 412 737 829 987 21.0 28.2 31.5 43.8
(y)"
(z)
k
l/a
768 1,143 1,016 1,100 1,405 1,225 1,480 1,510 1,660 1,490 1,700 1,780 2,260 2,220 2 220 2'260 1:990 2,480 2.060 102.7 135.0 160 167 220 309 113 276 149 412 275 566 29.6 98.0 47.2 148.0 45.8 58.8 64.5 223.0 11,500 12,050 204 293 380 481 574 '94.3 120 123 144
14
hiDj(),O',. k
(T) '18
501 730 730 713 981 936 1070 1130 1065 1290 1062 1160 1410 1380 1320 1480 1340 1530 1160 60.3 .89.0 85.1 124.6 148 256 72.6 262 101.3 406 211 586 15.4 56.7 21.6 90.5 26.5 30.1 37.5 145.5 1218-' 5950 92.8 118.0 205.0 227.0 266.0 33.3 44.4 42.8 58.3
L"Np P
60,500 89 000 94'200 93:300 119,000 129,300 157,000 159,000 154,000 163,500 164,000 174 000 222:ooo 232,000 236,000 236,000 249 000 247:OOO 258,000 2 170 3:020 3,400 5,180 3,800 12,140 3,040 10,150 5,030 16,700 13,500 40,000 286 1,620 408 2,810 560 890 1,330 7,300 251,000 602,000 4,760 7,920 11,100 14,300 19,040 1,225 1730 1:975 2.590
I
Duplicate tests,
varied from point to point in specific runs by as much as the following: water, 62-65' C.; 92% glycerol, 65-66' C.; L-M oil, 66.5-67" C.; A-12 oil, 65-68.5' C. I n runs a t higher agitator speeds the variation was less. The heat flow was then reversed (i.e,, steam was used in the coil and water in jacket), and data were obtained with the same agitator on water, L-M oil, and A-12 oil. The results are given in Table 11,runs 40 to 50. The results of these fifty runs were used to obtain a correlation involving the physical properties of the fluids and the dimensions of the equipment with the heat transfer coefficients for the jacket (Figures 3 and 4). A similar correlation was made for the coil; the final correlation for the coil is also given in Figure 4. CHECK WITH BATCH TESTS
The batch tests were made t o see what the coefficients would be without the coils in place, in order to represent the case where heat of reaction or sensible heat is removed or supplied through a jacket. The results of the batch tests are given in Table I11 (runs 51 through 82) and are plotted in Figure 5. Water and A-12 oil were heated or cooled in the same agitator and coil used in the steady-state tests. For the batch tests it was difficult t o obtain consistent results because of the rapid change of temperature of liquids in the vessel. For water this rate was 12' t o 14" C. per minute a t the end
of the test period, when the steam or water flow rates had become sufficiently steady to measure. Further, a considerable time lag existed in the heat quantities obtained from the cooling water or the steam, so that it was impossible t o check the data. All results given are based on the temperature rise or fall of the liquid as a measure of the quantity of heat transferred. I n the batch heating tests, difficulty was encountered in keeping the steam pressure constant. The results in Figure 5 were not so consistent as for the steady-state tests. An air-actuated steam valve was installed which maintained a constant pressure in the steam jacket. Three tests were made a t different agitator speeds (runs 80 to 82) which gave good agreement with the steady-state tests. Apparently, reproducible results can be obtained with batchwise heating if the steam pressure can be controlled accurately through sufficiently large reducing valves. To confirm the correlation, data were obtained from largescale equipment. Two pieces of plant equipment five times the dimensions of the test equipment were available. The results (runs 83 to 85) are also shown in Figure 5. The result for the coil is in good agreement; however, as in the small-scale batch tests, the results obtained for the jacket were only fair. For the tests with the jacket it was difficult to keep the steam pressure constant because of the large volume in the jacket. The results from all the batch tests indicate that the coil does not influence the magnitude of the heat transfer coefficient obtained for the jacket, within the range of conditions tested.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
514
Vol. 36, No. 6
3 000 2 000
I000
80 0 600 400
30 0
20 0 6 00
80 60 40
30
20
IO
Figure 4.
