HEAT TRANSMISSION
SYMPOSIUM (Pages 691-7101 Held under the auspices of the Division of Industrial and Engineering Chemistry of the American Chemiaal Society at Yale University, New Haven, Conn., December 30 and 31, 1935.
Heat Transmission with High-Boiling Organic Compounds The purpose of this paper is to review briefly the characteristics of high-boiling
E. F. HOLSER The Dow Chemical Company, Midland, Mich.
692
INDUSTRIAL AND ENGINEERING CHEMISTRY
VOL. 28, NO. 6
range as water (Figure 1). This p r o p e r t y promotes rapid and easy circulation. Neither the liquid nor vapor is toxic, and neither has any corrosive action on metals. Each is, however, more difficult to hold in vessels and pipes than water and steam, necessitating more care in making joints and connections. A wide variety of Dowtherm applications has been proposed and considered for industrial heating and cooling operations; particularly in the last year with the stepping up of industrial activity, a number of new installations were placed in operation. Most numerous are the installations which use a Dowtherm boiler to generate vapor for heating stills, working on high-boiling chemical compounds which require close temperature control, or which for various reasons cannot be satisfactorily operated by direct firing. Platen presses requiring close control and high temperature, such as are used for some types of rubber products and molded synthetic resin products, have been equipped with Dowthenn liquid and vapor heating. A successful application is in the preparation of a variety of products that must be boiled or otherwise processed in jacketed kettles and that require higher temperatures than can readily be obtained FIGURE1. ABSOLUTEVISCOSITY-TEMPERATURE CURVESFOR DowTHERM A AND C COMPARED WITH WATER AND MERCURY with steam a t pressures the jackets will stand. Liquid systems have been applied in a number of plication and dealt with the practical problems involved in cmes where a cooling agent was required but where water their use. was unsatisfactory because of corrosive action, scale formation, The product which has proved most suitable for general and excessive heat loss. One case now under serious conapplication is the eutectic mixture consisting of 75 per cent sideration is that of a furnace which, owing to the nature of diphenyl oxide and 25 per cent diphenyl now available under the conditions inside, cannot be maintained with refractory the trade name Dowtherm A. The name Dowtherm is used walls. The present installation employs a steel shell with an to designate all compounds offered by this company for heat outer jacket through which water is circulated to keep the transfer purposes; A, B, C, etc., designate the particular comsteel furnace wall cool. Serious corrosion and B sizable heat pound or mixture, A number of compounds have been sugloss result. The plant had use for 125 pounds per square gested and tried. Certain of these have appeared promising inch of process steam, but because of the large size of the fura t first for heat transfer work, but further experience has found nace jacket it was impractical to design for any such pressure. them unsuitable in one or more particulars. One product, The jacket containing Dowtherm liquid will generate vapor Dowtherm C which has been reported in previous papers, has a t atmospheric pressure. The 500" F. vapor will then be been used in a few instances, but Dowthenn A is utilized in piped off to a heat exchanger where 125 pounds of steam presthe greater number of working installations. This company sure will be generated to supplement the regular plant steam is continuing its research work for new and better heat transsupply. Thus the cooling of the furnace wall will be accomfer materials, and probably additional new Dowtherm prodplished and at the same time the heat loss turned to useful ucts will be made available from time to time. The discusaccount. sion in this paper will be confined principally to Dowtherm A, Practically all Dowtherm industrial heating installations and the heat transfer data presented will apply to this may be classified as follows: (1) liquid convection, (2) conmaterial. densing vapor, and (3) boiling liquid. Heat absorbers, either the forced or natural circulation type, work in the same Dowtherm A manner as hot water and steam boilers, the heat transfer being The uses of Dowtherm A as a means of transferring heat are from the products of combustion through tubes or metal sursimilar to those of water and steam, except that Dowtherm faces to a heating liquid, usually