942
I
INDUSTRIAL AND ENGINEERING CHEMISTRY
The question occurs a t once, “Are there any legitimate fundamental common-sense reasons for the wide margin between these two groups?” The answer is clearly affirmative. For, while the so-called developmental group consists of products which have been subjected either directly or indirectly to competitive developments of a chemical or economic nature, the stabilized group is made up of products whose production and costs had been reduced many years ago to a comparatively stable basis. All three groups must be included in any general measure of price changes for the industry as a whole, but in view of the heterogeneity of the industry the precise significance of such an indicator is questionable. On the other hand, it could be argued that if the industry is to be broken down into groups of component parts, one should go the limit and draw no inferences from the price history of any part larger than a single product. But perhaps there is something in the story the figures tell, and a tendency to separate into two groups is plain. In short, from the point of view of the consumer, the contributions to economic progress made by the chemical industry have been outstanding. I n the increase in production, assumed equivalent to consumption, a composite of leading chemicals outdistanced all competing industries. Similarly, in the improvement in net exports the industry was far ahead of the field. Finally, although the average price reduction for the industry as a whole was somewhat less than that for the reference standard of all industries, examination of the components used in the preparation of the Chemical & Metallurgical Engineering index revealed that a n important group of so-called developmental chemicals showed, as a whole, an average price reduction second only to rubber, an industry whose principal raw material has undergone a 60 per cent decline in price.
Conclusions Concrete statistical evidence has been submitted to show that, relative to other leading industries, the chemical industry has established an outstanding record of achieve-
VOL. 30, NO. 8
ment during the last few years in direct contributions to economic progress. The progress made by the industry in the satisfaction of man’s material needs has been compared statistically with the showings of other industries. In each of the analyses the performance of the chemical industry has been outstanding. It led the field for progress achieved both in employment and in pay rolls, and its showing with regard to wages was well above average and not far short of the leaders. It was the preeminent industry in regard to improvement in profits. Its progress in consumption, or production, was well ahead of the other industries; it was in the lead in net exports and an important part of the industry was in the front rank of all industries in reductions in prices. On the basis, therefore, of direct contributions to economic progress, measurable in pounds and dollars, the chemical industry has done more to improve the status of labor, of capital, and of the consumer than any of the leading industries with which it has been compared. T o this concrete statistical showing there should be added the immense but immeasurable benefits arising from the hormonelike importance in our economy of relatively minute proportions of certain chemicals, such as rubber antioxidants in automobile tires and chlorine in water purification, which do much more than can be shown by figures to increase the satisfaction of man’s material needs.
Literature Cited (1) Chem. & Met. Eng., issue of September, 1937, on “Facts and Figures of Am. Chem. Ind.,” and statistics in each issue. (2) Ibid., 44, 541 (1937). (3) Haynes, Williams, “Chemical Economics,” p. 11, New York, D. Van Nostrand Co., 1933. (4) IND. ENG.CHEM.,26, 3-10 (1934); 28, 153-8 (1936); 30, 7-14 (1938). (5) Morrison, A. C., “Man in a Chemical World,” p. 41, New York, Charles Soribner’s Sons, 1937. (6) Ibid.,p. 113. Presented before the generalmeeting at the 95th Meeting of the American Chemical Society. Dallas, Texas, April 18 t o 22,
R W I D I V ~May D 20, 1938. 1938
Heat Transfer Coefficients in Staggered Tube Banks INFLUENCE OF TUBE SHAPE
T
HE widespread use of air conditioning, the continued popularity of air dryers, and the increased use of economizers and similar methods of recovering waste heat have emphasized the importance of methods of heating or cooling air and waste gases. In all of these processes it is necessary to circulate and alter the temperature of large volumes of gases. The design of any piece of heat transfer equipment to heat or cool large quantities of air should, therefore, arrive at some compromise between the pressure drop through the apparatus .and the rates of heat transfer obtained per unit area of surface. It has been established that the rate of heat transfer is proportional to some power of the pressure drop for
