I N D U S T R I A L A N D E N G I N E E R I K G C H E M I ST R Y
152
furoyl chloride.- The-yield was 5645 grams or 89.5 per cent4 of the calculated amount of furoyl chloride boiling a t 59.561.5' C./7 mm. The 'combined fore- and after-runs weighed 130-150 grams, in addition to a residue of about 100 grams of carbonaceous material. The low- and high-boiling fractions were found to contain much furoyl chloride which could be recovered by redistillation. It was convenient to transform it to furamide by adding it to concentrated ammonia water. Thus, furoyl chloride can be prepared on a semi-commercial 4
The yield is based on the amount of furoic acid available.
Vol. 24, No. 2
scale in 89.5 per cent yield by the action of thionyl chloride on furoic acid in benzene. LITERATURE CITED (1) Baum, Ber., 37, 2949 (1904). ( 2 ) Bogert and Stull, J.Am. Chem. Soc., 48, 248 (1926). (3) Frankland and Aston, J. Chem. Soc., 79, 511 (1901). (4) Gelissen and Van Roon, Rec. frav. chim., 43, 359 (1924). (5) Gilman and Hewlett, Iowa State College J . Sci., 4, 27 (1929) (6) Lies-Bodart, Ann., 100, 325 (1856). (7) Maxim, Bul. SOC. chim. Romania, 12, 33 (1930). RECEIVEDSeptember 23, 1931.
Heat Transfer in Stream-Line Flow II. Experiments with Glycerol THOMAS BRADFORD DREW,Department of Chemical Engineering, Massachuseits Institute
oj
Technology,
Cambridge, Mass.
N
I
T H E first paper of this fluids done were c o n s i d e r e d . NEW DA T A are reported f o r heat lransfer series (4,5 ) t h e p r e s e n t The n-butanol data, a l t h o u g h to glycerol as it jlows in dream-line motion a u t h o r , in collaboration clearly of less reliability than through a horizontal, standard '/B-inch iron-pipewith Hogan and McAdams, disthose for oil, seemed to indicate size copper tube, steam-heated over 61.75 inches cussed the then available data on a curve distinctly different from (156.8 cm.) of its lenglh. The apparatus used, heat transfer from pipe to fluid that defined by the oil data. As for the case of modified streampossible reasons for the discrepwhich is capable of unusual precision and has line flow of liquids in horizontal ancy between n-butanol and the negligible heat losses, is described in detail. round pipes. Most of the exhydrocarbon oil, differences in On a plot of (temperature rise + initial perimental work examined had Grashof number or in temperatemperature difference) us. Wc/kL, the runs b e e n c a r r i e d o u t in s t e a m ture-variation of viscosity were with a n initial temperature difference of 65" C. heated double-pipe a p p a r a t u s suggested. so that the temperature of the fall on a curfie substantially higher than do runs The need for heat-transmistube wall was, in each case, subsion studies in the region of with a n initial temperalure difference of 30" C. stantially uniform. Hence, the stream-line flow with fluids other Both curves are higher than 2he theoretical line than hydrocarbon oils, and in the r e s u l t s were p r o p e r l y com,for zero temperature difference. For a n initial turbulent range with fluids other parable with the t h e o r e t i c a l temperature difference of 65" C. the curue f o r than hydrocarbon oils, water, formula of Graetz ( 7 )and Nusselt (131 which *vresuuvoses a conglycerol lies below that for a hydrocarbon oil. and air, has long been apparent. - * stant temperature wall. It was Partlv to satisfv this need and shown that, although the theoretical equation failed consider- partly to supply additional data 0; non-isotGermal fluid fricably of representing the experimental results, the data of tion in pipes, work was started in 1930 by Harrison (8),under known reliability could be correlated with some degree of the direction of C. S. Keevi1,l to develop an apparatus that satisfaction by -the use of the dimensionless coordinates should satisfy the three following requirements: suggested by the theory-(h - t J / T - 11) and Wc/kL. In 1. It must he possible to make the necessary heat measurethe range of modified stream-line motion, for a given Wc/kL ments with substantially calorimetric precision and reproducibility. and wall temperature, the observed temperature rise was 2. Perfect operation must be possible with no more than larger than that predicted by the Graetz theory, which 1 gallon of fluid in the system so that the cost of the fluid may assumes a parabolic distribution of mass velocity. It was not limit one's choice. 3. Precise pressure-drop measurements must be possible over suggested that this effect was due to free convection currents. part of the heated length. The data at hand when the paper was written were, with the exception of a few tests on water, obtained by experimenta- During 1930-31, Botzow and Wilson ( 2 ) , continuing the work tion with hydrocarbon oils. In the two best and most com- under the direction of the author, completely rebuilt Harriplete investigations the same oil had been used. Therefore, son's apparatus and succeeded in satisfying the first two rethe authors could in no way detect with certainty possible quirements to a reasonable degree. These men were followed deviations between the results for various fluids. During in the summer of 1931 by Rynalski and Huntington (16) the discussion (4)Sherwood reported a series of experiments who, after making several noteworthy improvements in the by Kiley and Mangsen (12) on heating oil, and some work by equipment, carried out a successful series of runs using glycerol Petrie (14) on heating n-butanol. The first of these sets of as the fluid. Since these glycerol data show a distinct deviadata agreed well with the empirical curve by which the tion from the line given previously for oils, and are of an authors had represented the results of Holden (9) and of T h i t e unusually high order of reproducibility, it has seemed desirable (16), both of whom worked with a similar oil. Since Kiley t o publish them immediately and to describe the apparatus and Mangsen had used several different lengths of pipe, the with which they were obtained. agreement showed that variations in pipe length were properly 1 A t present professor of chemical engineering, Oregon State Agriaccounted for by the proposed method of plotting if similar cultural College, Corvallis, Ore .