in turbulent flow, or to a boilcan be used a t higher temperature levels with relatively little ing liquid. or no 'pressure. Indirect heating may be accomplished by Heating apparatus such as stills, heating coils, and jackets methods similar to hot water heating, with no pressure, up to work on the liquid-convection and condensing-vapor classiapproximately 500 " F., the atmospheric boiling point. Howfication. Vapor systems always operate with saturated ever, the most important applications are those in which the vapor; superheating of the vapor is not recommended since it material is boiled and the heat of vaporization used. Vapor has no advantages. installations usually work in the range from 500" to 750" F., The most important facts that a prospective user of a new corresponding to vapor pressures from atmospheric to about heating medium must know are the heat transfer characteris135 pounds gage. The material is exceedingly stable in the tics of the material. With an organic compound such as temperature ranges mentioned. It has a freezing point of Dowtherm the user has a choice between liquid- and vapor56" F. which is low enough for it to remain liquid a t ordinary phase heating, and, if a knowledge of the individual or film room temperatures. If freezing temperatures are encouncoefficient of heat transfer for various conditions is available, tered, no harm results since the material does not expand on the matter of making a choice and proportioning the equipment is greatly facilitated. With this in mind the writer has freezing but actually contracts slightly. The liquid viscosity is very low and is in the same general endeavored to accumulate reliable data from experimental
JUNE, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
693
TABLEI. FILMCOEFFICIENTS, DOWTHERM TO STEAM RE HEATER^
Steam Flow Lb./hr. 75000 77083 86042 87916 92083 9562d 103000
Gage Steam Steam Pressure Temp. In Lb./ao. F: . _ in. 396.7 495.3 397.3 497.7 395.1 499.4 399.1 500.8 397.1 501.5 398 478.0 411.5 495.0
Steam Temp. Out F. 697.3 702.3 700.0 697.6 697.5 690.6 700.8
Dowtherm Vapor Temp. F. 716.9 713.3 715.3 709.8 708.1 708.7 710.9
.4v. Steam Velocity Ft./sce: , ~. 25.25 26.92 30.2 30.5 32.1 32.7 34.6
Total Heat Added to Steam B . 1. u . / h r . 9,050.000 9,400,000 10,220,000 10,290,000 10,720,000 12,370,000 12,800,000
Over-all Computed Film Coefficient Coefficient of For Dow Heat Transfer, For steam 6 therm,. Log Mean U. Baped ha, based h d , based Temp. Diff. on 0. D. on 0 . d . on 0. d. O
F.
83.3 68.7 75.8 69.3 66.0 83.5 67.2
27.15 34.2 33.7 37.0 40.6 37.0 47.5
75.1 76.5 83.9 85.0 88.8 91.3 97.0
47.8 74.1 66.4 79.1 93.0 74.4 123,5
Average 7 3 . 4 36.7 85.4 79.8 Single-pass, vertical, straight-tube type with eteam through tubes and Dowtherm vapor outside tubes. Outside area of tubes = 4000 sq. ft.; 0 . d. of tubes = 0.5 inch; i. d. of tubes = 0.370 inch; length of tubes = 20 feet; No. of tubes = 1525. b Computed b y formula 11, p. 169, Chap. VII, reference 7. c Computed by combination of ha; assumed K / L for scale of 760 referred t o steam side; K / L for steel pipe of ,5250 and experimentally determined U a
and operating installations for the various film coefficients over temperature and velocity ranges ordinarily encountered, and to compare these with the latest and best accepted theoretical determinations. Heat transfer in boilers and heat absorbers using Dowtherm will be discussed first. In any type of boiler the principal resistance to heat flow is encountered on the gas side. The film coefficient on the gas side in the furnace section where both radiation and convection take place is somewhat higher than in the straight convection section, but is still low and lies in the range of 3 to 10 B. t. u. per hour per square foot per O F. The film coefficient on the boiling liquid side is relatively high (in the range of 500 to 2000 B. t. u. or more) although in the case of Dowtherm it is considera(b1yless than with water, as will be shown later. This results in control of the over-all coefficient by the individual coefficient on the gas side. The heat transfer problem with Dowtherm boilers can therefore be considered the same as with steam boiler practice for similar furnace temperature conditions. The average temperature difference between gas and liquid will usually be less with Dowtherm because of the higher temperature of the liquid. Also the temperature difference between the metal and the liquid will be slightly higher with Dowtherm than with water, because of the lower film coefficient, between the metal and liquid.