C. C. WINDING Cornel1 University, Ithaca,N. Y.
any one type of apparatus, so that theoretically it should be possible to design air heaters that would operate somewhere near the minimum point on a summation curve of power and eqiiipment costs. One of the most important types of heat transfer apparatus for heating or cooling gases is a bank of staggered tubes arranged in a duct so that the air passes normally to the tube bank. Heating steam, or the cooling medium, is passed through the inside of the tubes. Recently a few shapes other than round have been used in air heaters, usually flat plates with the rounded narrow edges facing the direction of air flow. The original purpose of this work was to investigate
AUGUST. 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
The heat transfer coefficients from condensing steam to air are given for staggered banks of round, oval, and strearnline tubes. Streamline tubes should give a much lower pressure drop through the tube bank, but the data show that this advantage is offset by lower coefficients of heat transfer in all rows except the first and second. The oval tubes give definitely lower rates of heat transfer than either of the other two shapes. The data for the round tubes are compared with the various relations that have been proposed to correlate the air film coefficients with the variables influencing the rates of heat transfer. For a constant film temperature the relation of thermal conductance and mass velocity has been expressed by the equation h = aGn,where u and n are constants. This type of equation does not fit the experimental data and does not agree with previous data.
the possible use of commercially available shapes that would decrease the pressure drop across the tube bank and yet give a high enough rate of heat transfer to make their use practical. The smoke pictures of Lohrisch (6, 7) indicate that there is less actual blanketing around streamline sections than for round tubes under conditions of isothermal flow. This fact suggested the use of streamline tubes, which were readily available commercially, in place of the usual round tubes, with the idea in mind that the better contact of the air around the tube would more than offset the lower rates of heat transfer due to the decreased turbulence. The streamline section would, in addition, cause a much lower pressure drop through the tube bank. Oval tubes were also available and were chosen as a possible compromise between the round and streamline shapes. Any benefits obtained from the use of shapes other than round would, of course, have to be of sufficient magnitude to offset the increased construction costs caused by the odd shapes. The common method of rolling-in the tubes in the tube sheet would be impossible with shapes other than round, and a more expensive welding process would have to be used.
Previous Work Hughes (6)measured the amount of heat transferred from condensing steam to air for single tubes of both round and streamline cross section. He found that the streamline tubes gave about 17 per cent greater rates of heat transfer than round tubes having the same area per foot. He also noted that when the streamline tubes were placed with the sharp side facing upstream, the rates were only about 50 per cent of the values obtained when they were properly aligned. These data indicate that the diameter term appearing in most of the equations (1, 2, 9, 10) for the fJm conductance of gases flowing normally to tubes and tube banks is justifiable only when the equations are limited to round tubes, and that the insertion of other shapes of equal width would change
943
the conductance greatly although the D term would remain the same. It should be realized that the data of Hughes apply only to single tubes, and the results cannot be extended to cover the case of tube banks. A review of the work on single tubes is beyond the scope of this paper, but the comparative value of the streamline shape as obtained by Hughes is interesting. Several authors have presented data and equations for banks of staggered tubes. Colburn (.2) plotted the data of six authors and found that the curve can be represented over the range of Reynolds numbers from 2000 to 40,000 by the following equation: = 0.33
($3
(&E)
-0.4
Reiher (IO) has done the most comprehensive work in obtaining data for tube banks. He used two different arrangements of tubes, staggered and in line, and two different tube spacings across the duct. His data were all obtained for the cooling of air by cold water running through the tubes. Reiher's results indicate that the spacing of the tubes across the duct has little, if any, influence on the conductance. Based on dimensional analysis, Reiher correlated his data by the expression:
This equation is valid only for banks of five or more rows, as he found that the conductance increased with the number ~f rows until the fifth row, after which it remained substantially constant, The Prandtl group was left out in this equation, but for air a t ordinary temperatures the value of this group would be nearly constant. McAdams (8) showed how this equation agrees with the data of five authors. Monrad (9) evaluated the viscosity and thermal conductivity items in the Reiher equation in terms of the absolute temperature and simplified the results as much as possible to obtain the relation : h =
1.75 G'/aT'*3 D'/3
His own data for pipe-still convection sections fit the same equation with the coefficient 1.6 in place of 1.75. Griffiths and Awbery (4 investigated the conductance for single tubes within tube banks, heating the experimental tube and those in the near vicinity. The tubes were heated by internal electrical resistance heaters, and the heat input was measured by the current consumed. A relatively wide spacing between the tubes in any one row was used; the ratio of tube spacing to diameter was 0.85. They found that the conductance increased up to the third row, after which it remained constant. A complete review of the literature will not be given here since both Colburn (2) and McAdams (8) summarized all the available previous work.
