234
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Vol. 20, No. 3
Heat Transfer for Oils and Water in Pipes’ F. H. Morris and Walter G. Whitman STANDARD OIL COMPANY (INDIANA), W H I T I N G , I N D .
Film coefficients of heat transfer have been determined for three petroleum qils and for water flowing through the tube of a horizontal double-pipe heat exchanger. The experiments cover both heating with steam and cooling with water under similar conditions. The flow was in the turbulent or semiturbulent regimes. Linear velocity varied from 1 to 20 feet per second, viscosity ran from 0.5 to 55 centipoises, and the heattransfer coefficients on oil covered a range from 10 to 700 B. t. u. per hour per square foot per degree Fahrenheit. The data for oils and water can be correlated on the basis of Nusselt’s theoretical equation, which states that 9he heat-transfer coefficient is a function of the velocity,
viscosity, density, thermal conductivity, specific heat, and pipe diameter, arranged in dimensionless groups. The quantitative conclusions are expressed graphically, since no simple equation has been found which will apply over the whole experimental range. Physical properties of the liquid are taken at the temperature of the main body of the liquid rather than at the customary film temperature. On this basis the cooling coefficients fall about 25 per cent lower than those for heating. The results from heating water with steam agree reasonably with those published by other investigators. Data on coefficients for heating and cooling oil are not available for comparison.
* . . . . . ...... LTHOUGH the heating and cooling of liquids in pipes are fundamental to many industrial operations, scarcely any investigations of the heat-transfer rates have been published which consider liquids other than water. Most of the data on the heating of water have been correlated by McAdams and Frost*in the form of an equation which adequately handles this important case. The chemical engineer, however, deals with many other liquids and is interested in cooling as well as heating them. I n the petroleum industry, especially, the rational design of equipment such as pipe stills, heat exchangers, and coolers demands a reliable method for predicting heat-transfer coefficients for oil flowing in pipes. The work described in this paper was undertaken to supply a basis for a general determination of such coefficients. I n order to make sure that the experimental method and apparatus gave results in accord with those of others, a few runs were made heating water, but the greater part of the work was with petroleum products having a wide range of viscosities and in half of the experiments the oils were cooled.
A
Theoretical Considerations
The modern treatment of heat flow through a series of resistances by evaluating each resistance independently of the others is now so generally accepted that its discussion here appears unnecessary. Following this principle, the problem of heat transfer with liquids in pipes devolves into a study of the coefficient between the liquid and the pipe itself, disregarding the particular heating or cooling phenomena which occur on the other side of the pipe. Coefficients of this sort are often designated as “film coefficients,” a term derived from the convenient concept of fluid films at the boundaries of a fluid. The variables which might be expected to govern the film coefficient for liquids flowing in turbulent motion in pipes are the diameter of the pipe, the density, specific heat, viscosity, and thermal conductivity of the liquid, and the velocity of flow. In a given piece of experimental apparatus the first is fixed. Furthermore, the four physical properties of the fluid are not mutually independent but are determined by the nature of the particular liquid and by its temperature. 1 Presented before the Division of Petroleum Chemistry a t the 74th Meeting of the American Chemical Society, Detroit, Mich., September 6 to 10, 1927. 1 Ref&woling Eng., 10, 323 (1924).
The problem of so generalizing data taken on one heat exchanger and with a limited number of liquids that they can be used to predict coefficients for wholly different conditions is best handled with the aid of dimensional analysis. By this principle, which has been applied to the closely related problem of fluid friction with notable success, the independent and dependent variables assumed to be important to the problem are gathered into dimensionless groups. The analysis shows that a particular variable affects the others only as it affects the group or groups in which it occurs. Dimensional analysis has two limitations. It throws no light on the validity of the assumptions as to which variables are important to the problem. Furthermore, it gives no hint of the functional relationship between the various dimensionless groups. Its great power lies in the inferences it allows regarding the effect of variables which are constant in a given set of experiments. I n this particular case the diameter of the pipe, for instance, is the same throughout and the density of the liquids is so nearly constant that no independent determination of its effect is possible, yet if the analysis is properly made the effect of both can be predicted from an experimental determination of the group functions. Another advantage of the analysis is that the problem is simplified to a determination of a functional relationship between three variables instead of seven. The application of the analysis, first made by Nusselt,3 yields the equation
* For the nomenclature
used throughout article see end of paper.
It should again be emphasized that the functions 4 and $ can be determined only by experiment, since the analysis places no limit whatever on their form. Another dimensionless group sometimes introduced into the equation is the ratio of the clear length of the pipe to its diameter. There is no question that excessive turbulence near a sudden contraction in cross section or an elbow, for instance, causes a local increase in coefficient. Hence, a higher value of the average coefficient would be obtained in a short pipe than in a long one. In the experiments here reported only one pipe was used. Since, therefore, no inde8 Mitt. tiber Forschungsarbeiten, Heft 80-96 (1910); 2. Vcr. deut. Ing., 63, 1750, 1808 (1909).