Final Correlation for Coil and Jacket Heat Transfer Coefficients
DISCUSSION
Initial tests with water under steady-state conditions indicated that there is some variation in the liquid temperature when agitated at nominal speeds, Le., from 75 r.p.m. to the highest speed possible without sucking air into the liquid. While time might have been taken to explore the temperatures of the liquid to obtain a n average temperature in each test, it was felt that temperatures taken a t fixed points (locations generally used in large equipment) would be sufficient. The steady-state test data were used as the basis for correlation because this method was fairly reproducible and the physical properties of the liquid were kept constant. With a particular liquid the temperature was practically constant for all agitator speeds used. The results in Table 11, which were made at 200 r.p.m. with water, show variations as much as 17.5% from the average. The tests with water are the only ones in whirh the results from duplicate tests are given, because they showed the greatest variation. This was expected because “dirt film coefficients” would affect the highest coefficients most; further, the cooling water and condensing steam coefficients in the coil and jacket were the same order of magnitude as coefficients expected for the outside of the coil and the inside surface of the vessel,
Figure 2 shows how the heat transfer coefficients change witb agitator speeds when heating or cooling liquids. I n general the coefficients increase in value for agitator speeds up to 300 r.p.m., ‘ and the coil and jacket heat transfer coefficients are of the same order of magnitude. The tests with high-pressure steani shoa that, under certain conditions resulting from high temperature difference and surface temperatures above the boiling point, the coefficients obtained are better than can be secured by agita. tion with a flat paddle. I n the tests with SO-pound per square inch steam in the jacket, steam bubbles formed which circub t e d the water down the inside of the coil. The correlation of heat transfer coefficients in this paper does not include the tests where a gas was entrained in the liquid, as would be the case at high agitator speeds or with the temperature of the surface above the normal boiling point. A plot of the Reynolds dimensionless group for agitation, L2Np/r, against the Nusselt dimensionless group, hD& dernonstrates the influence that both agitator speed and liquid temperature have on the surface heat transfer coefficient. These results are shown in Figure 3A for runs 1 to 39 and 42 to 50; the lines have a slope of 2/a. All the factors but N in these di. mensionless groups were held practically constant for each of the groups of data shown. The data for A-12 oil also show the effect
June, 1944
51%
Table 111. Run No. 51 62 63 64 66 66 67 68 69 60 61
69 63 64 66 66 67 68 69 70 71 72 7 .1 .74 76
Liquid Paddle Dimensions, De th Ft. Speed, 2.h. L W B R.P.M. 0.83
0.60 0.10 0.15
0.83
0.60 0.10 0.15
0.83
0.60 0.10 0.16
0.83
0.60 0.10 0.16
0.83
0.60 0.10 0.15
Eii
79 80 81 82
1.0
0.60 0.10 0.17
125 125 200 300 350 125 125 125 200 300 350 100 100 100 275 276 100 100 100 276 275 100 1 no
448 448 131 125 200
Coil No. 1
Np. .l in place
0011
1
Np. 1 in plaoe None
None
.... .... ....
Temperature,
Results of Batch Teats O
C.
h
hi Small-Scale EauiDment. A-12 Oil 46.j 86.0 103.2 * 22.9 45.0 16.8 86.2 101.3 31.6 79.2 91.8 144.0 76.7 93.1 40.8 56.6 ... 21 11.9 30.0 101 61.0 *.. 28.6 102.4 74.2 16.3 44.0 18.3 12.0 18.2 46.1 16.8 19 38.7 .., 11
tc
ho
tj
- -
.. ... ... ... ...
... ... ... ... ...
... ... ... ...
... ... ... ... ...
