1382
INDUSTRIAL AND ENGINEERING CHEMISTRY
(11) Molitor, Paper presented before the Petroleum Division at the 81st Meeting of the American Chemical Society, Indianapolis, Ind., March 30 to April 3, 1931. (12) Moureu and Dufraisse, Chem. Rev., 3, 113 (1927). (13) Moureu and Dufraisse, Compt. rend., 174, 258 (1922). (14) Norris and Thole, J . Inst. Petroleum Tech., 15, 681 (1929). (15) Ramsey, IND.EXG. CHEY.,24, 539 (1932).
Vol. 24, No. 12
(16) Voorhees and Eisinger, Am. Petroleum Inst., Proc. 9th Ann. Meeting, 10, No. 2, Sect. 11, 169 (1929). (17) Wagner and Hyman, J . Inst. Petroleum Tech., 15, 674 (1929). (18) Zublin, Oil Gas J., 29, 26 (1931). RECEIVED July 6, 1932. Presented before the Division of Petroleum Chemistry a t the S2nd Meeting of the American Chemical Society, Buffalo, N. Y., August 31 to September 4, 1931.
Heat Transmission from Metal Surfaces to Boiling Liquids I. Effect of Physical Properties of Boiling Liquid on Liquid Film Coefficient D. S. CRYDERAND E. R. GILLILAND, Pennsylvania S t a t e College, State College, Pa.
T
HE data available in the Direct measurements of boiling-liquid Jilm it impossible to determine acculiterature relating to the coeficientsof heat transmissionWere carried out rately from the over-all coeffidirect measurement of cient the individual coefficient for the liquid film coefficient for by Of an evaporator 'Onthe boiling-liquid film. These heat transmission between metal sisting O f an electrically heated brass lube SUSdifficulties were avoided in the surfaces and boiling liquids are pended in the boiling liquid. By means of present study by measuring divery meager. suitable thermocouples, temperatures of both the rectly the heat transferred from Linden and &tontillon (ff), pipe and liquid were measured at varying an electrically h e a t e d , c l e a n , working with a small inclinedbrass surface to the boiling liquid. temperature differences for each of eleven different tube evaporator, calculated the The correlation of boilingb o i l i n g-li q u i d film coefficient h7Uids. liquid film coefficients involves Dimensionally sound equations have been the consideration of a large for water inside a copper pipe developed correlating the heat transmission conumber of variables. Some of from direct measurements of the temperatures of the outer eficients so obtained the physical properties these have already been discussed (1, I,16,IS). surface of t h e p i p e a n d of of the boiling liquids. T h e m o s t important varithe main body of the liquid. able is the rate of circulation of The temperature drop through the pipe wall was estimated from the known value of thermal the liquid past the heated surface. As Badger points out ( 2 ) , the result of this circulation is a function of the number of conductivity for copper. Jakob and Fritz (10) measured the boiling-liquid film impacts of liquid particles on unit area of the heating surface. coefficients for water, using electrically heated horizontal This latter again should be a function of the Reynolds crimetal plates. Polished, sanded, and grooved surfaces were terion, DGIZ. The difficulty in the evaluation of D, the employed. As might be expected, the grooved and sanded shape factor, and of G, the mass velocity of the liquid, is surfaces gave the highest values for the coefficient of heat obviated in the present case by the use of a single heating transmission] since they provided the greatest number of unit. The further effects'bf variation in shape factor will be made one of the subjects of further investigation. The nuclei for bubble formation. present study was conPractically all of the fined to the investigainformation, however, tion of the effect on the is confined t o t h e liquid film coefficient of over-all heat transfer the properties of the coefficients] based on liquid and of temperaapparent temperature ture difference. Varid i f f e r e n c e s between able G, which is decondensing steam and pendent mainly on the boiling liquid. These rate of heat transfer over-all coefficients inand the physical arclude the condensingrangement of the heatsteam film, pipe wall, ing apparatus, can in scale, a n d boilingthe present case b e liquid film. The unmade a function of the certainty involved in temperature difference estimating the coeffiand of the physical cients f o r t h e conproperties of the liquids densing vapor, and the used. Other variables variable resistance of the scale deposited on FIGURE 1. DIAGRAM OF APPAR.4TUS FOR hfE.4SURING BOILING-LIQUID considered in this investigation, which may FILMCOEFFICIEKTS the metal surface, make
December. 1932
INDUSTRIAL AND ENGINEERING CHEMISTRY
possibly affect the circulation of the liquid and the properties of the liquid film, are thermal conductivity, specific heat, viscosity, density, and surface tension of the boiling liquid.