Apparatus and Procedure As mentioned previously, the streamline and oval-shaped tubing was available commercially. This tubing, as well as the round, was all drawn from 8. A. E. 1010 steel with a tolerance of 0.01 inch in the outside diameter dimension. A crosssection view illustrating the shapes and dimensions is given in Figure 1. The wall thickness was 0.065 inch in all cases. The dimensions of the oval and streamline shapes were such that the area per foot of tubing was the same as that of the round tubes. End plates carrying '/*-inch pipe nipples were welded to both ends of each tube.
INDUSTRIAL AND ENGINEERING CHEMISTRY
944
The apparatus employed in the present investigation is shown diagrammatically in Figure 2: Air was forced through the system from a blower with a capacity of 500 cubic feet per minute. The blower was connected to a 5-foot length of 3-inch pipe by means of a flanged reducer carrying a butterfly valve. The rates of flow of air were regulated both by this valve and a speed control on the motor driving the blower. Four feet from the entrance of the 3-inch pipe, a Pitot tube was installed to measure the rate of flow. The pipe was connected to the duct being used by a galvanized-iron reducer approximately 2 feet long. This tapered connection reduced the turbulence caused by the sudden enlargement. The duct itself was 5 feet long and 12 inches high, with a width that varied with the shape of the tubes it contained. The first row of tubes in any tube bank was 3 feet from the front end of the duct to allow for a calming section before the tube bank.
SHAPES OF TUBES FIGURE 1. CROSS-SECTIONAL The bank of round tubes consisted of eight rows containing alternate three and two tubes. The three-tube rows were set on 2-inch centers, with 1/2-inch spaces between each tube and l/dinch spaces between the two outside tubes and the walls of the d,uct. The two-tube rows had the same spacing between tubes, but each tube was offset from the tubes in the preceding row SO that the center of the tube coincided with the center of the space between the tubes in the adjacent rows; this arrangement has been described as a staggered-tube bank. The distance between rows was inch. In order to secure the same cross-sectional area in all the rows, wooden dummy half-tubes were placed against the duct walls in the two-tube rows. This arrangement gave a total duct width of 6 inches, 4'i2 inches of which were occupied by the tubes and 11/2 inches by the spaces between the tubes. The minimum cross section was constant for all rows and equal to '/8 square foot. BLOWER THERMOM ETCR DUCT PITOT TUBE
3" PIPE FIGURE 2. DIAGRAM OF APPARATUS
The oval and streamline banks were arranged so that the spacings between the tubes and between the rows were identical with the round tube arrangement. Half-tubes were inserted in the two-tube rows as before so that the minimum cross-sectionalarea was kept at 0.125 square foot. To accomplish this result, narrower ducts and different reducers were used for each shape, but the height and length of the ducts were the same as those used for the round tubes. Four rows of tubes were used in these banks. Figure 3 is a cross-sectional view of the duct showing a three-tube row of round tubes and illustrating the method employed to introduce the steam and collect the condensate: Steam passed from supply line a through a reducing valve and into separator b to remove entrained water. This separator was placed as close to the heating tube as possible so that the connecting line between the separator and the tube being heated was ap roximately a 12-inch length of l/d-inch pipe. This pipe was jageted with a length of 3/r-inch pipe forming a heater, c. With the valve arrangement, steam was supplied to the heater from the high-pressure side of the reducing valve so that higher pressures could be maintained in the annular space in the heater than