I
APPAHATUS
The fundamental idea noon which the desien of the anparatus is based was deve1;ped during the stu& of another problem in this laboratory---that of the peripheral variation of tlie heat flux from the outer surface of ail internally heated pipe (6). A central pipe contaiuing the cold fluid is surrounded by a steam jacket whicli is placed vithin a larger steam jacket. Condensate formed on the outer wall of the central pipe can be collected separately from the condensate in the lareer steam iacket. In this way, if dry steam is s u p plied to t h e smaller jacket, the heat transferred by it to the outer walls of the inside pipe and thence t*, the fluid can be determined with precision, since the usual large c o r r e c t i o n for heat lossesto the morn is made negligible. The necessity for thus measuring the quantity of h e a t t r a n s m i t t e d t o tlie Auid arises from t h e difficulty of e n s u r i n g perfect mixing of the liquid before the thermometer a t the outlet of tho heat exchanger is r e a c h e d . I n stream-line flow experiments little reliance can be placed upon the rise in fluid
temperature as nieasured directly, unless heat-balance data accuracy are to serve as a TESTSECTION.Figure 1 shows the heat exchanger in its present state. With the exception of air vent 2, which has heen added since the completion of their work, the apparatus is as it was used by Ityiialski and Huntington. The fluid to be heated passes through the standard */s-ind iron-pipe-ske drawn copper tube, M , the dimensions of which are given in Table I and shown in Figure 1 (b). At 5 inches (12.7 em.) and a t 01 inches (154.9 cm.) from the inlet, four small holes, 90" auart, are drilled throukh the tube wall to serve as pressure taps. About each set of holes is a piezometer ring which was constructed by reami n g o u t a '/*-inch brass T until it would slip over the copper pipe, arid then soldering it in place oyer the holes w i t h the side outlet projecting u p ward. Five thermocouples, A , B, C, D, and E, are affixed to the outer surface of tbe pipe a t the locations shown. All except D are on the upper side of tlie pipe. D is d i a m e t r i c a l l y opposite C. The c o p per pipe extends horiOf
154
INDUSTRIAL AND ENGINEERING CHEMISTRY
zontally through the slightly inclined inner steam jacket, S, which communicates by the opening, 0, with outer jacket, J . The inner jacket, IC', is made up of three pieces of standard 11/2-inch brass pipe and two standard brass T's with 3/cinch side outlets, arranged as shown in Figure 1 (a). One-hole rubber stoppers set in the side outlets of the T's permit the passage into the space between jackets N and J of the two copper-tubing pressure leads. Three small holes in the central section of brass pipe are provided for the various thermocouple wires. The opening, 0, 3'/2 inches (8.89 em.) long by 11/2 inches (3.81 em.) wide, is prevented by a sheetbrass shield from admitting any drip from the top of the outer jacket, J . The shield is supported about midway between the two jackets by short posts (not shown) that rise from jacket N . There is no direct thermal contact between the shield and the outer jacket. By soldering on pieces of heavy copper wire, a small bead (somewhat exaggerated in the diagram) was formed about the outer edges of opening 0. Thus any drip that might fall on the outside of jacket N is prevented from flowing into the opening. The ends of the jacket, N , are closed by l/l&ch thick brass disks, soldered in place, through each of which the copper pipe, M, passes by way of a suitably located hole. The rubber stoppers, X, serve to insulate pipe 111 from jacket N . The heated length is measured between the inner faces of the stoppers. A l/r-inch copper tube conducts the condensate out of the lowest point of the inner jacket to a mercury seal (not shown), which is immersed in an ice bath. The outer steam jacket, J , consists merely of a short length of standard 3l/tinch iron pipe, closed by two standard pipe caps. The caps are drilled and tapped for ll/tinch pipe so that the ends of the inner jacket may be screwed into them. The means of egress for the thermocouple wires and pressure leads, of steam admission, and of condensate withdrawal are obvious from the diagram. A small opening (not shown) in the right-hand pipe cap leads to a manometer for the measurement of steam pressure.