EXPERIMENTAL PROCEDURE HEATING VNIT. The details of the heating unit and general arrangement of the apparatus are given in Figures 1 and 2. Since the reliability of the results depends mainly on the
FIGURE 2.
DETAILS OF ELECTRIC4LLY H E 4 T E D I 3 R 4 S S
TUBE
uniformity and accuracy of measurement of temperature of the heating surface, great care was taken in the assembly of the heating unit. It consisted essentially of a resistancewound alundum core placed concentrically in a brass tube. Brass disks were silver-soldered to the ends of the tube, and the resistance leads brought through the disks as shown. In order to secure uniformity of surface temperature, the heating unit was assembled and the power applied while the unit was immersed in water. The surface temperature was obtained by means of five chromel-cope1thermocouples, silversoldered to various points in the surface and ends of the unit. Khen a difference in surface temperature a t some point was noticed, the unit was taken apart, and the insulation and number of turns a t that point were varied. This was repeated until no difference could be noted by measurement of the e. m. f. with a Brown portable potentiometer reading to 0.01 mv. (corresponding to 0.2' F.). Several different methods of attaching the thermocouple tips to the metal surface were tried. It was impossible to detect any difference in the reading of a couple with imbedded leads, as advocated by Colburn and Hougen (6), and of one from which the leads were taken off directly into the solution. This was due to a combination of sereral factors: (1) Small thermocouple wires (No. 30) were chosen. (2) The wires were led into a solution which, in most cases, was only a few degrees lower in temperature than the heating unit. ( 3 ) The wall of the brass pipe was 1/8 inch thick (0.79 inch i. d., 1.04 inch 0. d.). As a consequence, the heat loss by conduction along the thermocouple wires was negligible, and, in addition, minute differences in the surface temperature were equalized by the high conductivity of the tube. As a precaution, however, the leads of the thermocouple placed in the middle of the tube were imbedded for a short distance from the tip, and this thermocouple was opposed to the one placed in the solution 0.5 inch from the tube and in the same horizontal plane. Temperature differences were thus read directly, and the uniformity of the surface temperature checked by reading the other four thermocouples. Power supply to the heating unit was regulated by means of a water-cooled rheostat and measured by a calibrated ammeter and voltmeter. The length of the pipe was 0.328 foot and the external area of the unit was 0.10 square foot. The resistance of the heating element was approximately 14 ohms, which made it possible
1383
to supply heat a t any rate up to 24,000 B. t. u. per hour per square foot of heating surface. GENERALAPPARATUS.The apparatus set up was very simple. It consisted essentially of a lagged boiler containing the liquid to be evaporated and a glass bell jar, inside of which was suspended the heating unit. A vapor line from the top of the bell jar carried the vapor generated by the heating unit to the external condensing system from which it could be withdrawn and measured, or returned to the boiler. Condensation in this vapor line was prevented by jacketing it with vapor from the boiler itself, The latter vapor stream was carried to a separate condenser and returned to the boiler. A clearance of 0.5 inch between the bottom of the bell jar and the bottom of the boiler provided circulation between the external liquid and the liquid in the interior of the bell jar. At the start of a run the liquid was brought to the boiling point by means of the boiler winding. After equilibrium conditions were obtained, the current in the heating unit was turned on. After constant conditions were again obtained (usually 30 minutes) readings were taken of volume of distillate, temperature difference, amperage, voltage, etc. After each run the heating unit was removed and the surface polished. Appreciable tarnishing occurred only with methanol, n-butyl alcohol, carbon tetrachloride, and the sodium sulfate solution. Preliminary runs with the heating unit suspended in the bell jar as shown and with water as the liquid, showed that the discrepancy between the heat s u p plied to the heating unit in the form of electrical energy and the heat recovered in the condensed vapor averaged less than one per cent. These results showed that the external heat losses were negligible and gave assurance as to the validity of the experimental technic employed.
2
5
i 0
30
FIGURE3. HEATTRANSMISSION COEFFICIENTS FOR VARIOUSBOILINGLIQUIDS
MODIFICATION FOR SALTSOLUTION. Trouble was experienced in the evaporation of salt solutions because of the fact that there was a tendency for the nonvolatile component to
1384
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 24, No. 12
TABLE I. PHYSICAL PROPERTIES OF LIQUIDS AT NORMAL BOILINQ POINT LIQUID Water 9.6 % NazSOc soln. 9.1% NaCl s o h .