Dowtherm Vapor for Steam Superheating and Reheating In the plant of The Dow Chemical Company there is one large-size high-pressure (1400 pounds per square inch) steam boiler employing the once-through type of flow, in which Dowtherm vapor is generated a t 725" F. and utilized to superheat the steam and then reheat it after expanding through the high-pressure turbine. This unit was recently described by Killeffer ( 6 ) . The unit is shown diagrammatically in Figure 2 . Since the quantity of steam flow is measured and accurate measurements are available of the Dowtherm vapor temperature and steam inlet and outlet temperatures, it is simple to determine the over-all coefficient of heat transfer from condensing Dowtherm vapor to superheated steam flowing through vertical tubes a t a known velocity. The individual film coefficients were computed for steam a t the known conditions and the results are given in Table I.
Test R u n of Dowtherm Forced-Circulation Boiler A small oil-fired Dowtherm boiler of the forced-circulation type (manufacturer's rating, 4,000,000 B. t. u. per hour) has the liquid pumped first through the furnace or radiant section, then through a convection bank, and finally to a vapor-separating drum. For a test, vapor from the drum was piped to the shell of a small horizontal shell-and-tube type of condenser.
Water was passed through the tubes, and the temperature rise was noted. The water was then passed over a weir where its quantity was measured. From these data the total heat absorption was computed for five different rates of firing. In the boiler, flue-gas temperatures were measured by means of thermocouples a t the entrance to the convection section a t the top of the furnace and a t the breeching. There is some question as to the accuracy of the temperature readings in the furnace proper owing to the effect of radiation from thermocouples to the relatively cold furnace tubes. This would affect only the over-all heat transfer coefficient data for the boiler. The quantity of oil burned was also measured so as to permit calculation of boiler efficiencies. The boiler data are tabulated in Table I1 and the condenser data in Table 111. The Dowtherm condensate is subcooled in the condenser to a considerable extent, particularly on the lighter loads, indicating that there was a considerable excess of surface in the condenser, which accounts for the rather low over-all coefficient of heat transfer.
Electrical Immersion Heater Test for Dowtherm Heat Transfer An electrical immersion heater was made from an iron pipe inch 0 . d. and l/ja inch i. d. The ends were closed so that only the outer surface was in contact with the liquid. The heater was immersed in a 3-liter flask containing 1700 cc. of NEW POWER HOUSEAND COKNECTING PIPE LINES,Dow CHEMICAL COMPANY
INDUSTRIAL AND ENGINEERING CHEMISTRY
694
VOL. 28, NO.6
FIGURE 2. FLOWDIAGRAM OF STEAMBOILERUNIT (1400-Pom~SERIESTYPE) USING DOWTHERM FOR INDIRECT SUPERHEATING AND REHEATING OF STEAM
Dowtherm. The current was adjusted to give several different rates of heat input to the heater. The temperature of the pipe was measured by the change in resistance method. The resistance of the pipe was measured a t room temperature, in boiling water, and in boiling Dowtherm, and a resistancetemperature graph was plotted. This graph was used for determination of the pipe temperature during the test runs. The temperature of the boiling liquid was measured by a mercury thermometer. The following tabulation gives the results of various runs:
Watts Input (Total) 706 930 966 1029 1060 1160 1162 1162
Watts per Sq.
