INDUSTRIAL A N D ENGINEERING CHEMISTRY
June, 1931
compared with that of the silicates indicates that these unoxidized sulfides may be responsible for the hard deposits in economisers and preheaters. Because the temperatures here are low compared with those in the boiler the sulfur remains after oxidation as sulfate. A large part of the sulfur in these deposits, therefore, comes from the ash particles, and not from condensation of sulfuric acid vapor in the gases. Only traces of sulfide sulfur in pulverized-fuel ash were found and the deposits in the economizers and preheaters, for the most part, are not adherent as in stoker-fired boilers. This may be attributed to the more complete oxidation of the sulfur in pulverized fuel. Acknowledgments
This investigation was conducted under the supervision D. B*Keyes, head Of the Division Of Industria’ to whom the author expresses his appreciation for many kind Of
62 5
suggestions and criticisms concerning the work. Acknowledgment is also made to L. F. Dobry for assistance in the laboratory work on catalysis. Literature Cited (1) Ardern and Wheeler, Interim Report, Ministry of Transport, London, 1929. ( 2 ) Derl, Chcm.-Zfg.,46,693 (1921). (3) Bodenstein and Pohl, Z.Elcklrochcm., 11, 373 (1905). (4) Fichter and Shaffner, Helo. chim. acta, 3, 869 (1920). (5) Haller, J . SOC.Chem. I n d . , 38, 52 (1919). (6) Holmes, Ramsay, and Elder, IND. ENG.CHEM.,21, 850 (1929). (7) Huttia and Lurman, Z . anaew. Chem., 89, 759 (1926). (8) Johnstone, University of Illinois Eng. Expt. Sta., Circ. 20 (1929). (9) Ries and Clark, IND. ENC. CHBM.,18, 747 (1926). (10) Sherman et al., Bur. Mines, Bull. 834 (1931);M d . En&, 48, 1115, 1389 (1926); see also Barkley, Bur. Mines, Tech. P o p n 486 (1928). (11) Taylor and Johnstone, IND. ENG.CHRM.,Anal. Ed., 1, 197 (1929). (12) Thompson and Tilling, J . SOC. Chem. I n d . , 48, 37 (1924).
Heat Transfer to Liquids in Viscous Flow’ C. G. Kirkbride2and W. L. McCabe DEPARTYEKT O F CHEMICAL ENGINEERING, UNIVERSITY
OF
MICKIGAN, ANN ARBOR,Mxcn.
New data are reported on the transfer of heat into The mechanism of such flow NDER ordinary conliquids flowing at-velocities below the isothermal critiis the same as that of natuditions] when heat is cal velocity. These and other data are correlated by ral convection, and the two t r a n s m i t t e d from a the Nusselt-Grober theory, which expresses the film processes are controlled by solid surface to a non-boiling coefficient in the form: the same variables. Therfluid that is in forced flow, mal t u r b u l e n t flow apparthe v e l o c i t y of the fluid is greater than the correspondently forms a lower limit to where h = point film coefficient, D = tube diameter, t h e v e l o c i t y range correi n g i s o t h e r m a l critical veL = tube length, k = thermal conductivity, Y = mass locity as determined by Reysponding to viscous flow, just velocity, and c = heat capacity. The experimental nolds’ criterion. As a result as viscous flow sets a lower results are compared with the theoretical calculations many able i n v e s t i g a t i o n s v e l o c i t y limit to turbulent of Nusselt and Grober. have c e n t e r e d on this case, flow. AS shown by Colburn but v e r y l i t t l e work h a s and Hougen, it is questionbeen reported on heat transfer in the analogous case able whether or not thermal turbulent flow is of much signifiwhere the fluid moves a t a velocity below the isothermal cance in horizontal flow, where the movement of fluid due to critical velocity. This paper reports new experimental data natural convection is a t right angles to the forced flow. on the latter subject, and correlates these and other existing Nusselt-Grober Theory data with the Nusselt-Grober theory of heat transfer to fluids in viscous flow. Nusselt (9) carried through a theoretical solution of the following problem: Assume a fluid flowing through a horiExperimental and Theoretical Results to Date zontal tube a t a constant mass velocity (below the isothermal critical) and a t a constant entrance temperature. Let the Colburn and Hougen (Z), in a paper on the flow of fluids a t fluid be cooled by maintaining the tube wall a t a constant low velocities, have described the work previous to their temperature. In order that entrance effects may be elimiown covering the problem of this article. I n addition to the nated] assume that the fluid has passed through a “calming references cited by them, it should be noted that some of section” before reaching the cooling surface. the low-velocity data on heat transfer t o oils determined by (1) How will the mean fluid temperature vary along the hlorris and Whitman (8) fall in the range of viscous flow. tube? These data will be mentioned later. How much heat will be transferred through a given length Colburn and Hougen ( 2 ) used a vertical 3-inch tube 7 feet of (2) tube? long. Their experiments were confined to water flowing a t (3) How will the film coefficient vary with the tube length very low velocities. These investigators were studying the and velocity and properties of the fluid? mechanism of heat flow from vertical walls to fluids exhibiting In his attack of the problem Nusselt makes these assumpthe type of flow described by Colburn and Hougen as “thermal tions: turbulent.” Under such conditions the mean velocity of (1) The tube wall is smooth. the fluid is of minor consequence, and the only effective motion (2) The flow is viscous, and the velocity distribution over of the fluid is that set up by natural convection due to the any cross section is a paraboloid of revolution, as given by the differences in density caused by the temperature gradient. eauation
U
1 Received
February 2, 1931. Present address, Standard Oil Co. (Indiana), Whiting, Ind.