SP. HEAT,C 1.0"
sucrose s o h . Methanol Kerosene Gasoline CCh n-GHsOH Literature citation (8). b Measured. e Literature citation (7). d Literature citation ( 9 ) .
0.9Ob 0.92"
0.90" 0.900 0.81" 0.62z" 0.65 0.54C 0.212" 0.832"
SP. GR.,S 0.958" 1.045) 1.03) 1.07) 1.055) 1.155b 0.75'3 0.793, 0.739b 1.50a 0.744"
VISCOSITY, Z 0.284" 0.368) 0.347" 0.356) 0.475) 0.576 0.334" 0.30) 0.32b 0.497" 0.421"
THERMAL CONDUCK 0.414d 0.413" 0.403" 0.366" 0.356a 0.377" 0.119' 0.08/
TIVITY,
0 . os/ 0.064" 0.092"
SURFACE TENSION,y 0.130" 0.131" 0.132" 0 . 128" 0.132O 0.1515 0.04190 0.0332~ 0.03060~ 0.0441" 0.0364"
LATENTHEAT OF VAPORIZA- SZDZK TION,
L
972
... ... ...
... ... ... ...
470
83.5 258
za 18.0 9.8 11.1 10.0 4.0 29.4 19.4 20.0 14.5 13.3 7.37
Z1 -
SDr 0.622 0.946 0.85 0.885 1.56 1.79 3.4 3.39 4.35 3.5 6.28
E
K 0.687 0.801 0.79 0.852 1.2 1.22 1.75 2.44 2.16 1.75 3.8
' Literature citation (6).
f
Taken as constant..
.
o Taken as the surface tension of the normal paraffin hydrocarbon having the boiling point nearest t o that at which thesample boiled in the apparatus.
concentrate inside the bell jar. For these runs the bell jar was removed and the heating unit suspended in the main body of the liquid. The recirculated liquid entering the boiler from the condenser was preheated to boiling temperature by passing it through several turns of copper placed a t the circumference of the boiler. Obviously, with this arrangement no direct measurement of the amount of evaporation could be made. Therefore, the coefficient of heat transmission could be calculated only from measurement of electrical energy input to the heater, and the temperature difference between heating surface and boiling liquid. In order to justify the use of this modified arrangement, runs were made both with and without the bell jar, using several pure liquids in the boiler, The values for electrical energy input and the corresponding values of temperature differences, obtained by using both arrangements, checked with sufficient precision as to justify either method for the measurement of the coefficient of heat transmission. Naturally in all cases where this concentration effect was not appreciable-i. e., for pure liquids-the bell jar was used in order to provide an independent check on the heat input to the heater.
cleaned and the thermocouples and cleanliness of the heating surface rechecked, using water. The values for the physical properties of the liquid and the sources of information are listed in Table I. An inspection of the data shows the range in values of the main variables to be: h, from 100 to 4000 B. t. u. per hour per square foot per O F.; At, from 2.2 to 22" F.; viscosity, 0.284 to 0.57 centipoise; thermal conductivity, 0,064 to 0.414 B. t. u. per (hour)(square foot)(' F. per foot); and surface tension from 0.0306 to 0.151 poundal per foot. The errors involved in the values assigned to the other quantities are not so definitely known. However, with the exception of values for surface tension and thermal conductivity of the gasoline and kerosene, the error should not be greater than 10 per cent of the actual value. A considerable error in surface tension values causes only slight error in predicting the value of h. Moreover, as shown later, correlation of the data is obtained with the omission of surface tension. Viscosities at the boiling point were obtained by extrapolation from measurements a t various temperatures in an Ostwald pipet, calibrated with a sugar solution.