VOL. 30, NO. 8
existed in the internal pipe. With this arrangement it was possible t o supply steam to the tube being heated, f, at a temperature above the condensation temperature at the existing barometric pressure. By regulating the pressure of the steam in the heater, it was possible to raise this temperature as much as 2' F. The temperatures were read by thermometer d, placed directly in the steam line,.e, as shown. The entire supply system was insulated with standard 85 per cent magnesia pipe covering. Since the tube bank was narrow, the center tubes only were used to secure data. The end plates of the tubes were set into the wooden duct, g, as indicated. The mixture of steam and condensate from the bottom of the tube under examination was discharged through a special separator, It. This separator consisted of an inner cylinder, 10 inches high and 1 1 / 2 inches in diameter, set in and completely surrounded by an outer jacket 21/r inches in diameter and 10 inches high. The outlet ni ple from the bottom of the heating tube extended downward aiout 3 inches into the inner cylinder, so that any condensed water was thrown down into and retained in this cylinder. The uncondensed steam escaped through four l/c-inch holes at the top of the inner cylinder to the outer jacket and from the bottom of this jacket was discharged to the air through a 8/16-inch vent tube. Thus the water in the inner cylinder was surrounded by steam at the same temperature, so that neither condensation of steam nor evaporation of water could occur in the inner cylinder. The separator and the line connecting it t o the heating tube were insulated. Although thiR method of securing a dry steam supply and removing the condensate formed might not be satisfactory for large steam demands, it proved to be very suitable for the low rates of flow of steam required in these experiments. Results were reproducible within 2 per cent at the highest air velocities and within 3 per cent at the lowest air velocities. The operation of the apparatus was very simple. An initial period of about 30 minutes was allowed t o obtain constant conditions, with the valve at the bottom of the condensate collector open. At zero time this valve was closed, and condensate was allowed to collect for 20 to 30 minutes, depending on the rate of flow of the air. At the end of this time the valve was opened, and the condensate was drained into a tared beaker that contained approximately 150 grams of ice. The ice made the'weighing of the hot condensate much simpler, as enough cooling took place to prevent an appreciable loss of weight during the weighing. The Pitot tube manometer and the air and steam temperatures were read at least three times during each run to obtain average values. The heater on the inlet steam line was regulated so that the temperature of the entering steam was kept from 0.5" to 1" F. above its condensat i o n temperature. a This slight amount of superheat h a d no appreciable effect on the heat content of the steam, yet it made certain that no c o n d e n s a t i o n took place in the s u p p l y lines and b that dry steam was f u r n i s h e d to the tube.
Results A s u m m a r y of ' t h e data obtained in the various exp e r i m e n t s is presented in Table I. No a t t e m p t w a s made to m e a s u r e independently the t h e r m a l conductance of the air film.
FIGURE 3. CROSSSECTIONOF DUCT
AUGUST, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
TABLE I. SUMMARY OF RESULTS Row No.