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
626 = velocity a t distance
where u
r from the center of the pipe
ro = pipe radius Unv
= average velocity of fluid, defined as total volumetric
flow per unit time divided by the cross section of the pipea (3) The heat developed by friction can be neglected in comparison with that transferred t o the fluid. (4) . The temperature gradients parallel t o the tube axis are small in comparison with those in radial directions.
The second of these assumptions is the most questionable of the four. It will be discussed later. The equations developed to answer the first two questions are not reproduced, since it is only the answer to the third that is of importance here. The point film coefficient was calculated by the usual equation :
Vol. 23, No. 6 L - 1 4 . 6 3 4 P5 ~
f,, - t,
= At =
Atl
+ 0.0135e-212.18
Pe
D
+ 0.0987e
+ ...... 1 =
Substitution of ( L e - t,) and (6t/6r) 5 and 6 into Equation 2 gives:
Al,@(Pe r
-
ro
-DL
-88.7Pc
ti)
(6)
from Equations
hD - = k L - 14.634Pe 5
2.996e
- 14 634PeLD
0.821e
+ 2.228e
- 88 7
~4 e D
+ 1.006e
-88.7Pe L
+ 0.0987e
-212 18Pe
+ .
-212 1RPe--L D
+ 0.0135e
+ ... (7)
Equation 7 can be written as
= the film coefficient a t a given point
where h k
ro
= thermal conductivity of fluid = radius of tube
-
(E)
t, = tau =
= temperature gradient in fluid at tube wall r=m
tube wall temperature (assumed constant) average temperature of fluid
Susselt, in calculating t,, the average temperature of the fluid, really determined the average temperature across the tube section, as defined by the equation
where t
=
temperature of fluid at a distance r from the tube axis
Since coefficients based on such an average are inconvenient and unusual, Grober (4) modified Nusselt’s results (see also Merkel, 7) by defining t., in the more usual way as the average temperature of the flowing fluid, defined by the equation:
(4)
Nusselt’s equation for the wall temperature gradient
is :
(g)
=
-2 D
12.996e
- 14.634Pe A
r-rn
+ 1.006e-212.18Pe + . . .
=
+ 2.228e -88.7Pe
L 5
-$!xke$)
where Atl = temperature difference between fluid and tube a t tube entrance D = diameter of tube x = a function . k k Pe = -= = Peclkt number D ~ a o p C DVC k = thermal conductivity of fluid uaV = average linear velocity of fluid p = densityof fluid c = heat capacity of fluid v = average mass velocity of fluid L = tube length
-
Grober’s expression for the point temperature difference - tu), is:
(tav
I In
all equations consistent units are assumed.
h plot of Equation 7 is shown in Figure 1. The plotting of this equation for low values of PeL/D cannot be done accurately, since only three terms of each of the two infinite series are given, and for low values of PeL/D the series do not converge rapidly enough to give accurate results with only three terms. It is interesting to note that there is no viscosity term in Equations 7 or 8. As PeL/D increases, either because of increasing L or k or of decreasing D, v, or c, hD/k rapidly approaches a limiting value of 3.65. Thus, if one follows the coefficient along a tube of considerable length, the coefficient is infinitely great a t the fluid entrance (owing to an infinite temperature gradient a t this point), drops very rapidly, and then approaches asymptotically a constant value of 3.65 k/D. When kL/D2uc is 0.06, the coefficient is only 1 per cent above the minimum. Effect of T e m p e r a t u r e Gradient on Velocity Distribution
It is readily apparent that Nusselt’s assumption of parabolic velocity distribution (true only for isothermal viscous flow) introduces an error in the theory. In the first place, differences in density due to the temperature gradients tend to generate cross currents of a natural convection type. These currents are probably mild in comparison with the forced flow except for low velocities, but they disturb the normal velocity distribution and, if they are appreciable, should increase the heat-transfer coefficient somewhat. In the second place, even if eddies or non-symmetrical convection currents are disregarded, the temperature gradient can be expected to exert an effect on the flow, owing to the change in the temperature gradients caused by the radial flow of fluid that follows the changing of the fluid viscosity in the layers near the tube wall. If the liquid is being heated, this effect increases the velocity and temperature gradients at the tube wall over those of isothermal flow, and therefore increases the coefficient. This subject is discussed more fully by Keevil and McAdams ( 5 ) . Still a third possible effect of the temperature gradient on the velocity gradient is the induction of actual eddies by the radial flow of the fluid. These, if they occur, should result in an increase in the coefficient. It can be expected, then, that actual coefficients will be higher than corresponding to Equation 7 . For the far end
I X D U S T R I A L AND ENGINEERING CHEMISTRY
June, 1931
of a long pipe, however, (large values of kL/D2vc) the temperature gradient is small, the distortion of the velocity distribution curve is small, and the theoretical coefficients should he approached in practice.