March, 1928
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
235
pendent evaluation of end effects could be made, end effects scraped flush with the outer surface of the tube. Since were avoided as far as possible by extending the pipe twenty they were short-circuited by the lead, they were assumed diameters on either side of the heating surface with un- to give the temperature of the outer surface of the tube. changed cross section-i. e., by introducing two so-called To carry the wires through the wall of the outer jacket "calming" sections. For this reason uniform velocity three l'lz-inch by 3/4-in~h crosses were inserted in the conditions may be expected throughout the portion of the l'lrinch pipe opposite the couples. Each wire passed tube where heat is being transferred and the calculated through an insulated stuffing box screwed into one of the coefficients may be considered as applying to pipes of infinite 3/4-inch branches which lay horizontally. This construction permitted the use of fairly high pressures in the annulength . McAdams and Frost have shown that for water being lar space when desired. The actual box construction is heated the function #(cz/k) can be dropped without great not shown in Figure 1, but the location of the thermocouples . error and 4(Dup/z) can be expressed as constant X ( . D u p / ~ ) ~ . *is~ given. The exchanger was connected up for continuous recycling However, where oils of widely varying viscosity are considered, and particularly when a correlation is attempted of the liquid under investigation. For the heating runs it between the data on oil and on water, it is quite conceivable was pumped from a small tank through a calibrated orifice that neither of these simplifications may be permissible. to the heat exchanger and back to the tank through a waterAn immediate question that arises in the application of cooled coil. I n cooling runs the liquid was heated to the the theoretical equation to experimental data concerns the desired temperature in a gas-fired pipe still before passing selection of the values of the physical properties to be used to the exchanger. The heating or cooling medium flowed in the correlation. Previous experimenters have in general countercurrently through the jacket. No readings were taken until the system had come to taken the properties at the mean film temperature-that is, a t the arithmetic mean between the average temperature of equilibrium as shown by the constancy of the temperature the liquid and that of the inner pipe surface. This selection of the liquid entering the exchanger tube. A run consisted is admittedly arbitrary, however, and the published data of five sets of readings of temperatures and orifice data, are inadequate to support it against numerous other assump- occupying about 5 minutes a set. The time necessary to tions which might be advanced. The theoretical con- reach equilibrium for a new run was from half an hour to siderations involved appear to be too complicated to permit several hours in some cases. The heat flowing through the wall of the tube was calcua rigorous solution of the problem which is also simple enough for engineering use. Hence, a practical approxi- lated from the change in temperature of the central stream, mation based on experimental data is probably the best its quantity, and its specific heat. Errors from radiation compromise. Evidence will be given later to show that and conduction were thereby reduced to the heat passing the use of the properties of the main body of the liquid through the lagged portion of the tube extending beyond affords a better correlation of data for heating and cooling the heating surface, and a few sample calculations showed and gives a method of calculation more easily applied to this to be negligible. The temperature difference through the wall of the tube design problems. Another advantage accrues kom this procedure in that the type of flow, laminar or turbulent, was calculated from the heat flow and dimensions of the probably depends on the properties of the body of the liquid tube, using 35 B. t. u. per hour per square foot per degree and there is therefore less uncertainty in the applicability Fahrenheit per foot for the thermal conductivity of the of the data in and near the critical range. (low-carbon) steel. For oil runs this temperature difference Apparatus and Method
The heat exchanger used for the determination of coefficients is shown diagrammatically in Figure 1. The tube through which the liquid under investigation flowed was a standard '/*-inch steel pipe with internal and external diameters of 0.62 and 0.84 inch. The jacket was of ll/,-inch standard pipe, having an actual inside diameter of 1.61 inches, The tube extended a foot on either side of the heating surface with unchanged cross section. Turbulence chambers, A, were inserted in order to obtain a thorough mixing of the stream leaving the exchanger, so that the temperature read would be a true average for the stream. It was thought that the changes in direction and velocity of the heating or cooling medium leaving the jacket would insure sufficient mixing to accomplish the same purpose for the outside fluid. The exchanger was thoroughly lagged with asbestos pipe-covering extending past all thermocouples. All temperatures were measured with No. 24 gage ironconstantan thermocouples calibrated in place. A Leeds and Korthrup Type K potentiometer was used, giving a least reading of one microvolt which corresponds to about 0.03' F. Seven temperatures were read. In addition to the couples in both streams entering and leaving, three couples were peened into slots in the tube wall with lead
-THLRHPCOUPLL -TURBULENCE CHAMBER
Figure 1-Heat
Exchanger