CORRELATION OF DATA
1 FIGURE4. COMPARISON OF DATAON WATER METHOD OF CHECKINQ RESULTS. A partial list of the data obtained is given in Table 11. Twelve different runs were made for each of the following liquids: Water, methanol, carbon tetrachloride, n-butyl alcohol, 26 per cent glycerol solution, gasoline, kerosene, 25 per cent sucrose solution, 9.1 per cent sodium chloride solution, 9.6 per cent sodium sulfate solution, and 26 per cent sodium chloride solution. Each run was performed in duplicate, and after a series of runs had been made with one liquid, the apparatus was
As a first step in the correlation of data, the coefficients obtained for the various liquids were plotted against the temperature difference on logarithmic paper as shown in Figure 3. An inspection of the diagram shows that the data for the liquids chosen can be represented by a system of straight lines, all of which have the same slope of 2.4. The absolute values for the coefficients of heat transmission corresponding to a given At vary with the physical properties of the liquid, but the rate of increase of h with increasing At is constant. A possible explanation for this constancy of slope is that the rate of change in physical properties of the liquids with change in temperature is practically the same. Similar slopes were obtained by Linden and Montillon (11) and by Jakob and Fritz (10) for water alone. The close agreement between the results of the present study and those of the investigators mentioned, in spite of the wide difference in the type of apparatus employed, is rather remarkable. A comparison of the data is presented in Figure 4. With the exception of curve 5 the data represent heat transmission coefficients from fresh copper surfaces to water boiling a t 212" F. Curve 5 represents the coefficients obtained with a chromium-plated copper surface and water. Although Linden and Montillon calculate their slope to be 2.5, an examination shows that their data can be represented just as accurately by a line with a slope of 2.4. The profound effect of surface conditions on the absolute values of the heat transmission coefficient is brought out in Figure 4. By substituting a grooved copper surface (curve 1) for a sanded copper surface (curve 3), an approximate fortyfold increase in heat transmission coefficient was obtained.
I N D U S T R I A L A .N D E N G I N E E R I N G C H E R.I I S T R Y
December, 1932
1385
TABLE11. EXPERIMENTAL A N D CALCULATED DATAON HEATTRANSFER COEFFICIENTS &/ea
Rus €3.
t . u./hr.
&/Ob
B . t . u./hr.
W A T E R (HEATISG
4 5
377 481 586 836 1130 1460 1880 2290 95 215 370 400 606 701 830 991 1140 1300 1450 1660 1870 2070 2280 987 690 1300 1640 2080
6
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
F.
RUN
h
At
s q . ft./
O
F.
KSIT HORIZOSTIL)
377 480 585 838 1130 1460 1880 2300 93 212 377 401 596 708 837
1290 1650 2090
3.2 3.3 3.6 4.1 4.7 5.1 5.5 5,s 2.5 2.9 3.3 3.3 3.8 4.0 4.1 4.4 4.7 4.9 5.1 5.2 5.5 5.6 5.8 4.4 4.0 4.9 5.2 5.6
470 572 698 826 971 1120 1270 1470 1650 1870 2070 469 574 703 826 972 1120 1270 1460 1650 1860 2060 26%
3.6 4.0 4.1 4.3 4.4 4.4 4.5 4.8 4.9 5.1 5.2 3.7 4.0 4.1 4.3 4.4 4.5 4.7 4.8 4.9 5.1 5.2 91 216 380 481 596 716 852 994 1130 1290 1450 1650 1870
60
61 62
63 64 653, 65b
2.7 3.6 4.1 4.4 4.7 4.9 5.2 5.5 5.8 6.0
6.3 6.4 6.6
65 67 68 69 70 71 72 73 74 75 76 77
91 210 367 475 580 705 844 988 1130 1280 1460 1660 1860
93 212 374 478 585 708 839 994 1120 1290 1460 1650 1870
7.7 10.7 13.2 14.4 15.0 15.8 16.2 17.0 17.5 18.2 19.0 19.8 20.3
93 202 78 208 376 480 678 708 830 981 1120 1290 1440 1640 1860