627
two oils, one a light and the other a heavy fuel oil. The viscosity of oil No. 1 was 6.1 centipoises a t 200" F. and 9.3 a t 90" F. The viscosity of oil No. 2 was 36.3 a t 200" F. and 43.0 a t 90" F. The temperature-viscosity curves for both oils are straight, if plotted on log-log paper. The tube was found to be clean when the experiments were completed. Data and Calculations
The observed data and the results of the calculations are shown in Tables I, 11, and 111. The heat flow in each water run was calculated from the rate of flow and the temperature rise of 03 eo ,,, .,* ,,* ,, the water, while in the oil runs the heat transferred was calculated from the electrical measure merits, with proper radiation corrections' The Figure 1-Theoretical Point Coefficient Curve, Constant Wall T e m p e r a t u r e temperature rise of the oil was rather small, and the A theoretical calculation of the corrections to be applied precision obtainable by computing the heat flow by oil temto the Xusselt-Grober equation is not promising. The follow- perature rise was less accurate than that from the electrical ing experiments were conducted to obtain a design curve for flow, However, in all runs the alternative method was this type of heat transfer, and to compare actual results applied as a check, and the heat balances so obtained were with the theoretical Nusselt-Grober curve. satisfactory, as is shown in Table 11. The average film coefficient h,, was calculated in the usual Experimental way by the equation: The apparatus is shown in Figure 2. The heating tube I! was a standard steel pipe 0.82 inch inside diameter and 10 ll,, = (9) sDL( A t L feet long. A calming section 5 feet long was used t o eliminate entrance effects. Electric heat was used. The entire tube was lagged with a 11/2-inch layer of magnesia. il constant- where iz,, = average liquid film coefficient, B. t. u. per square foot per hour per ' F. speed, positive-displacement pump was used, and the rate of D = inside tube diameter, feet liquid flow through the heating section was controlled by L = tube length, feet adjusting the proportion of liquid by-passed around the tube Ata. = average temp:rature difference between tube wall and sent back to the storage tank. The liquid leaving the and fluid, F. = heat flow, B. t. u. per hour heating section was sent through a mixer before its temq perature was measured, so a true average exit temperature could be obtained. The average temperature difference, Atav, was calculated The mixing device consisted of a 3/rinch pipe reaching very by the equation: nearlv to the bottom of a CUD constructed of an 8-inch length of a il/?-inch pipe that was closed a t the bottom with a cap. tl tz The effectiveness of the mixer was tested by measuring the At,, = t, - (10) 2 temperature of the liquid a t various points in the annular space between the inner and outer tubes. With the most where f, = average wall temperature, as determined by the viscous oil used, no temperature variation was found. arithmetic average of the six tube thermocouples, Tube temperatures were obtained by brazing six copperF. constantan thermocouples a t 2-foot intervals on the heating tl = average entrance temperature of liquid, 'F. section. The hot junctions were brazed into grooves on the t2 = average exit temperature of the liquid, ' F. side of the tube and the brazing filed flush to the MAGNESIA P I E LAGGING tube surface. Asbestos tubing was slipped over '*OM A To each of the twelve wires and the w i r e s w e r e Ap '' HEATING E L E M E N T FROM C TO D wrapped once around the pipe to prevent heat conduction away from the junction ( 2 ) . The heating section, with the six thermocouples installed, was wrapped with l / & x h asbestos 8 THERMOCOUPLES EVENLY SPACED F R O M C T O D paper, and over this was wound chrome1 wire a t a constant pitch. Over the heating wire was STORffif TANK WEIGH T A N K placed a 1l/Tinch layer of magnesia pipe lagging. The temperature of the entrance liquid was measured a t the point of discharge from the storage tank, and the exit temperature a t the mixing cup. Thermocouples, sealed in glass tubes filled Fieure 2-Diafirarn of Apparatus with benzene (for thermal contact), were used for The use of the arithmetic fluid temperature is justified liquid temperature measurements. All thermocouples were by the fact that, since the heating coil was wound with a calibrated. Radiation losses were obtained, and plotted against the constant pitch, the heat input per unit area of heating surface differences in temperature between tube wall and room. was constant, and the fluid temperature should increase nearly The points obtained fell very well on a smooth curve. The linearly with tube length. The above method of calculating Atau was thought to be the best approximation to the true radiation curve is shown in Figure 3. The experiments were carried out with water and with Ataa defined by the equation : 2
01
.0*
+ .07
.OLI
,IO
A3
+
O
INDUSTRIAL A N D ENGINEERING CHEMISTRY
628 Table I-Individual
Tube Temperatures and Average Wall Tempera tures
OBSERVEDT U B ETHERMOCOUPLE READINCS~
RUN 1
2
3
4
F.
5
6
.v. WALL TEMP,
F. 142.5 107.5 108.5 105.5 106.5 97.0 99.5 106.3 105.0 97.0
' F.
' F.
F.