never exceeded 16 per cent of the difference between the temperature of the inner tube surface and that of the body of the liquid. When, as in most oil runs, the rise or fall in temperature of the central stream was less than 30' F., the average stream temperature was taken as the arithmetic mean of the initial and final readings. When the change was greater the average temperature was obtained by means of a graphical integration assuming the internal film coefficient to vary inversely as the square root of the viscosity. This correction in no case made a change in the calculated coefficient greater than 4 per cent. In the runs where water was heated by steam the temperature of the inner surface of the pipe wzis czlculated as above. The average temperature of the water was obtained by subtracting from the steam temperature the logarithmic mean
INDUSTRIAL A N D EiYGISEERING CHEMISTRY
236
of the temperature differences between water and steam at the entrance and exit of the tube. Knowing the quantity of heat exchanged, the kemperatures of the inner pipe wall and of the body of the stream, the film coefficient could be calculated from the equation
Q/e = hAAt Data
The range of the data is given in Table I. Table I-Range of Data HEATING RUNS High Low Ratio Linear velocity, u 19.5 0.9 22 Viscosity E 55 0.5 110 169 83 Temperaiure of liquid, a F. DV/z 313 5.0 63 310 1 . 2 260 CZ/k hD/k 300 16 4890 h 1560 40 39 Total number of runs 56
COOLING RUNS High Low Ratio 16.9 1.1 15 15.6 0 . 5 31 512 115 365 7 . 6 48 4.2 22 94 110 51 5590 50 700 14 62
Gravities and designations of the oils used in the experiments are shown in Table 11. Table 11-Data
RUNS B1-B13 El-El5 Cl-CZ2 Fl-F4 F10-F26 F5-F9
OA. P. I. 36.8 35.8
OIL
1 }
on 0118
No. 1 gas oil No. 2 gas oil
29.4
0.879
No. 2 straw oil
29.5 22.9
0.879 0.917
Light motor oil
The viscosities of these oils are plotted on Figure 2. 0
0
8
a
6
6
4
A
2
xB
E
>
B :: 5
T E M P E R A T U R E -DEGR(EES
F
Figure 2
Specific heats were taken from the equation of Fortsch and Whitmana4 c =
(t
+ 670) (2.10 - sp
gr)
2030
where c = specific heat t = temperature in a F. sp. gr. = specific gravity of the oil a t 60" F.
k for oils was taken as 0.078 independent of the temperatu3.e. As the data in the literature are meager and contradictory, it was thought best to use a constant value for all cases. That this procedure does not lead to great error is indicated 4
Ind. Eng Chem , 18, 795 (1926).
by the agreement, within the experimental error, of data on the three oils with film temperatures from 80" to 370" F. The values of k for water given by Jakob6 were used in computing the water runs. His equation, converted to English units, is as follows: k = 0.304 (1 4-0.00175 t) where t is the temperature in O F. The data from the runs are shown in Table I11 with important calculated results. These calculations were simplified by the use of plots and, taking into account the accuracy of the data, a precision greater than 3 per cent was not attempted in the calculations. In this table V = up = average mass velocity of the liquid in the tube. tl and tz are the temperatures of the liquid entering and leaving. t, is the external temperature of the tube wall a t the center of the heating section. TI and I", are the temperatures of the heating or cooling medium entering and leaving the exchanger. Q / e is the quantity of heat flowing through the tube wall in B. t. u. per hour. At is the temperature difference between the internal surface of the tube and the average liquid temperature. All temperatures are expressed in degrees Fahrenheit. The meaning of the other symbols is given in the table of nomenclature at the end of the paper. Correlation of Data
60'76g3. 0.841 0.846
No. 1 straw oil
Vol. 20, No. 3
The Nusselt theoretical formulation for analyzing the results having been tentatively accepted, it was first necessary to select the temperature a t which the physical properties of the liquid are to be taken. It has been generally assumed in the past that the heat-transfer coefficient is governed by the properties of the liquid a t the mean film temperature. If this were true an oil flowing through a given pipe a t a given velocity would have the same coefficient whether it were being heated or cooled provided the film temperatures were the same. When the data were calculated using the film properties, it was found that for given values of D V / z and cz/k, the value of hD/k for cooling runs was more than double that for heating. It was seen that the two sets of data would be brought toward each other if the properties were taken at the main stream temperature; hence all runs were recalculated on this basis. This threw the cooling data below the heating, but the divergence was not so great as before. Taking the most viscous oil, for example, interpolation of the data on light motor oil shows that, when DV/z = 25 and c z / k = 100, the cooling coefficient is 270 per cent of the heating if the film properties are used. If, on the other hand, the main stream properties are taken, the cooling coefficient is 61 per cent of the heating. The data were then recalculated, the temperature being taken at a point one-fourth the thickness of the film from the main stream. This gave the best correlation of the data as a whole, but the heating data, which are t h e more reliable, were not so consistent as when the main stream temperature was used. The properties df the main stream were adopted for the correlation here presented for the following reasons: (1) The heating data are most consistent on that basis. (2) While the cooling coefficients average about 25 per cent below the heating, the agreement in each set is satisfactory for engineering practice. (3) The use of main stream properties is much easier for the designer, since either of the other methods necessitates a calculation of the pipe temperature by trial and error. (4) Since the type of flow probably depends on the main stream properties, there is less uncertainty in the application of the data in the critical range.