Ft. 14,340 19,000 19,700 21,000 21,600 23,500 23,700 23,700
B. t. u. per Sq.Ft. per Hr.
49,200 64,800 67,000 71.600 73,700 80,000 81 000 8l:OOO
-Temp.,
Metal pipe
512.6 514.4 514.4 609.0 609.0
618.0 518.0 518.0
a
F.-
Boilin liquids 496 4 489.2
489 ' 2 489.2 491.0 492.8 492.8
Film Coefficient h B. t. u./& Ft./H:./" F. Temp. (Boiling Diff. Liquid)
16.2 25.2
3030 2570
19:s 19.8 27.0 26.2 25.2
3&0 3720 2960 3220 3220
This experiment shows clearly the extremely high value of the film coefficient for the boiling liquid which may be reached. The conditions were undoubtedly very favorable and possibly could not be duplicated in actual commercial installations. The data, however, show that, if reasonable care is taken to secure unrestricted circulation in Dowtherm boilers of natural
circulation type, there need be no fear that heating surfaces will be overheated or that decomposition of the material will take place. The test data give several over-all coefficients of heat transfer for a number of specific cases. Because of the wide variety of conditions and types of proposed Dowtherm installations which are being brought up by prospective users, it has been felt for some time that in the absence of a complete range of experimentally determined data, a theoretical calculation of data by the best known and accepted heat transfer formulas for liquid and vapor film coefficients would be of assistance. A careful analysis was made of the film or individual coefficient of heat transfer for Dowtherrd-i. e., the heat transfer per square foot per hour per ' F. temperature difference between the Dowtherm and the metal wall of the tube or container for both liquid and vapor. When the coefficients for the material on the other side of the tube are determined, the individual film coefficients can be combined to give an overall coefficient by means of the following relationship: 1
u = -1+ -L+ -1 hi
where U
K
hz
= over-all coefficient, B. t. u./(hr.) (sq. ft.) (" F.) hl = film coefficient for Dowtherm, B. t. u./(hr.)(sq. ft.) (" F.1
JUNE, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
L = thickness of tube wall, ft. = thermal conductivity of tube material, B. t. u./(hr.) (sq. f t . ) (" F.)/ft. hz = film coefficient for material being heated, B. t. u./(hr.) (sq. ft.) (" F.)
695
5,000
K
The film coefficients of Dowtherm A for various conditions were analyzed by the McAdams method (7, Chapter VII, page 169). McAdam states that the individual film coefficients for fluids flowing in turbulent motion through horizontal pipes, in cases where the Reynolds number exceeds 10,000, can best be correlated for different conditions of flow by means of the following equations: Heating: Cooling:
WQO 2,000
1,000
700 Q 500
.c 300 200
hD =0.0225 K
100
70
50
-=
30
where it = film coefficient, B. t. u./(hr.) (sq. ft.) (" F. temp. dX. between fluid and pipe) D = inside diam. of pipe, ft. K = thermal conductivity of fluid, B. t. u./(hr.) (sq. ft.) (" F./ft.) G = mass velocity of fluid, lb./(hr.) ( s . ft. cross section) p = abs. viscosity of fluid, lb./(hr.) ( f t l C, = sp. heat of fluid, B. t. u./(lb.) (" F.) For the case of Dowtherm A flowing in the liquid state through a 2-inch pipe a t a velocity of 3 feet per second and with an average liquid temperature of 500" F., the film coefficient would be found as follows: D = 0.167 f t . G = mass velocity = 3 X 3600 X 54.1 = 587,000lb./(hr.)
(sq. ft.) 54.1 = density of Dowtherm A at 500" F. (lb./cu. ft.) __ 54*1 = 0.867 = sp. gr. of Dowtherm A 62.4 p = 2.42 X 0.336 = 0.81 lb./(hr.)(ft.) 0.336 = abs. viscosity in centipoises of pure diphenyl oxide at 500" F. (but the liquid viscosity is not appreciably changed by the added 25 per cent diphenyl) C, = sp. heat of Dowtherm A liquid at 500" F. = 0.63 B. t. u./(lb.) (" F.) From Weber's equation for thermal conductivity we have :
K
= 0.864 X sp. heat X sp. gr. X mol. wt. of diphenyl oxide = 170.08 mol. wt. of diphenyl = 154.08 mol. wt. of Dowtherm A = (0.735)(170.08) (0.265) (154.08) = 165.9 K = (0.864)(0.63)(0.867) a K = (0.471)(0.1735) = 0.0818
+
Substituting in McAdams' formula for the film coefficient under heating conditions :
4
5
7
20
10
30 50 70 100 0'0'
200 300
500 700 loo0
FIGURE 3. DESIGNCHARTFOR COMPARISON OF FILM CoEFFICIENTS OF HEATTRANSFER OF WATER AND DOWTHERM
h =
(0.0225)(0.0818) (0.167)(587,000) 0.167 0.81
(
((0'63)(0'81))0*4 = 267.5 B. t. u./(hr.) 0.0818
(" F.) (sq. ft.)