140 105.5 104.0 103.5 104.5 95.5 99.0 103.5 103.5 96.0
115.2 101.0 101.2 99.0 101.0 94.0 96.0 101.0 100.0 94.0
105.0 97.0 97.0 93 96.5 93.0 95.0 98.3 99.0 94.0
140.2 105.0 105.2 104.0 105.4 95.2 98.8 104.3 103.0 95.8
11 12 13 14 15 16 17 18 19 20
101.5 100.5 100.0 105.5 90.5 86.5 82.; 82.0 93.0 99.0
104.5 103.0 101.5 105.5 91.0 86.5 83.0 82.5 91.0 98.5
102.5 101.5 97.5 100.0 89.0 85.5 81.5 80.5 87.0 92.5
100.0 101.5 96.0 97.5 88.0 84.0 80.5 78.7 86.5 91.0
98.0 100.5 91.0 91.0 85.5 82.5 79.0 76.5 82.0 85.5
97.5 96 90.5 86.0 84.0 82.0 79.0 75.0 70.0 82.5
21 22 23 24 25 26 27 28 29 30
121.5 92.0 92.5 97.5 109.5 103.5 102.5 86.5 89.5 94.0
116.5 87.5 90.5 95.0 107.0 101.5 98.5 86.5 89.0 93.5
107.5 86.5 87.5 90.5 101.0 97.0 96.0 86.5 87.5 91.5
105.5 85.0 86.0 90.0 98.0 95.5 93.5 85.5 87.0 91.0
95.0 81.0 82.0 84.0 92.5 90.0 89.5 84.0 84.5 87.5
31 32 33 34 35 36 37 3s 39 40
112.5 102.5 100.0 97.0 100.0 97.0 96.5 100.2 110.0 112.5
107.5 99.0 98.0 95.0 99.5 96.0 95.2 99.8 107.0 112.3
101.5 95.5 94.0 93.5 96.0 95.3 92.8 98.1 103.3 109.7
99.5 94.0 93.5 93.0 95.5 94.0 92.5 97.5 102.5 108.5
41 42 43 44 45 46 47 48 49 60
113.2 112.1 101.0 102.2 105.5 104.5 107.5 108.1 106.2 106.7
113.8 113.4 101.5 102.3 106.0 104.5 110.5 109.9 106.0 106.8
112.5 112.0 101.5 101.5 103.5 103.5 109.2 108.0 105.3 106.5
51 52 53 54 55 56 57 58 59 60
105.5 106.5 106.5 107.2 107.5 107.5 107.5 108.5 107.5 109.0
105.5 106.5 106.5 107.2 109.5 110.5 111.0 111.5 110.0 112.0
61 62 63 64 65 66 67 68
109.5 110.0 110.0 109.0 109.5 109.5 109.7 113 2
111.5 112.0 112.0 113.1 113.5 112.5 112.4 114.0
-
O
F.
RUN
ROOM TEMP.
F R O M ELECTRICAL M E A S U R E M E N T S
Cross
Radiation (Pig. 4)
Net
E . 1. u./hr
B.1. v./hr.
loo
163.5 108.5 110.0 110.5 111.5 97.0 102.5 108.5 105.5 98.5
' F.
Heat-Balance Data HEATFLOW
ARITHMETICAL
180 110.5 110.5 112.5 112.0 95.0 101.0 107.5 105.0 95.5
1 2 3 4
Table 11-Observed
Vol. 23, No. 6
FLUID
B . f . u./hr
E . 1. u./hr.
747 280 201 265 201 201 200 268 201 331
210 90 80 75 80 50 85 100 85 60
537 190 121 190 121 151 115 168 106 271
320
8 9 10
71 68 79 79 79 78 70 71 75 75
100.7 100.5 96.1 93.6 88.0 84.5 81.0 79.2 86.4 91.5
11 12 13 14 15 16 17 18 19 20
76 76 76 60 74 74 74 67 69 76
331 331 1000 1000 575 414 304 317 445 648
75 75 60 125 45 30 24 37 55 48
256 256 940 875 530 384 280 280 390 600
86.5 79.0 80.0 82.0 86.5 86.5 89.5 83 84.0 87.5
105.4 85.2 86.4 89.8 99.1 95.7 94.2 85.3 86.9 90.8
21 22 23 24 25 26 27 28 29 30
71 73 75 77 80 81 78 81 85 86
1020 304 414 525 648 476 400 304 385 385
100 40 35 40 58 46 50 1; 15
920 264 379 485 590 430 350 290 380 370
94.5 92.0 89.7 90.5 92.5 93.2 89.0 96 3 97.2 104.1
91 89.0 86.5 88.5 90.5 92.0 89.0 93.7 96.8 103.9
99.4 95.3 93.6 92.9 95.7 94.6 92.5 97.6 102.8 108.5
31 32 33 34 35 36 37 38 39 40
87 87 81 85 89 91 92 89 89 92
444 444 370 370 414 304 268 343 330 399
110.5 109.5 99.5 100.0 102.5 102,o 106,O 105.5 103.5 104.4
107.4 107.4 96.9 97.4 98.8 99.4 103.5 103.2 101.0 101.2
105.6 105.0 96.0 96.0 97.5 97.5 100.5 100.7 99.0 99.0
110.5 109.9 99.4 99.9 102.3 101.9 106.2 105.9 103.5 104.1
41 42 43 44 45 46 47 48 49 50
105.5 106,5 106.5 107.2 109.5 109.5 109.5 110.5 108.5 110.5
102.5 104,2 104.1 105.1 106.5 106.3 107.0 107.2 106.1 108.1
99.8 101.2 102.0 102.3 104.5 104.3 104.9 105.1 103.5 105.3
98.0 99.1 99.0 99.3 101.5 101.5 101.5 102.0 101.6 101.9
102.8 104.0 104.1 104.7 106.5 106.6 106.9 107.6 106.2 107 8
51 52 53 54 55 56 57 58 59 60
110.5 110.5 112.0 112.1 112.5 112.4 112.2 112.5
107.1 109.0 109.1 107.9 108.4 109.2 109.5 111.5
105.7 104.5 105.3 106.5 106.5 107.5 107.8 110.7
102.1 102.0 103.9 103.9 103.0 103.5 103.6 110 5
107.4 108.0 108.8 108.1 108.9 109.1 109.2 111.9
61 62 63 64 65 66 67 68
,
O
F.