HEATING Rum-The method of correlating the heating data described below consists essentially of successive 5
Ann
P h y s f k , 63, 537 (1920)
I N D U S T R I A L A V D E.VGI.VEERI,VG CHEMISTRY
March, 1928
237
Table 111-Data and Calculations RUN
V
ti
11
:r
1P
Tz
S E R I E S .I-RUNS
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 All A12
58.6 60.5 84.3 115 118 145 168 171 200 214 216 247
91.6 92.i 102.2 103.1 103.4 105.0 107.2 106.7 108.5 106.3 110.1 107.6
181.5 180.3 175.3 171.3 168.2 165.9 163.3 164.6 160.1 158.9 160.2 158.2
B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13
95.5 117 139 166 197 237 285 339 430 514 605 705 816
77.1 77.9 85.6 89.8 91.6 99.1 102.3 106.5 111.5 113.9 116.8 122.2 124.8
106.9 109.3 117.6 121.9 123.3 129.2 131.7 134.3 137.1 138.2 139.7 142.9 144.1
21(1.9
Q/e
110.6 210.2 210.3 209.9 210.5 210.2 210.4 210.1 210.4 210.1 210.5 210.8
2111 7
210.6 210.4 21(1. 210. I 210.7 210.5 210.8 210.4 211 . o 211.2
2
S E R I E S B--RUNS
!!!
E
E
869 8iO 1050 1370 1290 1520 1670 1870 1910 2180 2000 2570
81.5 83.7 116 155 157 195 220 224 258 272 276 313
1.17 1.18 1.18 1.22 1.24 1.25 1.26 1.25 1.27 1.28 1.29 1.30
53.6 71.4 94.5 120 144 181 223 266 338 403 474 538 615
426 566 751 954 1140 1440 1770 2120 2680 3200 3760 4270 4890
18.4 22.8 29.9 37.2 46.6 57.6 71.3 87.5 115 140 169 206 242
19.5 19.3 17.9 17.1 16.8 15.9 15.6 15.1 14.6 14.5 14.1 13.6 13.5
40.4 39.7 42.5 50.4 38.0 57.3 85.5 132 91.1 163 162 288 304 199 257 389 389 369 353 317 387 434
321 316 338 400 302 455 680 1050 725 1300 1290 2290 2420 1580 2040 3090 3090 2930 2810 2520 3080 3450
6.08 8.00 8.60 10.4 10.2 12.4 18.6 25.90 19.0 3a.8 31.3 82.4 81.9 40.0 51.8 106 101 90.9 80.4 67.9 85.7 102
87 92.5 89 90.5 92.5 92
43.6 55.7 60.1 187 84.0 128 141 83 75.5
347 433 478 1490 667 1020 1120 660 600
5.00 5.85 7.05 34.7 16.2 21.7 25.9 13.4 10.8
66.5 87.8 122 175 252 332 237 309 379 333 534 507 671 663 477
529 698 970 1390 2000 2640 1880 2460 3020 2650 4240 4030 5340 5270 3790
29.6 37.7 50.4 79.7 144 167 107 170 215 160 311 298 350 356 242
11.1 12.0 12.7 11.6 7.5 8.0 12.3 8.25 8.1 12.1 7.7 8.25 8.05 8 1 12.0
15.5 39.4 145 183 206 174 155 38.8 70.4 123 64.6 82.0 103 127 338 147 592 243 169 257 206 704 512 296 443 328
123 313 1150 1450 1640 1380 1230 308 559 978 514 651 819 1010 2680 1170 4710 1930 1340 2040 1640 5590 4070 2360 3520 2590
10.7 16.0 93.0 166 211 160 117 15.5 31.1 73.5 24.5 26.9 31.8 38.2 141 44.1 365 86.4 50.5 90.4 59.6 327 206 97.9 158 102
31.1 30.0 ,25 4.55 4.2 5.3 6.85 40.9 21,X 10.3 "7.7 36.0 35.4 39.4 13.3 40.9 6.35 22.6 38.2 24.6 36.6 8.7 13.9 27.4 19.2 29.1
A1
h
46.4 46.6 44.8 43.8 46.3 45.3 43.8 41.6 42.2 41.2 41.6 37.7
534 53 5 646 84 1 788 927 1020 1140 1160 1320 1210 1560
k
z
k
HEATING WATER WITH STEAM
HEATING GAS OIL WITH STEAM
115.7 112.6 104.0 98.5 96.0 88.5 84.7 80.3 74.2 70.6 66.9 62.3 59.1 S E R I E S C ' R U N S HEATING STRAW OIL WITH STEAM
c1 c2 c3 c4 c5 C6 c7 C8 c9 c10 c11 c12 C13 C14 C16 C16 C17 C18 c19 c20 c21 c22
147 205 210 261 262 316 352 382 385 441 465 491 501 506 622 690 694 696 700 739 885 1030
77.4 77.3 78.8 77.6 79.0 78.1 90.2 100.0 86.7 101.7 100.5 163.0 160.5 109.0 112.0 154.9 150.9 142.3 132.3 118.8 122.2 124.1
93.7 89.1 90.8 89.0 87.8 88.8 102.6 115.4 99.3 117.6 115.7 175.1 173.6 124.4 127.3 167.6 164.3 156.8 148.1 133.1 135.9 137.0
D1 D2 D3 D4 D5 D6 D7 D8 D9
444 519 649 766 768 790 793 80 1 895
86.1 85.7 85.4 139.6 107.7 117.2 124.2 99.2 88.7
91.9 92.0 90.8 148.0 113.5 124.7 131.7 105.1 93.5
El
82.6 115 164 234 253 3 16 334 335 413 492 562 587 672 682 739
150.3 138.7 130.5 141.2 210.0 197.6 132.3 191.1 194.4 132.5 200.2 188.6 190.0 191.8 132.6