100
101 102 103 104 105 106 107 108 109
QASOLINE
110 111 112 113 114 115
90 46 105 212 292 381 483 563 709 840 979 1140 1310 1480 1440 1660 1860
93 47 107 212 294 381 484 586 713 839 989 1130 1300 1470 1460 1650 1870
5.6 4.5 6.0 7.4 8.5 9.5 10.3 11.0 11.5 12.2 12.6 13.2 13.7 14.1 14.1 14.5 15.0
sq. ft
f
/ O F
26%
440 760
9.1 11.5 13.7 14.7 15.9 16.6 17.4 18.4 18.9 20.0 20.6 21.4 22.0
100 180 280 330 370 430 470 540 600
650 700 770 850
(HEATING UNIT HORIZONTAL)
SUCROSE (AEATIIG
839 990 1130 1300 1460 1650 9 .1%
NaCl
8.0
10.1 11.7 14.6 18.1 19.8
120 210 330 580 802 950
93 212 381 484 586 713 839 989 1130 1300 1460 1650 9 6%
Na&Oa BY
150 151 152 153 164 155 NaCl
160 100 b
HORIZONTAL)
3.8 4.9 5.8 6.3 6.6 7.1 7.3 7.6 8.0 8.3 8.5 9.1
240 430 660
770 880 1000 1200 1300 1400 1600 1700
isoo
2.7 3.4 3.8 4.1 4.4 4.7 4.9 5.2 5.4 5.6 5.8 6.0
320 620 990 1200 1300 1500 1700 1900 2100 2300 2500 2700
2.5 3.2 3.6 4.4 4.1 4.5 4.7 4.9 5.1 5.4 5.6 5.9
370 670 1100 1300 1200 1600 1800 2000 2200 2400 2600 2800
BY W E I G H T (HEATING U N I T HORIZONTAL)
93 212 381 484 585 713 839 989 1130 1300 1460 1650 0
mxr
140 370 650 930
WEIGHT ( H E A T I S Q U N I T HORIZONT.4L)
93 212 381 586 484 716 839 989 1130 1300 1460 1650 26%
6.9 10.4 13.2 15.7
BY W E I G H T (HEATING UKIT HORIZONTAL)
132 133 134 135 136 137 138 139 140 141 142 143
120 196 281 331 390 448 520 580 640 710 760 830 920
690 780 860 950 1040 1020 1140 1250
93 212 381 484 586 713 839 989 1130 1300 1460 1650 1860
93 381 839 1460
120 121 122 123 124 125 126 127 128 129 130 131
330 610 920 1100 1300 1500 1600 1800 2000 2100 2300 2600 2800
620
2.2 2.7
XEROBENE (HEATING UNIT HORIZONTAL)
116 117 118 119
1300 1500 1800 2000 2200 2600 2800 3100 3300 3700 4000 1300 1500 1700 2000 2200 2500 2700 3100 3300 3700 4000
180 290 350 400 470 530
98 210
93 212 381 839 1460 1870
Y E T H l N O L ( H E A T I N G U N I T HORIZONTAL)
78 79 SO 81 82 83 84 85 86 87 88 89 90 91 92 95 96
F.
n - B U T Y L ALCOHOL (HE.4TING EXIT HORIZONTAL)
97 98 99
CARBON T E T R I C H L O R I D E ( H E A T I I G U I I T H O R I Z O N T I L )
66
B . t . u . hr.
B. 1. u.lhr.
N A T E R (HE.4TISG K K I T HORIZOATAL)
93 94
1200 1500 1600 2000 2400 2900 3400 4000 380 740 1100 1500 1600 1800 2000 2300 2400 2600 2900 3200 3400 3700 4000 2200 1800 2600 3200 3700
GLYCEROL B Y W E I G H T ( H E A T I N G U N I T HORIZOhTAL)
54 55 56 57 58 59
h
At
Q/Ob
B.t.u./hr.
WA'I?ER (HEATING UNIT VERTICAL)
32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
&/Sa
B. t. u./hr./
4.7 6.0 7.1 7.7 8.2 8.8 9.3 9.6 9.9 10.4 11.0 11.5
200 352 530 630 710 810 900 1030 1200 1200 1320 1400
Heat recovered. Electrical energy input,
The same authors found that a slight oxidation of surface Droduced a marked decrease in the liquid f ilm coefficient. The same effect has been observed by Pridgeon and Badger ( I S ) . The discrepancy between the values obtained by Linden and Montillon (curve 4) and by the present authors (curve 2) is undoubtedly due to the difference in the types of evaporators employed. With an inclined-tube evaporator
INDUSTRIAL AND ENGINEERING CHEMISTRY
1386
a considerable proportion of the total heat is transferred across a steam film inside the pipe, which would result in values much lower than those obtained for a boiling-liquid film. Moreover, as noted above, an almost imperceptible deposit of scale or difference in smoothness of surface causes
20
150 YO0
50
5
Vol. 24, No. 12
This method of plotting gives a system of lines representing the different liquids, all of the lines having a slope of 2.4.