'ROM TEMP. RISE O F
399 399 399 399 399 399 399 399 399 399 84 84 84 84 84 85 85 85 85 85
410 419 350 350 394 290 268 318 290 349 60 60 50 52 57 56 70 65 60 65
399 399 399 399 399 399 399 399 399 399 399 399 399 399 399 399 399 399
67 70 77 75 78 78 79 80
339 339 349 347 342 343 329 334 339 334
358 226 398 348 274 340 185 314 248 460
342 389 339 339 334 334 334 331 335 332
376 222 286 217 247 203 204 238 292 202
332 329 322 324 32 1 320 320 319
261 212 202 204 208 240 180 198
a Thermocouples numbered serially from liquid exit end to liquid entrance end of beating section.
Experimental Results
Figure 4 shows the curve obtained when h.,D/k is plotted against kL/D2vc on log-log paper. On this figure are also plotted those points from Morris and Whitman (8) that correspond to values of Reynolds' number below 2000, and hence might be expected t o fall in the viscous-flow range, Also there are plotted data kindly supplied by Morris4 from tests on a commercial heat exchanger. Morris' film coefficients 4 Experimental work conducted by F. H. Morris, under the auspices of the M. W. Kellogg Co.
were calculated from observed over-all coefficients, by using a steam film coefficient of 2000 B. t. u. per square feet per hour per degree Fahrenheit. The coordinates of the points from Morris and Whitman and Morris are given in Table IV. It will be noted that the points from the three sources determine a very fair curve, and that the data are well correlated by the two functions h,,D/k and PeL/D. It is especially striking that viscosity is not required in the correlation. The experimental data cover a viscosity range of from 0.6 to 50 centipoises, and yet the t,wo dimensionless groups indicated by the Nusselt-Grober theory corre1at.e the data within the experimental error, in spite of the fact that neither group contains a viscosity term. The data of Dittus (3) are not included in Table V. Dittus used an electrically heated tube and carried out his ex-
INDUSTRIAL A N D ENGINEERING CHEMISTRY
June, 1931
Table 111-Summary RUN
12
tl
1W
n
629
of Experimental Data and Values for P e L / D a n d h,,D/k hov
Pe-L
0.078 0.078 0.078
0.462 0.460 0.458 0.459 0.458 0.452 0.454 0.458 0.459 0.462
53.7 54.0 53.8 53.8 53.8 54.0 54.0 53.8 53.8 53.9
0.0362 0.0493 0.0496 0.0496 0.0495 0.0149 0.0315 0.0314 0.0252 0.00236
5.94 7.40 6.05 7.00 5.00 9.25 7.45 8.3 7.25 12.6
0.00837 0.00941 0.0206 0.0725 0.0430 0.0428 0.0430 0.1005 0.108 0,091
11.4 8.4 8.8 6.41 7.78 7.50 5.66 5.3 4.06 5.85
n
106 271
13.0 9.6 44.3 37.8 39.5 37.9 28.5 26.6 20.8 29.8
727.0 575.0 164.0 278 0 278.0 278.0 117.5 111.5 131.5
0.078 n. 078 0.345 0.350 0.347 0.346 0.344 0.343 0.350 0.348
0.452 0.453
79.2 86.4 91.5
256 256 985 745 007 349 232 228 330 510
1.0 1.0 1.0 1.0 1.0 1.0 1.0
53.9 53.9 62.24 62.22 62.20 62.22 62.24 62,26 62.15 62.20
81.0 81.5
87.5 91.0 101 0 97.0 95.0 83.0 84.5 89.5
105.4 85.2 86.4 89.8 99.1 95.7 94.2 85.3 86.9 90.8
730 287 322 434 517 337 261 205 248 330
22.2 23.5 24.0 26.0 23.3 20.4 17.7 25.2 27.6 29.2
96.8 74.5 97.2 105.5 92.8 81.3 74.0 298.0 298.0 216.0
0.351 0.346 0.346 0.347 0.351 0.350 0.350 0.346 0.348 0.349
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
62.11 62.22 62.22 62.20 62.11 62.14 62.14 62.20 62.20 62.17
98.0 96.0 93.0 92.0 94.6 93.0 90.5 96.0 102.0 98.5
99.4 95 3 93.6 92.9 95.7 94.6 92.5 97.6 102.8 108.5
330 302 283 260 350 255 222 235 280 349
15.9 21.4 19.5 22.5 25.5 25.9 23.0 24.9 15.8 21.2
87.7
0.351 0.351 0.350 0.350 0.351 0 351 0.350 0.363 0.354 0.078
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.444
62.10 62.10 62.15 62.15 62.11 62.11 62.15 62.08 62.06
40
81.5 81.5 80.5 83.0 84.0 87.0 85.5 90.0 87.0 97.0
41 42 43 44 45 46 47 48 49 50
99.0 97.0 90.0 90.5 91.6 91.5 92.5 93.0 93.0 91.5
100.0 98.5 91.0 92.0 92.4 92.5 94.0 95,o 94.0 93.5
110.5 109.9 99.4 99.9 102.3 101.9 106.2 105.9 103.5 104.1
339 339 349 347 342 343 329 334 339 334
14.4 13.0 18.3 18.7 15.5 16.0
2800.0 1635.0 4320.0 4340.0 3710.0 3690.0 1340.0 1710.0 2700,O 2500.0
0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078
56.6
0.078
0.444 0.443 0.442 0.443 0.443 0.443 0.443 0,443 0,443 0.443
51 52 53 54 55 56 57 58 59
92.5 92.3 93.5 92.5 93 0 93.5 93.0 93.2 94.0 94.5