125.5 118.7 113.9 124.2 179.8 173.3 119.4 168.4 173.0 122.1 182.4 171.9 175.1 176.4 124.6
85.1 123 141 143 157 160 161 165 165 165 172 252 282 394 431 474 474
149.8 155.8 362.3 477.6 568.1 486.7 413.2 138.9 201.3 317.8 163.7 140.5 142.3 133.0 244.9 130,6 376.1 181.1 134.9 171.9 137.9 310.8 244.1 162.4 196.6 155.4
141.8 142.2 296.3 385.7 454.9 396,6 342.4 130.3 180.1 270,O 148.2 130.1 131.5 124.6 218.7 123.1 330.6 166.5 126.8 159.5 129.6 281.6 222.8 152.0 182.7 146.0
215.9 204.7 204.3 204.4
211 .o 211..7 211.3 211.0 211.6 211.1 211.1 210.2 211.4 210.4 211.2
211.1 211.0 211.1 210.7 211.6 210.8 210.9 210.3 211.8 210.3 211.2
225.3 210.5 210.8
225.8 210.3 210.6
211.0 211.2 211.3
210.8 210.8 211.0
S E R I E S D-RUNS
120.1 119.3 119.8 75.1 111.0 98.1 90.9 118.3 116.5
Ell
E12 E13 E14 E15
66.0 68.0 70.0 79.2 115.4 122.9 82.1 116.3 121.6 89.5 139.4 127.7 140.7 139.5 97.2
51.3 51 . 6 51.4 53.0 68.9 64.9 53.6 64.7 65.3 55.7 69.8 6i.8 69.7 70.1 58, 1
S E R I E S F-RUNS
F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14
F15 F16 F17 F18 F19 F2O F21 F22 F23 F24 F25 F26
485
505 556 572 618 633 679 744 761
36.6 40.5 85.8 104.1 90.4 84.4 79.0 42.7 46.5 66.9 43.2 44,5 45.6 46.3 67.1 46.6 106.9 57.9 47.0 56.7 49.2 95.5 74.5 56.1 63.8 53.8
!?
74 53.5 55 23.9 24.5 47.5 45.5 26.0 27.1 30.0 33.7 41.5 39.5 38.5
HEATING LIGHT MOTOR OIL WITH S T B A Y
S E R I E S E--RUNS
E2 E3 E4 E5 E6 E7 E8 E9 E10
40;600 38,200 43,900 47,900
123.9 126.6 124.2 124.5 126.3 123.8 108.5 95.8 112.7 92.9 94.0 47.9 60.0 85.2 81.0 51.9 54.7 62.0 70.2 73.5 69.2 67.3
310 310 320 84 171 134 114 218 290
COOLING GAS OIL WITH WATER
54.1 54.7 55.3 58.1 78.1 75.9 58.3 73.8 75.6 61.2 82.3 79.3 81.9 82.7 64.8
70.8 59.5 50.8 51.3 75.2 58.2 41.5 59.1 57.1 35.1 46.2 47.1 36.3 38.7 28.3
COOLING STRAW O I L WITH WATER
39.9 42.6 91.0 116.2 107.0 97.5 88.8 43.7 49.5 73.0 46.0 46.0 47.3 48.5 75.5 49.1 125.4 63.2 49.8 61.9 52.2 111.2 84.7 61 .'3 71.1 59.1
99.4 95.8 183.8 228.0 289.8 255.4 213.1 81.5 118.9 172.3 94.4 71.1 68.4 57.5 84.1 53.5 106,9 67.8 53.5 62.3 50.9 68.5 65.6 54.3 55.1 49.4
,
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
238
T a b l e 111-Data
RUN
V
I1
SERIES -RUNS
G1 G2 G3 G4 G5 G6 G7 G8 G9 G10 G11 G12 G13 G14 G15 G16 G17 G18 GI9 G20 G2 1
55.5 95.0 96.1 101 108 111 111 112 112 157 159 222 225 234 322 323 455 485 616 767 so0
242.6 179.5 179.0 176.0 199.4 185.4 185.4 185.5 186.5 196.6 196.6 138.8 195.3 187.4 200.4 150.9 203.5 163,2 197.6 193.1 158.3
210.1 171.2 179.0 167.9 183.9 174.6 175.3 176.4 176.4 182.7 182.6 135.9 182.9 176.1 187.6 145.3 191.5 156.5 186.6 183.4 152.3
Ta
TI
IP
I2
58.5 45.5 46.0 46.5 53.7 48.1 48.4 48.6 49.0 50.8 57.1 43.4 64.0 59.8 75.6 53.9 89.1 67.4 94.8 99.8 77.0
and C a l c u l a t i o n s
45.0
39.5 47.5
39.6 49.8
51.5 43.2 57.0 48.2 58.6 60.8 51.6
55.0 44.0 61.3 50.4 63.1 65.9 55.0
approximations to determine the relationship between the three variables. Starting with a set of runs where one variable is reasonably constant, the function connecting the other two is derived graphically. This tentative relation can then be applied to other data in order to bring out the influence of the first variable. By familiar processes of trial and error a repetition of similar steps leads to successive expressions which are each more accurate and more generally applicable than those preceding. For the sake of brevity, let the modulus hD/k = M , Dup/z or DV/z = N , and cz/k = P. The Nusselt equation then becomes M = W)Ic(P) Since the equation was derived for turbulent flow conditions, only those runs having N greater than 15 were considered in determining the functions. This value is the