INDUSTRIAL A N D ENGINEERING CHEMISTRY
May, 1924
451
HEAT TRANSFER SYiMPOSIUM Presented before the Division of Industrial and Engineering Chemistry at the 67th Meeting of the American Chemical Society, Washington, D. C., April 21 to 26, 1924
Heat Transmission from Bare and Insulated Pipes' By R. H.Heilman MELLONINSTITUTEOF INDUSTRIAL RESEARCH, PITTSBURGH, PA.
BAREPIPEHEATLOSSES N ORDER to be able to estimate the saving that can be effected by insulating a steam line with a specified covering, it is first necessary to know accurately the heat loss from the bare line. Many investigators have studied the heat losses from bare pipes. Perhaps the most noteworthy of these experimentalists was the French physicist, PBclet. His experiments, however, were conducted at very low temperatures, and his results cannot be applied t o higher temperatures. Subsequent investigators confined themselves mostly to one pipe size only, whereas Mellon Institute has deemed it advisable to carry on the work to higher temperatures and to pipes of various sizes. It was thought here that more reliable data could be secured by testing pipes of various sizes under the same condition than by comparing the results of other investigations on pipes of various sizes under different conditions. Accordingly, tests have been made on 1, 3, and 18-inch standard steel pipes. The electrical method of testing is used at the Institute, as this method has proved t o be the most accurate in addition to being more easily controlled. The apparatus now used is the gradual development of about seven years' work on heat insulations, and the precision of the present method has been checked in several ways and found to be entirely satisfactory.
I
1-inch pipe could not greatly affect the room temperature. This pipe was run up to a temperature of 800" F. The average room temperature throughout this test was 81" F., and the temperature did not vary more than 1.8' F. during its progress. The 3-inch pipe was run up to a temperature of 760" F., and the 10-inch pipe to a temperature of 472' F. The values for the higher temperatures on the 10-inch pipe were obtained by extending the curve parallel to the curves obtained for the 1inch and the 3-inch pipes. This procedure was necessary because of the fact that the larger pipe could not be raised to the higher temperatures without considerably increasing the temperature of the room. 7.0
6.0
5.0
4.0
3.0
2.0
100
200
300
400
500
600
700
TEMPERATURE DIFFERENCE,"E, PIPETO ROOM FIO.
S-BARE
PIPE LOSS CURVES
S
The experimental curves for the 1, 3, and 10-inch pipes are shown in Fig. 1. These curves can be expressed approximately by the empirical equation
-+
H 250 + 10300.11 0.00098H 3.26 77 Td 103 Do." or ET = 3320 10300.11 Td 1020 in which H = B. t. u. loss per hour per square foot of bare pipe surface D = outer diameter of pipe, in inches Td = temperature difference between pipe surface and room, O F. Td =
+
FIG.I-BARE
PIPE LOSS CURVES
When conducting testg on bare pipes it is very desirable that the room temperature remain constant throughout the work, for the rate of heat loss is dependent upon the absolute temperature as well as upon the temperature difference. The 1-inch pipe was selected for test at the higher temperature, as the relatively small amount of heat loss from a 1
Received January 26, 1924.
- +
The loss in B. t. u. per square foot of pipe surface per hour per degree Fahrenheit temperature difference for various diameter pipes is given in Fig. 2. I n Table I the loss in dollars and cents and in pounds of coal per 100 lineal feet of horizontal bare iron pipe is tabulated for temperatures up to 664" F. This loss varies from $1.32 per 100 lineal feet of 0.5-inch pipe at 180" F., t o $297.50 per 100 lineal feet of 18-inch pipe a t 664' F. For superheated steam, a 10-degree temperature drop has been assumed from the steam to the outer surface of the pipe. For some conditions the drop may be greater than 10 degrees, as indicated by the tests of Eberle.2 However, it i s believed that for most cases the drop will not greatly exceed 10' F. 2
Mitteilungen iiber Fors6hungsarbeiten. Heft 78.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
452
Vol. 16, Nu. 5
LOS5ES F R O M
TABLEI HORIZONTALBAREIRON
STEAM PIPES.
FROM100
LINEALFEET O F PIPE PER MONTH O F 3 0 D A Y S WITH S T E A M I N ’ PIPE5 24 HOURS PER DAY. C O A L A T “4m PER T O N O F 2QOQLBS.
I N T H E S E TABLES COAL HAS BEEN FIGURED AT BOILER q O O N EXPENSE,ETC.,TAKEN A T * \ =
EFFICIENCY TAKEN
~
PER TON O F 2000 LB5.-
~ PER7 CENT. 0 AIR T E M P . ~ O O F .