94.0 92.2 95.0 94.5 94.5 95.0 95.5 95.3 96.0 96.0
102.8 104.0 104.1 104,7 106.5
16.8
106.9 107.6 106.2 107.8
342 339 339 339 334 334 334 331 335 332
2720 2670 2290 1950 1780 1470 888 1220 1600 1460
0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078
0.443 0.443 0.443 0.443 0.443 0.443 0.443 0.443 0.443 0.443
56.7 56.7 56.7 56.7 56.7 56.7 56.7 56.6 56.6 56.6
94.0 94.0 94.0 94.0 94.0 93.0 93.0
96.0
107.4 108.0 108.8 108.1 108.9 109.1 109.2 111.9
332 329 322 324 321 320 320 319
12.5 11.8 10.9 11.6 11.0 10.85
1420 1150 1100 1100 900 733 555 360
0.078 0.078 0.078 0.078 0.078 0.078 0.078
0.443 0.443 0.443 0.443 0.443 0.443 0.443 0.443
56.6 56.6 56.6 56.6 56.6 56.6
90.0 87.5 82.0 77.0 78.0 77.5 75.5 71.0 72.5 75.0
93.0 92.5 89.5 97.0
100.7 100.5
21 22 23 24 25 26 27 28 29 30
73.5 73.0 73.0 73.0 76.6 79.0 79.5
106.5
31 32 33 34 35 36 37 38 39
5 6
7 8
9 10
11 12 13 14 15 16 17 18
19 20
60
61 62 63 64 65
66
67 68
86.5
89.0 90.0 94.5 86.5
86.0
83.0 79.0 79.5 85.5 92.0 86.0
80.0
96.0
96.0 96.0
96.5 96.5 96.5 98.5
92.5
96.1
97.6 88.0 84.5 81.0
106.6
537 190 121
190 121 151 115 168
11.8
13.1 15.8 13.5 12.4 13.8 14.1 12.2 12.7 12.4 11.6 14.0 12.3
10.8
9.1
periments with oil and water, However, in his apparatus the calming section was heated as well as the heating surface proper. As a result, when the heat-transfer measurements were taken, the temperature gradients were already partially formed, Reference to Figure 1 will shorn that Dittus’ coefficients should be lower than those obtained where the calming section is not heated, and this was found to be true. In general, Dittus’ results fall below the curve of Figure 4. They were obtained on four different pipes, each with a different length of heated calming section, and are not, easy to correlate on a plot such as Figure 4. The following empirical equation has been derived from the experimental points of Figure 4 : - =
k
3.65
0.0065 +-
0.513 (12)
0.078
0.078 0.078 0.078 0.078 0.078
0.078
815.0
91.0
99.0 128.0 145.0 185.0 195.0 172,O 82.0 4050.0
1.0
0 078
Table IV-Coordinates
56.6
56.6 56.7 56.7 56.7 56.7 56.7 56.7 56.7 56.7
56.6
56.6
t Ll
Pe k
Z
6 D
0.00151
0.00148 0.00227 0,00228 0.00252
21.3 16.5 17.5 19.0 18.8 20.2 15.0 14.7 15 5
1970 1200 1410 1530 1600 1640 900 1450 840
0.113 0.1305 0.1485 0 1630 0 0398 0 0398 0 0557 0.139 0.133 0 122 0.094 0.0835 0.0654 0 062 0.0705 0.149 0.00164
3.10 4.16 3.80 4.39 4.97 5.05 4.50 4.62 3.04 18.7
0.00239 0.00405 0,00154 0.00154 0.00179 0.0018 0.00496 0,00388 0.00246
12.7 11.4 16.1 16.4 13.2 14.2 10.4 11.5 14.0 11.8
0.00268
14.7 12.4 13.8 12.4 10.7 11.2 10.9 10.2 12.3 10.8 0,0047 0.00578 0.00603 0.00605 0,0074 0.0091 0.0120
11.0 9.5 9.6 10.1 9.7 9.5 9,5
8 0 -
0.0185
MORRI~ (8)
A N D \\’HITMAS
g 2 k
Z
go.ooii9 :g:T! 1:;7.4;;:1460 0.00117 g:ggL;i5 t::: 18.3 1500
0.00122 0,00154 0.00153 0.00152
k
4.32 4.64 4.78 5.12 4.70 3.99 3.45 4.97 5.42 5.70
0 1255 0 160 0 123
DATA FROM
0.00634 16.2 1260 0.00330 1 3 . 2 540 0.00637 16.2 1380 0.00507 10.0 210 0,00545 16,7 1280 o,0122 6.2 76
Ao: : :0.00098 2i:E lEz: g:!; 24.8 2200
VCIIP
of Points Plotted In Figure 4
DATAF R O M MORRIS‘
Pe
& D
p
171.5 136.5 136.5 136.5 136.5 458,0 216.0 210.0 268.0 290.0
140.2 105.0 105.2 104.0 105.4 95.2 98.8 104.3 103.0 95.8
83.0 86.0 90.5 82.0 89.0
kL
C
6.77 8.45 6.3 8.0 5.72 10.5 8.5 9.45 8.25 14.4
123.5 103.0 103.5 102.0 102.0 90.5 96.0 102.0 99.5 87.5
1 2 3 4
--
k
Un v
g
Pe D
k 26 7
26 28 33 25 37 29 36 39 55 55
3 2 3 2 9
0 00119 755 0 000852 990 1060 0 00083
0 00067
00067 000353 000431 000369 0 000295 0 00025 0 000236 0 000214 0 00104 0 00105
0 0 0 0 8 0
8
0 0 50 0
25 7 25 3
v c Z 1290 1270 1540 620 725 875
2000 1660 1340 1920 1950
INDUSTRIAL AND ENGINEERING CHEiVISTRY
630
The full line of Figure 4 is a plot of Equation 12. The three sources of data show enough variation in the two variables, tube diameter and ratio of tube length to diameter, to justify their use in the plot. The tube proportions of the three sources are shown in Table V. Table V-Diameters
Vol. 23, N o . 6
the relation between the coefficient, h, the point temperature difference, At, and the average coefficient, ha,, can be shown to be :
a n d Proportions of Experimental Tubes l