An interesting comparison is the value worked out by this method for water, a t say 2 1 2 O F., flowing with a velocity of 3 feet per second through a 2-inch pipe. I n this case: h = 825 B.t. u./(hr.)(sq. ft.)(" F.)
From this same equation a design chart may be set up for an approximate method of evaluating h for Dowtherm A liquid flowing in clean pipes, using the standard formula:
Substituting G' for G and D' for D: D' = inside diam. of pipe, in. G' = mass velocity = lb./(sec.) (sq. ft.)
(E (G' hD' 12K= 0.0225 12 hD'
3
3600))'*'
0.0225 X 12K X 95.8
(%)0.4
(DY')Q.s
(%)om4
Substituting the values of K , p, and C, for different temperatures of Dowtherm A liquid, hD' can be plotted against D'G'. Figure 3 shows values of hD' against DIG' for several different temperatures of Dowtherm A liquid and for two different temperatures of water. Table IV gives intermediate
TABLE 11. BOILERDATA^ RunNo.
Furnaae Temp.
* F.
o
1 864 2 1105 3 1077 4 1090 5 1244 Boiler tube6 oonsist of a
Staok
Temp.
Dowtherm Dowtherm Log Mean Temp. In Temp. O u t Temp. Diff.
F. F. O F. O F. 629 606 616 ao 628 606 619 140 708 606 625 230 709 603 627 230 773 642 66 1 300 total of 1300 E q . ft. of 2-in. 0 . d. tubing. O
Total Heat Absorbed (Output)
E . t. u. / h r . 1,224,000 1,986,000 3,092.000 3,659,000 4.432.000
Av. Over-all Coefficient of Heat Transfer. U 1i.a 10.9 10.3 12.2 11.4
Fuel Oil Burned
Total Heat in Fuel (Input)
(18,60Lob'khT:u./lb.) 138 173 265 315 375
B . t . u./hr. 2,565,000 3,225,000 4,930,000 5,860,000 6.980.000
Percentage Efficiency, Ratio Output t o Input 47.8 61.6 62.8 62.5 63.5
HEATTRANSFER PLAYS AN IMPORTANT PARTIN
A
PHARMACEUTICAL MA~UTJFACTURING PLANT
1
data determined in calculations for Figure 3 from Weber's formula for K and McAdams' formula for h. Table IV shows that the main factors which cause the difference between water and Dowtherm are thermal conductivity ( K ) and viscosity (b) and, of these two, thermal conductivity has by far the greater effect since its value for water is approximately four times that of Dowtherm. If we determine an over-all coefficient for Dowtherm on one side of the tube and water on the other a t the above conditions, we find: U = 1
1 L
U = 1 825
+ 0.0004 +
1 825
-
1
- 0.00121 + 0.0004 + 0.00121 = 354
Although the data show that the heat transfer characteristics of liquid Dowtherm are considerably poorer than water, we should not forget to consider that in the case of Dowtherm a much higher temperature difference is obtainable that will offset the lower value of the heat transfer coefficient, so that the total heat transferred per unit of surface may be greater.