EXPERIMENTAL DATA OBTAINED ATTHE MELLON INSTITUTE. 4ro,
For saturated steam the temperature of the steam can be assumed as the temperature of the pipe, since tests by McMillanS indicate that the drop is very small. The heat loss from horizontal bare iron pipes 0.5 to 18 inches in diameter, for temperature differences of 50” to 800” F., is shown in Table 11. THERMAL CONDUCTIVITY OF PIPECOVERINGS The term “thermal conductivity’’ has been used rather loosely in the last few years. This lack of correct definition has therefore caused considerable misrepresentation on the Trans. Am. SOC.Mech. Eng., 37, 921 (1915).
Pipe Size Inches
Lineal
13,000.6.T.u.PER ‘-8. OF COAL- LABOR, OF C O A L FIRED AT*Sea PER TON.6OILER
PER TON, M A K l N G TOTAL VALUE
part of some experimentalists as to the true conductivity values of insulating materials reported by them. I n fact, there is practically no literature that presents the true conductivity values of pipe-covering materials tested, so that they may be applied in determining the heat loss for conditions not exactly like the test conditions under which the constants were determined. The true meaning of the term “thermal conductivity” of a material is the number of heat units transferred by conduction per unit area, across unit thickness, per degree difference of temperature between the faces, the direction of heat flow being perpendicuar to these faces. In terms of
TABLB 11-HEAT LOSSESFROM HORIZONTAL BAR^ IRON PIPES (In B. t. u. per square foot of pipe surface per hour per F. temperature difference. Air temperature 70’ F.)
Foot c Temperature Difference between Pipe Surface and Factora 5 0 ° F . 100°F. 150°F. 200°F. 2 5 0 ° F . 3OOOF. 350OF. 400’F. 450’F. 500’F. 2.48 2.70 2.95 3.21 3.51 3.84 4.20 5.41 0.220 4.57 4.97 5.25 2.36 2.57 2.80 3.07 3.36 3.68 4.04 4.42 4.81 a/r 0.275 2.29 2.50 2.73 3.00 3.29 3.60 3.95 5.16 4.34 4.73 1 0.344 2.24 2.45 2.68 2.94 3.23 3.54 3.89 5.09 4.28 4.67 l’/i 0.435 5.03 2.20 2.41 2.64 2.90 3.19 3.50 3.85 4.23 4.61 11/x 0.498 2.15 2.58 3.45 3.79 4.16 4.56 4.95 2 0.622 2.35 2.85 3.14 2.09 2.29 2.52 2.78 3.06 3.37 3.71 4.09 4.49 4.91 2l/r 0.753 2.05 2.25 2.47 2.73 3.00 3.31 3.69 4.03 4.43 4.85 3 0.917 2.02 2.22 2.69 2.97 3.27 2.43 3.61 3.98 4.38 4.80 3’/r 1.047 2.00 2.19 2.40 2.66 2.94 3.24 3.58 3.95 4 1.179 4.35 4.77 1.98 2.17 2.38 2.63 2.92 3.22 3.56 3.92 4.32 4.74 41/r 1.310 2.36 I .97 2.15 2.90 3.20 3.54 3.90 4.30 4.71 2 61 5 1.458 2.13 2.34 4.28 4.69 1.95 2.88 3.18 3.52 3.89 2.59 6 1.736 2.11 2.32 2.86 3.16 3.50 3.87 4.26 4.67 1.93 2.57 7 2.000 2.09 2.31 2.84 3.14 3.49 3.86 4.25 4.66 1.91 2.56 8 2.262 1.90 9 2.525 2.08 2.30 2.83 3.13 3.48 3.85 4.24 4.65 2.55 2.07 2.29 2.82 3.12 2.54 2.817 1.89 3.47 3.84 4.23 4.64 2.05 2.27 2.80 3.10 3.45 4.20 4.61 2.52 12 lo 3.344 1.87 3.81 2.04 2.25 1.86 2.78 3.08 3.43 3.79 4.18 4.59 2.50 14 3.663 1.85 2.03 2.23 2.76 2.48 3.06 3.41 3.77 4.16 4.57 16 4.184 2.02 2.22 2.75 3.05 3.39 3.75 4.14 4.55 2.47 1.84 18 4.717 o T o secure losses per lineal foot, multiply square foot losses in table by this factor. 1/2
Surrounding Air 550’F. B O O O F . 650°F. 700OF. 750°F. 800OF. 5.86 6.31 6.78 7.25 7.73 8.22 6.15 5.70 6.62 7.09 7.57 8.06 5.60 6.05 6.51 6.98 7.46 7.95 6.91 5.54 5.98 6.44 7.39 7.88 5.92 6.39 6.86 7.34 7.83 5.48 5.41 5.84 6.30 6.77 7.25 7.74 5.32 5.78 6.24 6.71 7.19 7.68 5.26 6.71 6.19 6.66 7.14 7.63 5.22 6.15 7.59 5.67 6.62 7.10 5.64 7.55 6.58 7.06 5.19 6.11 5.62 6.54 7.04 7.53 6.07 5.17 6.52 7.49 5.60 7.00 5.15 e.05 5.57 6.49 6.97 7.46 5.12 6.02 5.55 6.47 6.95 7.44 5.10 6.00 5.53 6.46 6.94 7.43 5.09 5.99 6.45 5.51 6.93 7.42 5.08 5.98 6.92 5.50 7.41 5.07 6.44 5.97 5.4s 6.89 7.38 6.41 5.94 5.05 6.87 6.36 6.39 6.92 5.46 5.03 6.85 5.44 7.34 4.99 6.37 5.90 5.42 6.83 7.32 4.98 6.35 5.88
May, 1924
INDUSTRIAL AND ENGINEERING CHEMISTRY