SOURCE
~
RATIOHEATED LENGTH ~ TO TUBE ~ DIAMETER
Inch 0.62
Morris and Whitman Moms Kirkbride and McCnbe
196 247
0.58
0 82
146
Comparison of Experimental Results with Nusselt-Grober Curve
Since the curve calculated from the Xusselt-Grober equations and plotted in Figure l is a point-by-point curve of hD/k vs. PeL/D, it should be possible, by integration of this curve, to compare the theory with experiment. It must be noted, however, that the data plotted in Figure 4 represent two different cases. The points determined by the authors correspond to the boundary condition of constant heat input per unit of length, while those of the other observers correspond more nearly to the case of constant wall temperature, since steam heating was used in determining these points. Theoretically, the curve of Figure 1 applies only to the case of constant wall temperature, since this boundary condition was in the integration of the partial differential equation that was assumed to apply to the process. If the corresponding curve were determined for the case of constant heat input per unit of length or, what amounts to the same thing,
~
~
~
~
E
The variation of At with respect to L, and of h with respect to L, can be expected to be different in the case of constant wall temperature than in the case of constant wall temperature gradient. However, either these differences are small or else the variation of (At)@) with respect to L is nearly the same in the two cases, because the points of Figure 4 blend well with each other, and determine a single curve. The points representing the two classes of experiment are consistent with each other within a reasonable experimental error, and the curve of Figure 4 can be used as a design curve for either case. Assuming that the curve of Figure 4 can be used as the h,,D/k vs. PeL/D curve for the case of constant wall temperature, it is interesting to plot the corresponding curve as calculated from Nusselt’s theory. From Equations 2, 9, 11, and 13 it can be shown that:
Equations 5 and 6 give the relation between the wall temperature gradient and PeL/D, and the point temperature difference and PeL/D, respectively. Equations 5 and 6 can be substituted in the integrals of Equation 15, and if Pe is considered constant so that d (Pck) =
(g)
dL
then,
D
Flgure 3-Curve for Radiation Corrections
constant wall temperature gradient, a curve differing from that of Figure 1 would be expected, because of the difference in boundary conditions. The Nusselt-Grober theory indicates that a point film coefficient is a function of the history of the heating or cooling of the fluid previous to the point in question, as well as of the usual variables of tube dimensions, fluid properties, and velocity. No point-by-point data are available to show whether or not this fact is of practical knportance, but apparently it has not been recognized previous to Nusselt’s paper (9). I n the general case, the relation between the point coefficient and the average coefficient depends on the definition of the average temperature difference. The most rational definition of this temperature differenceis that given by Equation 11 and where the average fluid temperature is that given by Equation 4. This is the average temperature difference that is usually used. By using Equations 2 , 9 , and 11 together with the equation: dp =
-k($
rsm
SD dL
Equation 17 can be approximately integrated by the graphical method, using Equations 5 and 6. The graphic integration of the numerator is complicated by the fact that the X-function becomes infinite when PeL/D is zero, and the area under the curve for a low value of PeL/D must be estimated. Also, neither of the functions can be accurately plotted for low values of PeL/D, because of the lack of terms. The result of the integration, therefore, must be approximate. The integrated curve is plotted as a dash line of Figure 4. It will be noted that there is a wide divergence between the actual and theoretical curves at low values of PeL/D, but the two curves come together at higher values of
PeL/D. Correlation between Heat Transfer in Turbulent and Viscous Flow