Small-Scale Equipment, Water 27.6 16.0 602 39.0 20.9 626 944 21.0 13.5 1350 29.0 24.1 21.0 17.6 900 104 321 83.5 585 73.0 123 121 424 60.0 103 1100 89.6 116.5 764 75 564 130.9 516 21.3 391 111.2 115.6 764 1370 128.3 96.1 675 840 22.6 990 82.1 621.5 . 86.9 652.0 80.3 . . . 775.0 79.6 Plant Equipment, Water 76.0 140 1190
83 4.16 3.00 0.50 0.75 70 84 85O 136:s a m-Phenylene diamine was the liquid used in run 85.
... ... ...
... ... ... ... ...
... ...
... ... ... ... ... ... .*. ...
... ... ...
... ... .. .. .. ...
... ...
... ... ...
:::
... ... ... ... ...
... ... ... ... ...
...
is6
that temperature and temperature difference have on the surface heat transfer coefficients. T o obtain the relation of coefficients to physical properties of the fluids, a graph was made of the Nusselt group divided by the Reynolds group to the */s power plotted against the Prandtl group, cp/k. Figure 3B indicates that, although there appears to be a rough variation with (cp/k)'la, some additional factor must be allowed for. The greatest discrepancy seems to be between the data for heating and for cooling. To bring these into agreement a graph (Figure 30) was made of the Nusselt group divided by the Prandtl group to the I/* power and the Reynolds group to the power, plotted against the viscosity ratio, pe/p, of the liquid a t the temperature of the wall and of the main body of the liquid. This plot indicates that a slope of -0.14, as found by Sieder and Tate (9) for flow inside pipes, is a fair value for the data obtained in this work. The data for both heating and cooling the different liquids seem to correlate fairly well when plotted as shown in Figure 4 and are represented by the line:
The equation obtained for the coil by a similar treatment of the data is:
Figure 5 shows the agreement of these equations with the results obtained for the batch tests. The results with and without
... ...
...
...
175
a
k 627 323 433 1970 559
... ... ... ... ...
hjDi k
..* ... ...
,..
163:6 400 392 223 164 230
1440 1240 3050 3060 2620
... ... ... ... ...
... ... .. ... ... *
... ... ... ...
... ... .. , ...
... ..... . 15.100
.. ..
803 1494 935 2710 1950 1420 1382 1017 1950 3500 1710 2260 2580 1572 1705 2015
... ...
8310
P
59.7 24.2 44.2 178.5 48.8
.... .. ... ... ... ..
1
988 922 1486 2180 1400
... ... ... ... ... ... ...
... ,.. ... ... ... ...
... ... I . .
10,170
.. .. ..
... ... ... ... i5:7 19.6 31.4 16.2 12.6 14.6
.... .. ... ...
... 606 1022 700 2130 1357 1020 998 930 1357 2370 1240 1590 1780 1170 1165 1457
...
3490 1560
1,183 200 2.030 2,280 2,485 361 270 786 306 508 418 65,000 %0,800 67,100 184,000 157,000 163 300 141:OOO 116,000 475,000 396,000 158,700 104,500 127,000 396,000 392,000 402,000 446,000 666,000 193,300 155,000 282,000 3,150,000 2,370,000 120,300
the coil in place are equally in agreement. As a further check the points obtained on the large-scale equipment are shown; the agreement is as good as that obtained with the small-batch tests. In both of these correlations the diameter of the jacket and the length of the paddle were chosen as length dimensions. Other factors could have been chosen, such as liquid depth, width of paddle, diameter of coil, or diameter of pipe in coil, and the same typical cprrelation obtained. It remains to be seen how each of these factors may change the correlation. It is not unlikely that ratios of some of -them can be used for correlating data, as done in regard to power required for agitation. The correlations proposed apply to the vessel and agitator arrangements geometrically similar to those used in these tests. Further work would be required to determine the effect of changing these ratios. COMPARISON WITH OTHER DATA
It is interesting to compare the results obtained for this one agitator arrangement with those reported several years ago by Hixson and Baum (6). These tests on the rate of fusion of solids in their own melts were with four-bladed, 45" pitched agitators, in vessels covering a sixfold range of sizes. The length of the four-bladed agitator was only one third the diameter of the vessel. Further, the heat transfer surfaces were not fixed a t a definite location, but were moving with the liquid. With assumptions as to the average position and size of the suspended solids, similar to those made by Hixson and Baum, the coefficients calculated from their results were found to be in reasonable agreement with the correlation for coil coefficients of Figure 4 and Equation 2. The extensive unpublished data of Gordon (4) are more nearly comparable with those of the present investigation, since he measured jacket coefficients in a 2-foot diameter vessel. After adjustment of his values for different agitator dimensions (by methods not reported here), his data on water and two oils were
INDUSTRIAL AND ENGINEERING CHEMISTRY
516
0 0
-
0 0
0
0
0
0
0
0
0
0
0
N
t
loooo.