lair
F. 1
2
3
4
5
6
7
8
tsteam O F
87.6 87.4 87.2 88.2 88.2 88.0 87.4 87.4 88.2 88.4 88.9 88.9 89.4 89.6 89.8 88.6 86.4 90.7 90.7 90.5 77.7 76.8 76.5 76.5 78.8 78.9 78.6 77.6 77.2 76.6 76.6 77.3 86.2 85.8 84.7 84.9
211.4 211.5 211.8 211.5 211.7 211.5 211.5 211.7 211.0 211.7 212.0 212.0 212.0 212.0 212.0 211.6 211.6 211.7 211.7 211.8 211.8 211.6 211.6 211.9 211.8 211.8 211.8 212.2 212.0 212.2 212.2 212.0 212.0 211.8 212.0 212.0
85.7 85.6 85.2 85.8 85.6 86.0 85.3 85.1 85.9 85.6 86.5 86.4 (86.7 86.5 86.9 85.5 83.5 83.5 87.1 86.5
211.2 211.7 211.7 211.7 211.7 211.3 211.7 211.3 212.0 212.0 212.0 211.8 212.0 212.0 212.0 211.6 211.6 212.0 211.6 212.0
82.9 82.9 82.5 83.1 82.7 82.9 82.2 81.9 82.4 82.6 83.5 83.5 83.5 88.7 88.7 81.2 81.0 84.0 83.3 81.9
212 211.5 211.3 211.3 211.7 212.5 212.5 211.8 212.2 212.8 212.0 212.0 212,o 212.2 212.2 212.0 211.6 211.6 211.6 211.6
At
4
U
c
B . t . u./ B . t . u./ghr.) L b . / ( h r . ) F. ( h r . ) ( t u b e ) ( s q , f t . ) ( F.) ( s p . j t . ) Round Tubes 609 536 473 403 327 758 665 610 566 509 907 811 735 631 545 888 835 747 645 570 975 897 768 655 977 871 783 656 965 853 742 622 899 786 71 1 581
12.5 11.0 9.7 8.3 6.7 15.6 13.6 12.5 11.7 10.5 18.8 16.8 15.3 13.1 11.4 18.4 17.0 15.7 13.6 12.0 18.5 16.9 14.5 12.3 18.7 16.6 15.0 12.3 18.2 16.0 13.9 11.8 18.2 15.9 14.2 11.6
11,000 9,400 7,520 5,740 4,000 10,700 8,800 7,300 6,200 5,000 10,660 9,240 7,470 5,550 4,060 10,480 9,360 7,360 6,190 4,660 10 500 0:100 6,800 4,700 10,580 9,050 6,870 4,670 10,760 8,780 6,910 4,440 10,670 9,130 7,200 4,770
125.5 609 126.1 553 126.5 479 125.9 409 126.1 348 125.3 775 126.4 679 126.2 613 126.1 592 126.4 539 125.5 837 125.4 741 125.3 662 125.5 581 125.1 512 126.1 796 128.1 742 128.5 652 124.5 577 125.5 520 Streamline Tubes 129.1 877 128.6 808 128.8 688 128.2 569 129.0 46 1 129.6 870 130.3 790 129.8 709 129.8 679 130.2 607 128.5 872 128.5 785 128.5 715 123.5 627 123.5 545 130.8 882 130.6 809 127.6 716 128.3 637 129.7 592
12.3 11.1 9.7 8.3 7.0 15.7 13.7 12.4 11.9 10.8 17.0 15.0 13.4 11.8 10.4 16.1 14.7 12.9 11.8 10.5
11,000 9,400 7,520 5,740 4,000 10,700 8,800 7,300 6,200 5,000 10,660 9,240 7,470 5,550 4,060 10,480 9,360 7,200 6,190 4,660
17.3 16.0 13.6 11.3 9.1 17.1 15.4 13.9 13.3 11.9 17.25 15.5 14.2 12.9 11.2 17.2 15.5 14.3 12.6 11.6
11,000 9,400 7.520 5,740 4,000 10,700 8,800 7,300 6,200 5,000 10,660 9,240 7,470 5,550 4,060 10,670 9,360 7,360 6,190 4,660
123.8 124.1 124.5 123.3 123.5 123.5 124.1 124.3 122.8 123.3 123.1 123.1 122.6 122.4 122.2 123.0 125.3 121 .o 121 .o 121.3 134.1 135.2 135.1 135.4 133.0 132.8 133.2 134.6 134.8 135,6 135.6 134.7 125.8 126.0 127.3 127.1
Oval Tubes 1
2
3
4
1
2
3
4
The over-all thermal resistance is the sum of the resistance of the steam film, the resistance of the tube wall, and the resistance of the film between the outside wall of the tube and the main body of the moving 'air stream. The resistance of the tube wall is small and constant. The resistance of the condensing steam film is small in comparison to the resistance of the air film but is not necessarily constant. Any possible variation in this value would, however, have no appreciabIe effect on the over-all refiistance. If a conservative value of 1000 is
945
taken for the steam film conductance, the sum of the resistances of the steam film and tube wall comprise only 2.5 per cent of the smallest over-all resistance. This value is so small that the over-all coefficient, if corrected for radiation, will be substantially identical with the coefficient for the air side.