Vol. 24, No 2
TABLE I. DIMENSIOIVS OF COPPER PIPE CM.
INCEES Inside diameter Outside diameter Total length Heated length Unheated length a t eaoh end Distance, inlet to thermocouples: A B C and D
E
Distance, inlet to pressure tap, F Distance between pressure taps, F and G Ratio, heated length t o inside diameter
0.281 0.405 66.0 61.75 2.13
0.714 1.029 167.6 156.8 5.4
0.63 3.0 33.0 63.0 5.0 56.0
1.6 7.6 83.8 160.0 12.7 142.2
220
Bakelite calming section: Inside diameter OutRide diameter Length runs 1-29 Length: runs 30-42
0.281 0.403 22.50 22.13
0.714 1.023 57.2 56.2
THERMOCOUPLES. The thermocouples on the wall of pipe M are junctions between No. 30 cotton-covered constantan wire and the metal of the tube, which serves as the second lead. The couples were attached by a method essentially that of Colburn and Hougen (3): A longitudinal slot 1 inch in length, and in width and depth equal to the diameter of the constantan wire, was cut in the surface of the copper. The insulation was removed from the tip of a piece of the wire, the cotton covering of which had been first impregnated with Bakelite varnish, and the wire was pressed into the slot. A drop of solder placed where the wire was bare formed the junction. Any excess of solder or projecting insulation was removed with fine emery cloth. In order to prevent the possible displacement of the thermocouples during the assembly of the apparatus, the insulated constantan wires were twisted once about the copper pipe at some distance from the junction. The thermocouples were calibrated in place.
AUXILIARY EQUIPMENT. The piping system by which the working fluid is delivered to and withdrawn from the test section is of brass or bronze, except for a short sight-glass by which suspended matter may be detected, and a calminglength of Bakelite tubing which precedes t h e copper pipe, M . The joints are made tight wherever necessary by solder or by
TABLE 11. DATAAND CALCULATIONS OF RYNALSKI AND HUNTINGTON (7)
(8)
(41
(5)
(6)
t2
TA
TB
TC
TD
OC,
O C .
'C.
OC.
(9)
(10)
(11)
(12)
TE
T
QS E . t . u.
QO R . t . u.
OC.
"C.
Hr.
Hr.
Q,q
WALL TEMPERATUREB
O
c.
(13)
-P5
(14) t2
-
(15) I1
7T T i %
We TL
hd k
h B . t . u. (Ft.*)(' P . ) ( H r . )
dc P
T - ti = 30' C. (approximately) 3.41 100.3 316 24.8 13.6 290 8.2 0.875 6.91 100.3 434 4.72 34.3 19.7 0.836 10.32 416 4.2 5.94 43.1 27.5 100.1 592 0.760 15.2 566 4.4 33.0 0.698 19.3 6.56 47.7 99.9 697 666 4.5 7.10 51.5 44.9 100.0 800 3.9 0.575 27.6 769 66.5 7.88 57.2 99.8 961 957 0.4 0.432 44.8 8.29 60.2 109.2 99.6 936 935 0.1 0.311 70.5 8 . 2 1 59.6 109.3 70.5 99.7 942 927 1 . 