It is interesting to compare the correlation of heat transfer in viscous flow with that in turbulent flow. I n turbulent
INDUSTtZIAL A N D ENGINEERING CHEMIXI’RY
June, 1931
flow hd/k has, in general, been expressed as a function of two groups of variables: Dv/Z and cZ/k, where Z is the viscosity. There has been some evidence that L / D should also be used, even in those cases where entrance turbulence effects
631
Equation 18 can be written as (6) : hD
= \LT
?,$)
(Pe.
(20)
Equation 20 corresponds to Equation 8 if 2 drops out as a variable and if the effects of Pe and LID are the same. Turbulent flow heat transfer data can be correlated by Equation 20 as well as by Equation 18,and Equation 20 can be used as a general type equation for heat transfer under both viscous and turbulent flow conditions. Acknowledgment
The authors are much indebted to Carl C. Monrad, of the Standard Oil Company of Indiana, for suggestions during this investigation and for his valuable bibliographic work in connection with the problem. Figure 4-Experimental
Average Coefficient Curve
are absent (1, 6). If this is 80, the turbulent flow equation takes the form: hD
Dv CZ L Z k D
(18)
Also, since (19)
Literature Cited
(1) Burbach, “Stromungswiderstand und WArmedbergang in Rohren.” Akad. Verlag, Leipzig, 1930. (2) Colburn and Hougen, IND. ENG. CHBM.,92, 522 (1930). (8) Dittus, University of California, Bull. 9, No. 11 (1929). (4) Graber, “Die Grundgesetze der Wirmeleitung und des Warmetiber ganges,” pp, 1 7 9 4 7 , Springer, Berlin, 1921. (a) Reevil and McAdams, Chem. Met. Eng., 86, 464 (1929). (6) Latzko, 2. angew. Math. Mech., p. 268 (1921). (7) Merkel, “Die Grundlagen der Warmeubertragubg,” p. 16, Steinkopff, Dresden and Leipzig. (8) Morris and Whitman, IND. ENG. CHEM.,90, 234 (1928). (9) Nusselt, Z. Ver. deuf. Ing., 64, 1154 (1910).
Manufacture of Charcoal in Japan‘ With Special Reference to Its Properties Ihachiro Miura Toxvo IMPERIAL UNIVBRSITY,KOMABA, TOKYO, JAPAN
I
N JAPAN about 80 per cent of the total forest production is now being used for firewood, and about 40 per cent of this is converted into charcoal. I n contrast with this only 40 per cent is said to be used for firewood in America and Germany, the remainder being manufactured into lumber. It is therefore obvious that the study of charcoal, which is the principal domestic fuel in Japan, is an important problem from the point of view of both the forest industry and the economies of daily life. For these reasons Japan has made significant progress in charcoal manufacture and is a t present producing several varieties, of which black or soft charcoal and white or hard charcoal are most common. Charcoal burning in Japan is usually accomplished by the use of various types of ovens characteristic of the Orient. Since Japanese charcoal, especially the white charcoal, is made in a special manner a t a very high temperature, the meiler is very seldom employed and the American brick kiln not a t all. Using more than ten kinds of ovens currently employed in Japan the writer has conducted experiments on the tempera* Received December 16, 1930.
ture of carbonization, the selection of materials for the construction of the ovens, the yield, and the properties of the charcoal produced. Charcoal is usually made by ovens of two general types: (1) earthen ovens, in which the materials remain within during the entire process, the combustion being stopped by closing all vents; and ( 2 ) stone ovens, from which the w h i t e hot contents are withdrawn and covered with a slightly moistened mixture of earth, ashes, and charcoal powder in order to extinguish the fire promptly. The charcoal made in the earthen ovens is black and of moderate hardness; hence it is called black or soft charcoal. This kind of charcoal is generally used for domestic purposes, but if made from coniferous wood it can be used in forges. The product of the stone ovens is white on account of the ash powder on its surface, is very hard and of the best quality, and a cross section has a metallic luster. It is called white or hard charcoal and is fitted not only for domestic use but also for other purposes, such as making confectionery and special cooking.