1
2
3
4 ROW
5
6
7
8
FIGURE 4. VARIATION OF COEFFICIENTWITH NUMBEROF Rows FOR THREETUBESHAPES
If a relative coefficient of blackness of 0.80 is assumed for the steel tubes, the radiation correction amounts to about 160 B. t. u./(square foot) (hour) or 63 B. t. u./(hour) (tube). The data as given have all been corrected for this radiation loss. Inasmuch as the steam temperature was substantially constant and the temperature of the tube wall and surroundings nearly constant, the same radiation correction is applied in all runs. Because the over-all coefficient is so nearly equal to the air side coefficient, U is the same as the air film coefficient, h. The variation of the coefficient with the number of rows for all three tube shapes is shown in Figure 4. The data are given for an air velocity of 8000 pounds/(square foot)(hour), but the percentage variation is nearly the same for all velocities. The conductance of the round tubes in the first row is only 64 per cent of its maximum value, increases to 83 per cent in the second, and becomes constant in the third and succeeding rows except for a small decrease in the last two rows. For a velocity of 7130 pounds/(square foot) (hour), Griffiths and Awbery (4) found that the conductance in the first row of tubes was 61 per cent of that in the third row, a result that is in good agreement with these data. The effect of the lower coefficient in the first two rows would decrease with the number of rows for a complete tube bank, so that the conductance would increase only slightly after the fifth row, as indicated by Reiher's work.
I
FIGURE 5. DATAFOR ROUNDTUBES AGAINST MASS VELOCITY
PLOTTED
The higher conductances in the bank beyond the first two rows are probably caused by the added turbulence imparted by the preceding rows. Reiher found that a grid placed in front of the bank caused an increase in the conductance in the
946
INDUSTRIAL AND ENGINEERING CHEMISTRY
were of the same order of magnitude as the pressure drop SO that accurate data could not be obtained without redesigning the apparatus. An accurate micromanometer has been obtained, and the equipment is being rebuilt so that pressure drop measurements can be obtained. Any complete comparison between the round and streamline shapes would have to include information on the pressure losses caused by the two shapes. The results with the oval tubes were rather inconclusive. There are no data available that give the magnitude of the pressure drop across tubes of this shape, nor are there any smoke pictures to indicate the degree of turbulence that would exist. Apparently the oval shapes are definitely inferior to either of the other two for any practical purpose. I n both the Reiher and Colburn equations, the significant properties of the air are evaluated a t the mean film temperature. For any one pipe diameter and constant film temperature, both equations reduce to h = aGn
FIGURE 6. COMPARISON OF DATAOF VARIOUSAUTHORS
first row. Any obstruction producing additional turbulence would probably cause an increase in the air film coefficient. The data for the streamline tubes substantiate this explanation. The coefficient for the first row is only slightly lower than that for the following rows. The streamline shape does not impart as much turbulence to the air stream, so that a constant value is reached in the second row. The streamline tubes give a n air film coefficient about 40 per cent greater than the round tubes in the first row. This might be due to the decreased eddying around the tube caused by the streamline shape, which would permit better contact of the moving air stream around the entire outside surface of the tube. Drew and Ryan (S), however, reported experiments showing that the greatest heat flux occurred at the front and the back of round tubes. These data were for single tubes, but the tubes in the first row of a tube bank should not vary greatly from the single-tube conditions. If the highest rates of heat transfer around the periphery are a t the front and back of a tube, then it is difficult to see how the streamline shape could increase the rates of heat transfer so markedly. Reiher (IO) obtained data on the surface temperature distribution for pipes exposed to a stream of air, using thermocouples imbedded in the pipe walls. In each case the pipe was carrying cold water while heated air was blownpast it. His data show maximum rates of heat flow at the front of