6 0.309 T - 11 = 38' C. 84.63 74.5 99.7 100.1 100.0 97.6 99.9 960 926 3.5 0.596 26.2 7.09 51.2 35.4 26 36.13 62.03 T ti = 45' C. (approximately) 1353 8.08 58.2 41.0 0.457 42.9 74.93 65.0 98.6 99.0 99.6 94.5 98.9 1460 7.3 22 60.19 54.73 8.59 61.8 43.5 1470 74.24 65.0 98.6 99.9 99.5 95.0 99.2 1510 2.6 0.446 46.9 23 65.75 54.10 8.81 63.5 43.7 47.0 0.7 0.455 74.23 64.5 97.7 98.8 99.2 94.7 98.4 1489 1478 24 66.00 54.07 T - ti = 65' C . (approximately) 4.03 29.0 7.2 60.5 100.0 100.5 753 704 6.5 0.915 7.52 100.0 96.8 100.1 94.48 8 10.54 34.35 3.4 0.880 9.81 4.91 35.4 9.4 99.70 61.0 99.9 100.6 100.5 98.0 100.3 887 857 19 13.75 3fi.70 5.00 36.0 9 .5 3 . 6 0.885 9.88 92.63 6 0 . 5 99.6 100.3 100.3 97.7 100.0 904 871 18 13.88 36.23 1112 2.2 0.861 12.72 11.2 6.12 44.1 90.90 58.0 99.6 100.3 99.9 96.5 99.9 1137 9 17.90 34.90 14.12 12.1 2.2 0.839 6.48 46.6 98.8 57.5 99.6 98.7 99.0 1198 1172 88.76 17 19.88 35.51 95.6 53.2 12.7 0.785 18.01 7.42 84.93 52.5 98.8 100.2 1540 1487 3.4 99.6 96.1 99.4 13.6 7.95 57.0 1.4 0.761 20.4 83.00 51.5 98.8 100.1 99.6 96.5 99.4 16fi7 1643 7.85 56.3 15.3 83.03 5 5 . 5 98.7 1571 1548 1.5 0.747 20.7 99.5 96.0 99.3 100.1 59.6 8.31 15.8 1733 -0.3 0.693 24.6 79.10 52.5 98.7 100.0 99.2 94.7 99.2 1728 17.2 8.41 60.2 94.4 99.4 1814 1802 0.7 0.634 28.5 99.2 75.77 53.5 99.0 100.5 17.2 8.45 60.5 1831 0,628 29.0 99.2 94.5 P9.5 1834 0.2 53.5 99.1 100.4 75.33 29.8 8.90 63.7 17.4 97.3 92.5 0.2 0.639 74.50 50.0 97.3 98.7 97.7 1898 1895 64.9 16.8 31.5 9.07 1985 -1.3 0.519 97.6 92.1 72.80 97.0 98.7 97.6 1960 49.0 43.8 9.09 64.8 20.2 98.9 92.1 2174 -1.4 0.492 65.87 98.6 100.1 9 9 . 1 2144 60.0 9.11 65.0 20.3 44.0 2181 -2.5 0.491 98.9 92.1 65.88 99.1 2128 50.0 98.6 100.2 24.4 9.38 66.9 55.9 2276 -0.3 0.417 99.9 92.0 61.72 97.5 99.0 98.5 2270 50.0 24.5 56.2 9.30 66.3 2263 2290 1.2 0.413 92.0 61.36 9 7 . 5 99.0 98.5 50.0 100.0 0 P taken a t l ' l (ti tt) for 95 per cent glycerol from tables of L. V. Cooks, J. SOC.Chem. I n d , , 48, 279T (19291, who gives, for example, pso = 0.64, p70 = 0.27, P S O 0.12, pino = 0.084, where the subsoript gives temperature in C . and viscosity unit is the poise. 42 38 34 33 31 32 37 36
9.38 14.06 20.75 26.42 37.88 69.00 97.19 97.38
96.45 95.27 92.61 90.37 86.93 81.93 80.97 81.02
69.76 69.67 68.93 68.45 69.23 68.37 72.54 72.68
83.5 82.5 80.5 79.0 79.0 77.5 79.0 79.0
100.0 100.0 99.7 99.6 99.6 99.2 99.0 99.2
100.2 100.0 100.0 100.0 100.0 100.0 99.6 99.6
101.0 101.0 100.8 100.5 100.7 100.7 100.6 100.6
100.0 99.0 98.2 97.8 97.5 96.3 96.7 96.7
-
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
February, 1932
15 i
-
10 .-
Q
9
G
0.6 0.1
0.6
-
-
0.5 I-
0.4
-
0.3 -
F
0.