For a given value of hD /(?)"there is a fivefold variation in the values of ( A ~ s ~ D * K ) / z ~ . If hD/K is plotted logarithmically against (AtS2D2K)/Z3, a similar system of lines is ob50 /mo /ma9 tained with the same slope (2.4), but with a wider variation in the position of the different lines. From these results it is evident that a dimensionally sound equation representing the data for all of the liquids used in these experiments is not obtained without the use of the variable surface tension. An equation omitting surface tension and expressing excellent correlation, was, however, obtained as follows: From Figure 3, h/(At)2.4 is shown to be a constant for all of the liquids Therefore, the following relation should hold: FIGURE5 . DATAPLOTTEDBY MEANSOF EQUATION 1 ~
roo
a marked difference in the values of heat transmission coefficients. The over-all coefficients obtained by Pridgeon and Badger (IS)and by Badger (3) for liquids of different boiling points, when plotted in the same manner, also gave straight lines, all of which had approximately the same slope. The slope in this case was approximately 1.0. Since the steam film coefficient decreases with increasing temperature drop, and the pipe wall resistance remains practically the same, it would be expected that the boiling film coefficient alone would increase more rapidly with temperature difference than the over-all coefficient. The experimental data, together with the calculated values of the corresponding heat transmission coefficients, are given in Table 11.
DERIVATION OF
By the trial and error method of solution of logarithmic equations, $' = 5.4, a' = 0.4, and p' = 1.2. Figure 6 shows the correlation obtained from the above equation rearranged as follows:
This equation, however, is not dimensionless.
5
/ i
EQU.kTIOKS
By the familiar methods of dimensional analysis (4,14) the proper correlation between the variables chosen was found to be:
The exponents a,0,and 4 for the three dimensionless groups were calculated from the experimental data by the solution of simultaneous logarithmic equations. The values finally derived were: = 0.38; a = 0.425, 0 = 2.39, and $ = 1.65. Figure 5 shows the excellent correlation obtained for all of the liquids used. The final equation is:
+
- _ - 0.38 (Ci)0.425 ( A t S 2 2 K ) 2 . 3 9(s__ . y ) l ''
(1) L
This equation, while dimensionally sound and representing good correlation of the experimental data, is rather unwieldy t? apply,. Moreover, accurate data on the physical properties of hquids at their boiling points are meager in many cases, especially values for surface tension. Omitting surface tension as a variable, the following relation should be obtained:
FIGURE6.
hT.4
I
PLOTTED BY MEANSOF EQUATION 2
I n Figure 7 the values of h alone are plotted as ordinates K CZ AtS2D2K ZZ 1.66 US. ~ ( g )( ~ ) 2 ' 3 g according to
(m)
Equation 1. This method of plotting shows more clearly the deviation in the values of the coefficient. hD -K_ - $ , ( ? ) a f ItS'2K)Pf These equations are offered merely as a means of correlating (2a) the data obtained in this investigation. No claim is made for AtS2D2K their general applicability. Dimensionless equations, used is plotted against 7for a long time in the correlation of heat transfer data, seem However, when hD on logarithmic paper, complete correlation is not obtained. to the authors the most logical method for the analysis of these
(
December, 1932
I N D U S T R I A L A h' D E N G I N E E R I N G C H E M I S T R Y
data. Moreover, it is not suggested that equally good correlation may not be obtained by the use of other diniensionless groups. I n addition, complicating factors, such as composition, cleanliness, position, etc., of the metal heating surface render the general prediction of values for the boilingliquid film coefficient impossible without exhaustive data.
1387
SAMPLE CALCUL-4TIONS
Run 101. Liquid being heated, n-butyl alcohol Density a t 20' C . (68' F.) = 0.81
Calibration correction to ammeter-voltmeter reading = 0.9765 Volume of condensate a t 20" C. (68" F ) = 376.0 cc. (22 cu. in.) Time of run = 18 min. Voltmeter readine = 50 volts Ammeter reading = 3.52 amp. At (av.) = 15.9' F. Electrical energy input = (50)(3.52) (0.9765)(3.414) = 586 B. t. u. /hr.