Film Coefficients for Dowtherm Vapor 1
McAdams (7) points out that the film coefficients in case of condensing vapors are largely determined by the conductivity, viscosity, and density of the condensate and the latent heat of
&+E+Z
= over-all coefficient of heat transfer = film coefficient for liquid Dowtherm hl, = film coefficient for water L = tube thickness, ft. K = thermal conductivity of tube metal
U
hld
900
3000
Assuming a tube wall 0.12 inch thick = 0.01 foot and K = 25 for steel:
_ -
0'01
K - X =
u=
1
+ 0.0004 267.5
1,000
700
0.0004
500
c
1 = 187 1 - 0.00374 + 0.0004 + 0.00121 + 82%
300 200
100
If the transfer were from water to water, the over-all coefficient of heat transfer would be found as follows, assuming the temperature differential between the two quantities of flowing water to be small enough so that hWwould be the same for both:
FIQURE 4. CIENTS OF
696
DESIGN CHART FOR COMPARISON OF FILM COEFFIHEATTRANSFER OF CONDENSING STEAM AND DowTHERM VAPOR
INDUSTRIAL AND ENGINEERING CHEMISTRY
JUNE, 1936
6517
For steam a t atmospheric pressure and 212" F., condensing on a single 1-inch 0 . d. horizontal tube, with a temperature difference between tube and steam of 10" F., the value of h is 2130. A design chart can be set u p for an approximate method of evaluating h for a single horizontal tube. Using D' for D,
condensation of the vapor. He also states (7, Chapter IX, page 262) that the recommended relation for the condensation of a pure saturated vapor in the absence of noncondensable gas, outside the tube of a horizontal multitubular condenser, is given by the equation:
where D
outside diam. of pipe, f t . gravitational constant, ft./(hr.)/(hr.) = 4.18 X 108 thermal conductivity of condensate, B. t. u./(hr.)(sq. ft.)(O F.(ft.) n = No. of pipes high, in horizontal multitubular condenser r = latent heat of condensation, B. t. u./lb. p = viscosity of condensate, lb./(ft,)(hr.) p = 2.42 X viscosity in centipoises p = density of condensate, Ib./cu. ft. At = temp. diE. between vapor and tube wall, O F. h = av. coefficient of heat transfer for entire wall, B. t. u./(hr.)(sq. ft.)(" F.) = g = k =
*
Substituting the values of k , p, T , and ,u a t different temperatures, h can be plotted against D'At. Figure 4 shows values of h against D'At for several temperatures of Dowtherm vapor. Data as determined for Figure 4 with intermediate steps are shown in Table V. Here again, in the case of vapors, the effect of liquid viscosity and thermal conductivity are clearly shown in the comparison of Dowtherm and steam; although the film coefficient is much lower for Dowtherm, it is nevertheless a satisfactory value, and, as previously pointed out, the heat transfer with Dowtherm may be fully as great or even greater per unit of surface because of the ease of obtaining higher average temperature differences. As a check on the theoretical determination of vapor film coefficients for Dowtherm, we have the experimental work of
For Dowtherm vapor a t atmospheric pressure and 500" F., oondensing on a single 1-inch 0. d. horizontal tube with temperature difference (At) between tube and vapor of 10" F., K = 0.0815 B. t.u./(hr.)(sq. ft.)(" FJft.) D = 54.1 Ib./cu. ft. g = r = D = D' = p = At =
4.18 X'108 123 B. t. u./lb. diam. of tube, f t . diam. of tube, in. ( = 1 in.) 0.81 lb./(ft.)(hr.) temp. diff. = IOo F.
TABLE IV.
TABLE 111. CONDENSER DATA" DawDowtherm therm Log Vapor Heat Conden- W ~ t e i Water Mean Absorbed by Temp. sate Temp. Temp. Temp. R u n No. Water In Temp.Out In out Diff. B. t. u./hr. F. O F . O F F. F. 1 1294000 549 161 96 118 440 2 1:9s6:000 571 232 91 126 460 3 3,092.000 590 380 97 155 460 4 3,659,000 592 400 98.6 167 455 5 4,432,000 460 633 98.6 183.2 490 a Condenser oontains forty-eight 1-in. 0 .d. tubes for a total of 110 sq. ft.