the tube and minimum rates a t the back. On the basis of these results the streamline shape might increase the heat flow because it decreases any eddying, etc., that occurs a t the back of a round tube. The work reported by Drew and Ryan appears to have been carefully done, however, so that their results are probably correct for single pipes. The changed conditions brought about by the entire tube bank may alter the conditions of the experiment to such an extent that it may not be possible to apply their data to even the first row of tubes in staggered banks. Additional work is in progress, and provisions to measure the variation in temperature around the tube will be made. It is unfortunate that aocurate pressure drop measurements were not made across the tube banks. With the small banks used, a very low pressure drop occurred. An attempt to measure this small drop with the apparatus available a t the time, showed that the fluctuations of the pressure in the duct
VOL. 30, NO. 8
where a is a constant including the values for the terms involving the properties of air a t the film temperature for which the equation is written. I n the experiment as performed, there is Rome variation in the mean film temperature with the rate of flow of the air, but this change is not great enough to alter the film properties significantly. If this is true, the thermal conductance in these data should vary directly with some power function of the mass velocity, provided all the possible variables affecting the heat transfer through the air fdm have been included in either the Reiher or Colburn equations. The data for the round tubes are plotted against the mass velocity in Figure 5. The values obtained for rows 3, 4,5, and 6 are the only ones that have been considered, since the coefficient varies with row position for the other rows but is substantially constant in this range. The data show a rather well-defined linear relation between the conductance and the mass velocity. Without attempting to explain this relation it is apparent that these data do not fit a n equation of the form, h = aG" (Figure 6 , curves BB and CC),which they must do if they are to conform with any of the previously men30
25
20 18
IG 14
h 12 IO
8
6
4
5
6
7
8 9 1 0
G x
16
15
20
25
30
FIGURE7. COMPARISON OF DATAWITH COLBURN'S RELATION
AUGUST. 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
tioned equations. This relation is not due to any peculiarities of the apparatus or method employed, since an analysis of Reiher’s own data reveals the same tendency. The data obtained by Reiher a t four different mean film temperatures were included in Figure 6, as well as the data obtained by the author and the few points given by Griffiths and Awbery. As the light lines through the data for any one constant film temperature indicate, the thermal conductance varies directly with the first power of the mass velocity when the other variables are held constant. Curves A A , BB, and CC are the equations of the various authors plotted a t the approximate mean film temperature (150’ F.) of the data obtained in this work. A comparison of the degree of curvature of these lines and that of any one set of data illustrates clearly that the data do not agree with the relations expressed by the
94 7
linear variation of thermal conductance with velocity, but the data are too few to draw definite conclusions. These experimental results should not be extended to other possible tube spacings and arrangements without additional data. The linear relation between the thermal conductance and the mass velocity has not been expressed as a definite mathematical equation because a great deal of additional data is needed over a much wider range of the variables involved before this can be done with any degree of surety. Work is under way a t present to extend the data over a wider range. It is recognized that expressions similar to the Reiher and Colburn equations are probably valid for single tubes, but the results obtained in this work throw some doubt on the advisability of attempting to adapt the singletube relations to staggered-tube banks, a t least without considering variables other than those usually included. With the data available it is difficult to conceive a relation that would correlate the data in a manner completely in agreement with the commonly accepted theories of heat transfer, but with the advent of more data it may be possible.