mean of several given in the literature as the critical. All plotting was done on logarithmic paper on which functions of the typey = mmare straight lines having the slope m. P is made up of physical properties and varies only with the temperature for a given oil. Therefore, runs were selected from each group having about the same temperature (so that P was constant) and M was plotted against N . The average slope of the lines thus found was about 1.02, showing that M is proportional to N1.02. M/N1.02was then plotted against P for all runs, giving a line with a slope about 0.5. This was tentatively assumed to be the relation between M and P, and M/P0.6was plotted against N for all data. It was found that the data, including water runs, lined up fairly well on this basis, but the line was not straight. Several forms of equation were tried on the curve, the most successful having the form
+
(Concluded)
Q/e
COOLING LIGHT MOTOR OIL WITH
43.8
+
+
This equation was rearranged and M / A N 3 BN2 CN D was plotted against P. The process was repeated until it became cyclic-that is, until M / 9 ( N ) plotted against P gave the same function for + ( P ) as had been used for finding q5(N). The final equation was M = (0.000016 Na - 0.017 N* 10.8 N - 53)Po.3' It must be emphasized that this equation is not suggested for general design purposes. It merely lines up this particular set of data for values above N = 15. Below that value and, indeed, above N = 400 the equation gives absurd results. Figure 3 shows a plot of M/(0.000016 N 3 - 0.017 N 2 10.8 N - 53) vs. P, for all runs having N greater than 15. It is seen that there' is little justification for other than a
+
+
Vol. 20, No. 3
7,090 2,920 3,100 3,020 6,300 4,490 4,200 3,820 4,280 8,250 8,400 2,300 10,500 9,900 15,600 6,490 20,800 11,900 25,700 28,100 17,400
AI WATER 166.9 129.5 128.2 125.1 137.1 131.3 131.4 131.9 131.9 131.8 131.4 93.6 123.7 120.7 116.3 93.3 105.6 90.9 93.8 84.7 75.9
h 26.0 13.8 14.7 14.7 28.0 20.9 19.5 17.7 19.8 38.2 39.0 15.0 51.9 50.1 81.8 42.5 120 80 167 202 140
h D
E
206 110 117 117 222 166 155 141 157 304 310 119 412 398 650 338 956 635 1330 1610 1110
9.30 7.65 7.60 7.64 11.2 9.62 9.69 9.85 9.92 15.7 15.9 8.8 22.5 20.7 34.4 16.0 51.3 30.0 64.2 75.5 45.5
k
c6
k' 25.5 49 50 52 39 46 46 45 44.5 40 40 94 40 44.5 37.5 76.5 36 62.6 38.5 40.5 68
straight line. It passes through the point (1,l) and has a slope of 0.37. I n Figure 4 M/P0.37 is plotted against N for all runs. The runs having N less than 15 are included for convenience. There has been published no satisfactory analysis of heat transfer for liquids in laminar flow. It is known, however, that under isothermal conditions the type of flow depends on N , and it may be assumed that when heat is flowing N will be an important, though perhaps not the sole governing factor. An inspection of the plot shows no sharp break in the trend of the data a t the isothermal critical point, indicating that the transfer of heat induces turbulent flow a t velocities considerably below the isothermal critical. About twenty runs were made at very low velocities, but these are not shown on the plot. Below N = 5 the scattering of points is so great as to show conclusively that the Nusselt relation is not valid in this region. At N = 1 there is a tenfold variation in values of M / P 0 . 3 7 . Since no satisfactory correlation of these data has been made, they are omitted from this paper though some weight was given to them in drawing the lower end of the curve shown. It is hoped that a t some future time these data can be amplified and correlated for presentation.