-
9 r.!
0
0 0
q
Figure 5.
0 0 0 0 0 0 0
0
0
-
i d 6
0 0 0-
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0
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N
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Vol. 36, No. 6
0 0
0
9 0
?
0
82 8
0
0
a o
-
0
r\l
0 0 0 0
v a
0 0
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0
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$ o 9
-
0 0
9
0 0
9
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N
2)
Batch Test Checks of Flat Paddle Correlation
found to be in good agreement with the correlation of jacket coefficients of Figure 4 and Equation 1. The data of Rhodes (8) are not easily comparable, since his agitator consisted of a propeller and draft tube arrangement. Those of Pierce and Terry (7) were obtained on the cooling of water by a lead coil lying against the yall of a 200-gallon tank. I17ith a reasonable assumption as t o the dimensions of their paddle agitator and adjustment for them, t h r roil coefficients reported are about 65y0of those predicted by Equation 2, in line with the fact that not all of the coil surface was freely exposed to the watel-. The data of King and Howard (6),obtained with a fine wire in a 1000-cc. beaker, require severe adjustment for variation in dimensions from those employed in this study, but could nevertheless be brought into close agreement. As mentioned above, more work will have to be done to determine the exact effect of changing each of the possible dimensions of agitator and vessel, and the type of agitator employed. ACKNOWLEDGMENT
The authors wish to thank W. H. McAdams for advice and assistance. NOMENCLATURE
B = clearance of paddle from center to bottom of vessel, ft. c = specific heat, P.c.u./(lb.)(" C.)
D, Di = inside diameter of vessel, ft. h,, hj = film coefficient of heat transfer for coil and jacket, respectively, P.c.u./(hr.)(sq. ft.)(" C.) k = thermal conductivity, P.c.u./(hr.)(sq. ft.)(' C./ft.) L = length of paddle, ft. m = slope of lines in figures N = shaft speed, revolytions/hr. t1 = av. liquid temp., C. tc = temp. of surface of coil, ' C. t, = temp. of surface of jacket, C. W = width of paddle, ft. 2 = liquid depth, ft. /J. = viscosity at av. temp., lb./(hr.)(ft.) po pi = viscosity at surface temp. of coil and jacket respectively, lb./(hr.)(ft.) pW = viscosity at surface temp., lb./(hr.)(ft.) p = density at av. temp., Ib./cu. ft. LITERATURE CITED (1) B a t e s , 0 . K.,
IND. E N G . C H E X . , 28, 494-8 (1936). ( 2 ) Colburn, A. P., Trans. Am. Inst. Chem. Engrs., 29, 174-211 (1933).
(3) Cragoe, C . S., N a t l . Bur. S t a n d a r d s , M i s e . P u b . 97 (1929). (4) Gordon, Moses, Univ. of Minn., Ph.D. thesis, J u n e , 1941. (5) Hixson, A. W., a n d Baum, S. J., IND.ENG.CHEM., 33, 1433-9 (1941). (6) K,ing, C. V., and Howard, P. L., Ibid.,29, 75-8 (1937). (7) Pierce, D. E., a n d T e r r y , P. B., Chem. & M e t . Eng., 30, 872-3 (1924). (8) Rhodes, F. H., IND.E N G . CHEM.,26, 944-6 (1934). (9) Sieder, E. N., a n d T a t e , G. E., Ibid.,28, 1429-35 (1936).