Acknowledgment
FOR STREAMLINE TUBESPLOTTED FIGURE 8. DATA AQAINST MASSVELOCITY
*
various equations. This does not mean that the proposed equations do not fit the existing data with sufficient accuracy for most purposes. Colburn’s relation fits Reiher’s data very closely if the corrections for variations in air film temperature are taken into account. Figure 7 compares the data with the Colburn relation using logarithmic coordinates. The data for rows 1, 2, and 3 were plotted on Figure 7, as well as Reiher’s data for the film temperature closest to that obtained in this work. The data for rows beyond the third fall so nearly on the same curve that slight discrepancies tend to mask the true shape of the curve. For this reason only the data for the third row were included. The Colburn equation is merely a close approximation of the curve that summarizes all the available data but is very nearly a straight line over the range considered. Both the author’s and Reiher’s data (Figure 7) show a considerably larger degree of curvature in this range. Reiher’s equation fits the author’s data even better than it does his own except a t the very low velocities. Monrad’s equation is probably not on the safe side for the evaluation of air film coefficients a t this temperature range, but does not give values greatly in excess of the data. Griffiths and Awbery obtained much higher values for the thermal conductance than those secured in this work. They isolated a single tube to test but heated all of the suqrounding tubes. With any ordinary tube spacing it would appear difficult to obtain the true temperature of the main air stream in front of the tube being investigated with such an arrangement. The heat radiated to any thermometer or thermocouple would be appreciable. Unless unusual precautions were taken to prevent errors due to this radiation, their results would be much higher. The air film coefficients obtained for the streamline tubes also vary linearly with the mass velocity. Figure 8 shows this relation for the rows giving approximately constant values. The data obtained with the oval tubes were not subjected to this analysis, as there appears to be a variation in the experimental values for each row. Any one row does show a
Most of the equipment used in this work was originally constructed by R. E. Brewster. Part of the data was taken from results secured in the unit operations laboratory course for students in chemical engineering. Grateful acknowledgment is made to the Summerill Tubing Company of Bridgeport, Pa., for the three shapes of tubing used.
Nomenclature a = a constant c = sp. heat at constant pressure at mean a m temp., B. t. u./ (lb.) (” F.) d, = distance between tubes, in. d, = outside diam. of tube, in. D = outside diam. of tube, ft. G = mass velocity, Ib./(hr.)(sq. ft.) h = coefficient of heat transfer from tube wall to air stream, B. t. u./(hr.)(sq ft.)(O F.) k = thermal conductivity at mean film temp., B. t. u./(hr.) (sq. ft.)(O F./ft.) = a constant p = quantity of heat transferred, B. t. u./(hr.)(tube) t = temp., F. T = abs. temp., O Rankin: Z’, = mean air-film temp., F. U = over-all coefficient of heat transfer, B. t. u./(hr.)(sq. ft.) (” F.). (Uandoh are equivalent forthese experiments.) At = temp. difference, F. fi = viscosity at mean film temp., lb./(hr.) (ft.) O
Literature Cited Chappell and McAdams, Trans. Am. SOC.Mech. Elagrs., 48, 1201 (1926). Colburn, Trans. Am. Inst. Chem. Engrs., 29, 197 (1933). Drew and Ryan, IND.ENQ.CREM.,23, 945 (1931). Griffiths and Awbery, Engineering, 136, 692 (1933). Hughes, Phil. Mag., 31, 118 (1916). Lohrisch, Mitt. Forschungsarbeiten, No. 322, 1 (1929). Lohrisch, in Wien-Harms’ Handbuch der Experimentalphysik, Vol. IX, p y t 1, Leipzig, AkademischeVerlagsgesellschaft,1929. McAdams, Heat Transmission,” p. 226, New York, McGrawHill Book Co., 1933. Monrad, IND.ENG.CHEW., 24, 505 (1932). Reiher, Mitt. Forschungsarbeiten, No. 269, 20 (1925). REC~IYED January 15, 1938.