Av Over-all Coef-ficient
U 25.2 39.2 61.0 73.0 82.0
COMPUTATIONS OF K, THERMAL CONDUCTIVITY, AND hD' PRODUCT OF FILM COEFFICIENT MULTIPLIED BY TUBE DIAMETER FOR DOWTHERM A LIQUIDFOR VARIOUS TEMPERATURES
q m
(25.g)(K)
( ~ ) " D'Q' '"
I(
K
0.1795
0.0740
10.49
2.56
1.420
1.350
3.455
0.910
0,1763
0,0790
7.78
2.27
1.062
1.925
4.375
54.1
0.870
0.1736
0.0823
6.85
2.16
0.915
2.330
5.04
0.911
50.4
0.807
0.1695
0.0780
6.87
2.16
0.846
2 , a90
5.16
0.763
46.9
0.750
0.1654
0.0730
7.10
2.19
0,805
2.350
5.15
€&.,
T
CP
300
0.50
1,550
58.6
0.957
400
0.57
1.078
56.7
500
0.63
0.895
eo0
0.66
700
0.88
p
Density
Mol. W t .
Po"
PO
10 100 1000 10 100 1000 10
100 1000 10 100 1000 10 100 1000
(D)at)O.S
hD'
6.3 39.8 251.0 6.3 39.8 251.0 6.3 39.8 251.0 6.3 39.8 2.51.0 6.3 39.8 251.0
21.75 137.7 868.0 27.6 174.0 1098.0 31.7 200.5 1264.0 32.45 205.0 1293.0 32.45 205.0 1293,O
COEFFICIENT h FOR DOWTHERM VAPOR FOR SEVERAL TEMPERATURES O F DOWTHERM AND TABLE V. CALCULATION" O F FILM FOR SEVERAL TEMPERATURE DIFFERENCES BETWEEX DOWTHERM AND TUBE WALL T
K
T
P
300
142
59.6
3560
0.074
0.000408
1.55
557.5 X 108
486
400
134
56.7
3215
0.079
0.000493
1.078
825 X 108
536
500
123
54.1
2935
0.0823
0.000658
0.895
843
x
108
553
600
110
50.4
2540
0.078
0.000477
0.811
687 X 100
512
700
97
46.9
2200
0.073
0.000390
0.763
456 X 108
462
P2
a n = 1; D' = 1 in.; g = 4.18 X 108.
P
10 100 500
10 100 500 10 100 500 10 100 500 10 100 500
0.5625 0.316 0.2113 0.5625 0.316 0.2113 0.5625 0.316 0.2113 0.6625 0.316 0.2113 0.5625 0.316 0.2113
370 207.5 138.8 407.5 229 153 420 236 157.6 390 219 146.3 353 197 132
698
INDUSTRIAL AND ENGINEERING CHEMISTRY
Badger, Monrad, and Diamond (1). Here the film coefficients were determined experimentally by the use of thermocouples attached to the tube walls, and their values for the diphenyl film coefficient ranged from about 250 to 600. Their determinations showed the film coefficient on the caustic side to be much higher (500 to 1200) so that the over-all coefficient ranged from about 160 to 400. McCabe (8) also determined that the film coefficient for diphenyl vapor is from 250 to 400 and that the asphalt film coefficient varies from 35 to 50. The over-all coefficient in this report varied from 30 to 42. To summarize, we can say that for heat transfer by liquid Dowthenn the film coefficient ill be much less than for water in on the Dowtherm side w equal tube sizes and velocities. Values for clean 2-inch steel tubes by this method of computation for various velocities will be as follows: Velooity of Liquid Dowtherm at 500’ F.
Ft./sec.