Til4 - 37.36
e
9
IO
20
15
40
30
RL wc
50
60
10
60
90 100
RISE/INITIAL TEMPERATURE DIFFERENCE) FOR GLYCEROL .4T SEVERAL FIGURE 3. PLOTOF Wc/kL VS. (TEMPERATURE INLETTEMPERATURES Wall temperature is about looo C.
a talc-sodium silicate cement. Progressive contamination of the heating surface has been so far reduced by using these materials of construction that cleaning of the copper pipe, although retained as a regular procedure, is almost unnecessary. The Bakelite calming section is insulated b> a vacuum jacket and buried in a box of loose magnesia lagging. The calibrated mercury thermometer a t the inlet of the calming section, as well as that a t the outlet of the copper pipe, is preceded by a motor-driven stirrer of variable speed. In experiments on glycerol, without steam in the jacket, no measurable rise in temperature of the working fluid was occasioned by the stirrers. In other respects the external equipment embodies no unusual features. The liquid under test map be either circulated through a calibrated orifice for measurement or discharged into a weighing tank. Suitable preheaters and coolers are, of course, included. Figure 2 is a photograph of the assembled apparatus.
EXPERIMENTS WITH GLYCEROL WORKINGFLUID.The glycerol used by Rynalski and Huntington in securing the following data was commercial c. P. g l y c e r ~ l . ~The apparent specific gravity (25"/25" C.) was initially 1.2488, as determined with a Geissler pycnometer. This corresponds to a water content of 5.12 per cent (1). A measurement of the refractive index gave an identical result for the water content. After twenty-nine runs, sufficient water had been picked up from the atmosphere to raise the percentage t o 5.75. At this point enough new glycerol was added to reduce the water content to 5.55 per cent. At the end of the experiments the amount of water present was 5.74 per cent. These slight variations in concentration had no discernible influence on the results. 2
Supplied by Lever Brothers, Cambridge, Mass
OPERATION.The heating medium in all the tests was slightly superheated (0.5"to 1" C.) steam which was delivered to the steam jacket a t such a rate that the pressure maintained therein was approximately 1 inch of water above atmospheric. The rate of flow of glycerol was determined by weighing the total quantity of liquid discharged during a given run. The runs varied in length from 20 minutes to 2 hours. h Leeds and Northrup portable potentiometer was used to read the thermocouples. The copper pipe was cleaned after runs 12, 19, and 29. OF GLYCEROL RUNSWITH No FLOW TABLE111. BLANK
RUN
CONDENshTE F R O M h S E R
J ~ C K E TN
Gramslhour 20 21
::!: f
Without vacuum jacket on calming eeation
30
0.94
With vacuum jacket
DATAAND CONPUTATIONS. In all, forty-two runs were made; they are numbered in chronological order. Of these, twenty-nine are listed in Table 11; and three "blanks," runs 20,21, and 30, during which there was no flow of glycerol, are shown in Table 111. Runs 1 t o 5, inclusive, were merely preliminary tests; the data for them are either incomplete or known to be erroneous in some particular. The operating conditions during runs 25, 27, and 35 fluctuated so widely that precise measurements were impossible; hence these runs are not reported. Runs 28 and 29 are omitted because they were made with a high inlet temperature (82" C.) and a t low rates of flow, prior to the installation of the vacuum jacket on the calming section. This jacket was used in runs subsequent to and including the thirtieth. The runs tabulated in Table I1 are given, for each inlet temperature level, in order of increasing mass velocity. The temperatures in columns 3 t o 9, inclusive, are arithmetic averages of from three to seventeen readings, depending on the length of the run. The wall temperatures reported in
INDUSTRIAL AND ENGINEERIKG CHEMISTRY
156
columns 5 to 9, inclusive, were found by averaging the readings of the potentiometer and finding from a calibration plot the temperature corresponding to the average. The mean wall temperature, T, was computed by the rule: T
=
f
[T"
+ 51 (Tc +
TD)]
KO weight was given to thermocouple, A , because its location is not within the heated length. The readings of thermocouple, E (column 9), were consistently low. This is now believed to have been caused by the accumulation of air in the right-hand end of jacket N [Figure 1 ( a ) ] ,for air vent 2 was not installed until the work with glycerol had been completed. I n runs subsequent to the installation, couple E has agreed substantially with C and D. If an air pocket was
Vol. 2E, No. 2
g~ = hrLd At,,.
where At,,,
=
T-
1
(t2
+ tl)
Figure 3 is a plot of columns 14 and 15 of Table 11, with Wc/liL as abscissas and (tz - t l ) / ( T - tl) as ordinates. A plot of h d / k vs. Wc/kL is shown in Figure 4. Rynalski and Huntington recorded the pressure drop due to fluid friction in the test length. These data are not reported here, because the manometric system in use was so sluggish, on account of the high viscosity of the glycerol, that satisfactory readings were practically impossible to obtain.