Figure.3
COOLIKGRuNs-Less precision is to be expected in the cooling data than in the heating. The external coefficients for cooling water are smaller, relative to the oil, than the steam coefficients. Therefore, end effects in the external coefficients become more important and though their magnitude at the ends can be estimated from the external pipe temperatures, there is no way of knowing how far the disturbances extend toward the center. It was assumed in the calculations that the disturbances were local and had little effect on the calculated internal coefficients; that is, the pipe temperature a t the center was used as an average pipe temperature. An alternate method of giving the end temperature half the weight of the central was tried on typical runs, but the data showed no greater consistency than when the end temperatures were disregarded. The difference between the coefficients calculated by the two methods seldom exceeded 10 per cent and since the first
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
March, 1928
was thought to give results nearer the truth it was adopted in the computation as recorded. A plot of the cooling data similar to Figure 3 shows considerable scattering of points. A line may be drawn with a slope anywhere from one-third to one-half with about equal precision. For convenient comparison with the heating data, the exponent of cz/k is taken as 0.37 and p
hD/k
i
s
shown plotted against D V / z in Figure 5. I n drawing a line through the data, the shape of the heating curve was retained, since the heating data are the more reliable and it seems logical to expect the same general type
239
It is evident from inspection of these equations that the water data of series A agrees with theirs in expressing the effect of DV/ZJ as practically an 0.8-power function. The comparison of actual coefficients a t equal values of DV/z/ is not so simple, however, owing to the uncertainty introduced by their end correction term. At DV/ZJ = 100 the coefficient h in our data is 442. If the "length" of the tube is taken as the length of the heating surface (as seems indicated by their paper), McAdams and Frost's equation predicts a coefficient of 408 for our tube when DV/z/ = 100. The observed value is only 9 per cent higher, and this should be regarded as an excellent check.
OV I
?
Figure 4
Figure 5
of function for the two cases. This is especially important in the region of low D V / z values where the cooling data considered done indicate a very rapid falling off in coefficient with decreasing DV/z. A few runs a t Lower velocities, while widely scattered, indicate that the sloping of the curve toward the horizontal is justified. The curve as drawn is 25 per cent below the heating line. Hence in design work only one curve i s needed, the calculated h f o r a liquid being cooled having 75 per cent of the value of h for a liquid being heated under the same body conditions.
If, however, our tube is considered to be free from end effects -i. e., of infinite length-owing to its extension well beyond the heated surface, their equation would predict that h = 325. Since experiments on one tube give no light on the subject of end effects and since the tube here used was particularly designed to avoid them as far as possible, it seems preferable to offer the coefficients here obtained as applying to pipes of infinite length. The designer of equipment can then apply such corrections for end effects as he deems advisable.
Comparison with Results of Others
As mentioned before, the short series of runs heating water was made in order to compare the results with those correlated by McAdams and Frost. Since the original data on which their work is based are not a t hand, the comparison cannot be made using the method employed in this paper. This makes it necessary to adopt their method, although it is thought to be less precise than the more general one adaptable to both water and oils. The principal points of divergence between the methods are these: (1) McAdams and Frost neglect any variation in cz/k, since they dealt only with water; (2) they use the properties of the film rather than those of the main stream; (3) they take a constant value of 0.329 for the thermal conductivity of water; and (4) they employ the arithmetic mean temperature difference in calculating h. The water data of series A were recalculated using their method throughout. hD/0.329 was plotted against DVlzj, giving a line with the eauation
(y)o'83 The equation given by McAdams and Frost is + y)),( - hD =
0.329
0.329
=
18.2
13.4 (I
DV
0.80
where T is the ratio of length of pipe to diameter.
Use of Data
For use in design Figure 3 can be considered as a plot of $ ( c z / k ) vs. (cz/k) and Figures 4 and 5 as plots of +(DV/z) vs. ( D B / z ) . The process of estimating h for a given set of conditions will be as follows: Calculate plots.
and k
Then
hD
-
(F) and 9 (7) from the 9 (y) . (F) and h is readily found.