Film Coefficient of Heat TranRfer, hid. B . t . u . / ( h p ) ( ! q . ft.) ( O F . diff. between lzquad and lube wall) 168.5 267.5 325.0 385.0 445.0
VOL. 28, NO. 6
Heat transfer coefficients in the case of Dowtherm vapor, according to theoretical calculations, are of the same range of magnitude as those of the liquid. They are, however, much lower than with steam; the film coefficients on the Dowtherm side of the tube range from about 150 to 420 B. t. u. per square foot per O F. temperature difference between the vapor and tube wall, 300 to 400 being a reasonable value to be expected in ordinary commercial practice. Combination of the above film coefficients for the Dowtherm side of heating surfaces with proper values for the ma-, terial being heated on the other side of the dividing walls should give reliable over-all values for heat transfer.
Literature Cited (1) Badger, W. L.,Monrad, C. C., and Diamond, H. W., Trana. Am. Inst. Chem. Engrs., 24, 56-78 (1930). (2) Grebe, J. J., Chem. & Met. Eng., 39, 213-16 (1932). (3) Grebe, J. J., Combustion, 3, 38-41 (1931). (4) Grebe, J. J., and Holser, E. F., Mech. Eng., 55, 369-73 (1933). (5) Heindel, R. L.,Jr., Chem. & Met. Eng., 41, 308-12 (1934). 27, 10-15 (1935). ( 0 ) Xilleffer, D.H . , IND.ENG.CHEM., (7) McAdams, W.H., “Heat Transmission,” 1 s t ed., 1933. (8) MoCabe, W.L., Univ. Mich., Eng. Research Bull. 23 (1932).
RECEIVED March 12,
1936.
Radiation Reaction at Any Point in a Furnace Cavity
T
HE necessary equations of condition and a procedure by means of which successive approximations converge toward a solution of the equilibrium at any, and hence all, points within a furnace cavity have been developed by the author for certain classes of conditions within the cavity. This involves a special treatment of the problem which deals with the net rate of exchange by radiation between a local reference zone a t the point under observation and the enclosure, including its contents. If the temperature and concentration gradients throughout the cavity may be approximated, then a knowledge concerning the latter phase of the subject alone, when introduced in the energy equation as applied to represent the equilibrium a t the local zone, is, with other well-known relations, sufficient to furnish information concerning some important practical conditions. Thus for a local reference zone, designated henceforth as point 0 zone, or simply as point 0, the relation Qv
= QK
+ Qc + R
(1)
holds if the state is steady. Here Q v represents the thermal energy release rate in the local zone represented by point 0. QK and Qc represent the net rate of exchange between point 0 zone and immediate vicinity, rewectively, by thermal conduction and convection. Rreprisents the net rate of exchange bettween the same zone and the enclosure, including its contents, by radiation. Qu, Q K , and Qc depend only on the local conditions. Expressions representing them for many cases are well known, and their values are susceptible to determination when temperatuies and gas concentrations in the vicinitv of Doint 0 are known. For some classes of , position of p o h t 0-i. e., a t the wal
W. J. Wohlenberg Yale University, New Haven, Conn.
Q v is zero. An exception in this respect is a wall location a t the surface of a fuel bed on a grate. Now Qv represents the rate of release of thermal energy by the combustion process a t this point. The term R, representing the net rate of exchange by radiation, depends on the conditions a t every point in the cavity which point 0 “sees.” Although the general form of the involved radiation equations is known, the particular arrangements which correctly represent the exchange for the above conditions are not well known. This involves the special treatment referred to before. Accordingly, this phase of the more general furnace equilibrium problem is dealt with in the present paper. It thus paves the way for the later presentation of the more complete procedure and, as before noted, furnishes relations by means of which some conditions of practical importance may be approximated directly without recourse to that procedure. Although the resulting relations are developed with the furnace cavity in mind, they are applicable to any cavity whatever, which falls as to class within the following specifications. Thus it is assumed that no other than thermal radiation need be considered. Then the black body is the standard of reference, and temperature is introduced on the basis of the Stefan-Boltzman law. It is also assumed that Lambert’s cosine law of radiation intensitv from surfaces approximates the actual conditions to within t h e desired- degr cy for the cases to be considered.