DISCCSSION OF RESULTS
Reference to Figure 3, on which the run number is given beside each point, shows that the observations for a single initial temperature difference lie on a well-defined curve. The curve is lowered bodily when the temperature difference is descreased, or, since the wall temperature was uniformly about 100' C., when the inlet temperature of the glycerol is raised. All the points are above the Graeta theoretical curve, which is that based on a parabolic mass-velocity distribution and hence on a zero temperature difference. All are below the line, C, used in the first paper of this series ( 5 ) to represent 20 30 40 60 80 IO0 A the results of Holden and White for Velocite B oil. The KL high degree of reproducibility attained by Rynalski and FIGURE 4. PLOTOF hdlk vs WclkL m o h f DATAON GLYCEROL Huntington may be best appreciated by comparing Figure 3 BY RYNALSKI AND HUNTINGTON of this paper with Figure 1 of the earlier article ( 5 ) , a t the h is baaed on an arithmetio mean, A 1 same time remembering that the present plot is drawn t o a truly the cause of the low readings so that the surface tem- scale between two and three times as large as was the earlier perature was actually as recorded, by referring to Figure 1 graph. ( a ) it appears that a maximum of one-sixth of the length of The vertical spread between the two curves, A and B, the heating surface might have been a t the relatively low tem- varies from about 5 per cent a t the extreme left of Figure 3, to perature listed in column 9. An average T, computed by 13 per cent a t the right. This deviation would be almost giving T Ea weight of one-sixth, differs but slightly from the within the experimental error for all data heretofore available. value found by the rule used. The horizontal spread varies from 50 per cent for small values The heat, QS, given up by the steam to pipe M is calculated of TVc/kL to about 20 per cent for large values. If the data from the weight of condensate in the inner jacket, N , after were to be recalculated, using the value of tz - tt computed subtracting the condensate collected in the blanks. The from the weight of steam condensed instead of using the correction, which is almost negligible, was taken as 3.6 directly measured rise in fluid temperature, both curves in grams per hour in runs 6 to 29; and as 0.9 gram per hour in the Figure 3 would be raised slightly by an amount that decreases later runs (Table 111). as Wc/kL increases (Table 11, column 13). However, the The specific heats, c, used in computing the values of possible correction is practically the same in magnitude and Wc/kL in column 15, as well as in obtaining the heat picked direction for each curve a t those values of Wc/kL where the up by the glycerol, are taken from the values given for 100 shift would be appreciable; hence the effect of the change in per cent glycerol by the International Critical Tables ( I O ) . basis would be merely t o make the curves A and B more It is possible that these values are slightly too low for the 94.5 nearly tangent to C a t small values of Wc/kL without causing per cent glycerol used by Rynalski and Huntington. How- a substantial alteration in the spread. Somewhat similarly, ever an estimated correction (doubtful a t best) was found to the result of changing, in any reasonable manner, the chosen be less than the probable error reported for the data on the method of finding the average wall temperature, T, would be pure liquid a t the temperatures involved (40-80" C.). The t o shift both curves simultaneously in the same direction value of c used in the calculations was taken a t the arith- without reducing the spread appreciably. This would occur metic mean of the terminal temperatures of the fluid. because the wall-temperature distributions are similar for the In finding the quantities Wc/kL and hd/k, the values of k various runs. The measurement most likely to be erroneous employed were those found by Kaye and Higgins in 1928 (11): is that of the wall temperature. Even if that determination is supposed doubtful by the improbably gross amount of B. t. u. kr = 0.163 (1 0.00053t) (ft.) (hr.)(" F.) =+=lo C., the ordinate of a given point would be altered by only about =t4 per cent in the worst case. where t = Centigrade temperature From these considerations it appears that the deviations At the higher temperatures (80" C.) the figures reported in the between the sets of data for the different inlet temperatures International Critical Tables are 18 per cent greater than the are considerably beyond the experimental error of the present results of Kaye and Higgins, and are believed to be of inferior work, unless it be supposed that the specific heat, c, and theraccuracy. The "density" of Kaye and Higgins' glycerol was mal conductivity, k , are grossly incorrect. I n the case of the 1.25 at 18" C. As in the case of the specific heat, the value latter physical property there may be some doubt as to the accuracy of the values chosen, as pointed out previously. of k was taken a t the average fluid temperature. The coefficient of heat transfer, h, which occurs in the To bring curves A and B together would require that the coefficient of temperature variation of k be negative and quantity hd/k of column 16 is defined by the relation-
+