DV -. Read $
cz
=
$
For instance, suppose a crude oil is being heated in a long 3-inch pipe. The oil is a t 150" F., and a t that temperature its density is 50 pounds per cubic foot, its viscosity 1.5 centipoises, and its specific heat 0.51. It is flowing with an average linear velocity of 2 feet per second. Then D V - Diip z
z - = cz
k
3.0; X 2 X *5O 1.3 0.51 X 1.5 = 9,8 0.078
-
From Figure 4,
@
From Figure 3,
(y) =
(F) . , ( 7 ) (2) $
hD k = @ h =
-
205
1600
= 2.3
D J7
$ = 3700 3700 X 0.078 = 91
3.Oi
240
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
It must again be emphasized that this is an instantaneous coefficient. If the oil changes greatly in temperature flowing through a pipe, it is not permissible to take its average temperature and from it calculate an average coefficient. In designing a piece of apparatus in which a liquid changes enough in temperature to have a great effect on its viscosity, it is suggested that the pipe be broken up into sections in which the viscosity does not change more than, say, threefold. An alternate and more precise method would be to integrate graphically an equation obtained from a heat balance on a differential length of pipe. Conclusion
Heat-transfer coefficients for oils and water flowing in turbulent motion in horizontal pipes have been determined. The results are correlated by means of the Kusselt type of equation. hD DV Figure 3 shows #(cz/k) plotted against ( c z l k ) and is to be used for both heating and cooling. Figure 4 shows @ ( D V / z vs. ) (DV/z) for heating runs.
Vol. 20, No. 3
Figure 5 shows @(DV/z) vs. (DV/z) for cooling runs. The line drawn gives values of (b(DV/z),which are 75 per cent of those given by the heating line of Figure 4. All properties of the liquid are to be taken a t the temperature of the main body of the liquid. Nomenclature
D = diameter of pipe in inches = film coefficient of heat transfer in B. t. u. per hour per square foot per degree Fahrenheit k = thermal conductivity in B. t. u. per hour per square foot per degree Fahrenheit per foot of thickness Q/e = total heat transferred in B. t. u. per hour P = density of liquid in pounds per cubic foot u = average velocity in feet per second v = up = mass velocity in pounds per square foot per second z = viscosity in centipoises A = area of internal heat-transfer surface of pipe in square h
feet c At
= =
specific heat difference between temperature of body of liquid and that of internal surface of pipe
M = hDlk N = DUp/z = D V / z
P = czlk 4 and ii. = functions to be determined by experiment
TRADE WASTES AND OXYGEN DEMAND Symposium presented before the Division of Water, Sewage, and Sanitation a t the 74th Meeting of the American Chemical Society, Detroit, hlich., September 5 t o 10, 1927
Chemical Treatment of Trade Waste IV-Wastes from Organic Ester Synthesis Foster D. Snell and Cornelia T. Snell PRATT INSTITUTE, BROOKLYN, X. Y .
The waste to be treated consists of a calcium sulfate sludge produced in the manufacture of organic esters. This sludge is highly contaminated and strongly acid, varying in acidity with time of discharge. Neutralization with lime followed by vacuum filtration offers the best method of treatment. The use of 240 pounds of lime per thousand gallons of effluent is required. The lime is to be fed as a 20 per cent slurry at a rate to correspond to the flow and the variable acidity of the effluent, necessitating a flexible control of the feeding system.
H E plant whose waste problems are under discussion is located in the Passaic Valley in New Jersey and has in the past used the Passaic River as a natural sewer for'its trade waste. This practice is now prohibited by law. A trunk sewer has been constructed into which the plant may deliver all sanitary waste and 10 per cent by volume of its trade waste.' The remaining liquid discharges may go to the river, but only in a purified condition such as not to be injurious to fish and plant life. The part of the plant under discussion is so located as to be unable to take advantage of the 10 per cent trade-waste allotment.
T
Nature of Wastes
Two trade-waste sewers were already in use in this part of the plant, the first concrete and the second an open earthen ditch. At the time of this investigation the former carried a stream of condenser water and the discharge from one set of stills in which organic esters were synthesized. It
led to a large receiving basin which remained from a previous method of treatment that had proved impractical. The earthen drain carried the discharge from a second set of ester stills, that from a drowning tank, and wash water from the nitrating department. It led directly to the river. The sanitary waste was handled by a separate system and does not enter into this problem. The flow of condenser water in the first sewer was fairly constant, about 1.5 cubic feet of practically pure water per minute. The discharge from the stills to this sewer takes place for about 45 minutes during the day, during which a maximum flow of over 11 cubic feet per minute is reached. The stills are then washed with water. The total volume of still discharge and washings was calculated from measurements of flow to be about 4500 gallons per day. While the waste is being drawn off from the stills the sludge is very highly acid with sulfuric and acetic acids, attaining a maximum normality of approximately 2.4. The washings are also acid t o a lesser degree. This waste is highly contaminated, is a dark brown, and carries a large amount of solid calcium sulfate. Tarry discharges from ethyl acetate stills occur about once a day. The sediment fails to settle to under 30 per cent on standing overnight. Total solids determined on the effluent neutralized with lime were found to be as great as 300,000 p. p. m. during the period of still discharge, but a t other times were relatively very low. In the determination of solids the samples were neutralized with measured volumes of approximately 0.8 ?j potassium hydroxide and evaporated to dryness a t 110" C.