(582) = 370 B. t. u./hr./sq. ft./" F. (0.1)(15.9) -AtS-2DK - (15.9) (0.744) 2 (1.04) (0.0922) - 1. 2 3 (0.421)3 hD-- (370)(1.04) = 4180 K 0.0922 CZ-- (0.832)(@.421) = 3,8 K 0.0922 za (0.421)2 - (0.744)(1.04)(0.0364) = 6'28
h =
g/
(!?)0'425
x'6l)?&(
= 115
SOMEKCLATURE = heat transfer coefficient, B. t. u./ft./hr./' F. K = thermal conductivity, B. t. u./ft./hr./' F.) C = specific heat, B. t. u./lb./" F. S = specific gravity At = temperature difference, ' F.
h OF DATAWITH EQUATION 1 FIGURE 7. COMPARISON
I n deriving these equations, the value for D was taken as the outside diameter of the tube. It is recognized that this procedure takes no account of shape factor, which should be a function of a linear dimension of the heating unit. This shape factor would probably take care of end effects on the type of turbulence created in the boiling liquid. This factor should certainly enter into a general consideration of heat transfer to a boiling liquid, and an investigation of the effect of variation in the dimensions of heating tubes on the heat transfer coefficient is already under way in this hboratory. In the present instance, however, the reservation should be kept in mind that the values of h calculated from the above equations include no such shape factor. Several of the runs mere made with the heating unit in a vertical position, employing water as the liquid. While the data are not sufficiently comprehensive to warrant definite conclusions, they seem to indicate that h varies with At to some power greater than 2.4. In other words, with the heating unit in a vertical position, increasing the heat transfer to the liquid causes a greater increase in turbulence than with the heating unit in a horizontal position. Further work is also being done on this phase of the problem.
= = 2 = L = Q = e = y
D
surface tension, poundals/ft. diameter of heating unit, in. viscosity, centipoises latent heat, B. t. u./lb. heat transferred, B. t. u. time, hr.
LITERATURE CITED (1) Badger, W.L., IXD.EXG.CHEM.,14, 808 (1922). ( 2 ) Badger, W. L., "Heat Transfer and Evaporation," p. 67, Chemical Catalog, 1926. (3) Badger, W. L. "Heat Transfer and Crystallization,'' Articles IV and V, Swenson Evaporator Co., 1928. (4) Bridgman, "Dimensional Analysis," Yale University Press, 1922. ( 5 ) Bridgman, Proc. Am. Acad. Arts Sci., 59 (7), 141 (1923). (6) Colburn and Hougen, ISD.EXG.CHEM.,22, 522 (1930). (7) Fortsch and Whitman, Ibid., 18, 795 (1926). (8) International Critical Tables. McGraw-Hill. 1926 i9) Jacob, Ann. Physik, 63, 537 i1920). (10) Jakob and Fritz, Forsch. Gebiete Ingenieurw., 2, 435 (1931). ENQ.CHEM.,22, 708 (1930). (11) Linden and Montillon, IND. (12) Poste, E. P., Ibid., 16,469 (1924). (13) Pridgeon and Badger, Ibid., 16,474 (1924). (14) Smith, J. F. D., Ibid., 23, 416 (1931).
Grateful acknowledgment is hereby made to T. B. Drew and W. H. McAdams for helpful criticisms and suggestions.
RECEIVED M a y 20, 1932. Part of thesis submitted by E. R. Gilliland in partial fulfilment of the requirements for the degree of master of science in chemical engineering at the Pennsylvania State College. E. R. Gilliland's present address is Massachusetts Institute of Technology, Cambridge, Mass
CBIKA TESTSXEW PrloToR FUEL. Use of charcoal gas for operating motor trucks and busses was recently d e ~ o n s t r a t e da t a conference held in China. according t o information made available by the Department of Commerce. T h e conference was attended mainly by engineers and highm-ay commissioners from fourteen Chnese provinces. These men are reported to have been favorably impressed with the possibility of materially reducing motor truck and bus operating costs through the adoption of the n e x fuel. T h e demonstrations.were made with busses constructed on -4merican lipht truck rhaseir. The cost of the new fuel is said t o be considerably less than the prevailing price of other motor fuels. Any considerable ex-
pansion of modern transportation in the interior of China depends upon cheap fuel, especially in sections where motor fuel costs are prohibitive because of high transportation charges and tax impositions. Ilunan Province is already operating 200 motor busses, including 8 which are powered with charcoal gas, over 700 miles of M-ell-constructed roads. and plans have been made for the construction of 500 miles of additional roads with provisions for connection n.ith adjoininp provinces. The vehicles using charcoal gas in the demonstration had to stop for refueling every 20 or 25 miles. The refueling required but a fen- minutes, and about 5 gallons of charcoal on each stop. I n certain parts of interior China there is a plentiful supply of charcoal.
-4C'KNOWLEDGMEST