the units generally used in power plant practice, this is equivalent to the heat transmitted in B. t. u. per hour through 1 square foot of material 1 inch thick and having 1" F. temperature difference between its faces. It is practically impossible to realize a condition in engineering or laboratory practice where the temperature difference between two faces 1 inch apart is only 1 degree, and the conductivity of an insulating material has therefore generally been taken as the average conductivity value through the whole test section. The conductivity thus obtained is plotted against the temperature difference between the two surfaces or between the inner surface and the room temperature. Plotting average conductivity against temperature difference a t the two surfaces for heat insulating materials may give in some cases, where single thicknesses are used, results sufficiently accurate for engineering purposes; but where compound sections are used, and where different external surfaces exist, as in coverings on various diameter pipes with a resulting change in the surface emissivity factor, it is not at all safe to use the values obtained from conductivity curves plotted against temperature difference. For instance, it is a well-known fact that the conductivity of heat insulating materials increases as the temperature increases. The conductivity value of a given material whose faces are a t 200" and 100" F. must therefore be lower than the conductivity for the same material having its faces a t 700" and 600" F., although the temperature difference is 100 degrees in each case, Hering4 has shown mathematically that when the conductivity of an insulating material is proportional to the absoluto temperature the equivalent conductivity for the whole thickness of the insulation is equal to the conductivity corresponding to the arithmetic mean of the two surface temperatures. In order that this proposition may be true, as brought out by Richards6 and Barrett,6 it is unnecessary that the conductivity be proportional to the absolute temperature, as has been assumed by Hering, but only that it be: a linear function of the temperature, such as K = a T b, where 1C is conductivity, T the temperature, and a and b are constants. In all the tests on commercial insulating coverings conducted during the investigation reported in this paper, there was no covering tested the conductivity of which did not obey a straight-line law. This fact reduces considerably the experimental work required to obtain true conductivity values for the insulating materials tested, as it is only necessary to measure the heat transmitted through the covering and the corresponding surface temperatures. Accordingly, it has been assumed that it is perfectly safe to use the equivalent conductivity values obtained in this work as the true value of thermal conductivity for the coverings tested. The curves shown in Figs. 3 and 47 were obtained from eighty-nine conductivity tests on commercial insulations 1, 2, and 3 inches thick. The thermal conductivity values obtained are plotted against the mean of the two surface temperatures. Where more than one thickness of a given brand of covering was tested, the conductivity for the average of all the coverings of a given thickness tested was calculated for each thickness, and the average of the conductivity curves for all the thicknesses tested was taken as the true conductivity of the material. For instance, in the case of Nonpareil
+
Trans. A m . Electrochem. SOL.,21, 520 (1912). Ibed., ai, 523 (1912). Trans. A m . SOC.Mech. Eng., 44, 312 (1922). The curves shown in Figs. 3, 4, 6 , 7 , 8,9, and 10,and Tables 1V and V and part of the text relating thereto are taken from a paper by the author which will appear shortly in the Journal of the American Society of Mechanicul Engineers. 4
453
covering, where 1, 2, and 3-inch thicknesses were tested, conductivity curves were calculated for 1, 2, and 3-inch thicknesses, and the average of these three curves was taken as the true conductivity curve for this product. This method was followed for all the coverings tested, with the exception of Asbestos Fire-Felt, in which case two separate conductivity curves are given, one for material 1 inch thick and the other for material 1.5 inches thick. The construction of Asbestos Fire-Felt is such that a greater proportion of hard, and consequently better conducting, material is contained in the covering 1 inch thick than in the covering 1.5 inches thick. This condition results in the thermal conductivity curve for the material 1 inch thick being higher than the curve for the material 1.5 inches thick. The outer surface temperatures of all the coverings tested were measured with thermocouples. The thermal conductivity curves for the following materials are included in Figs. 3 and 4: No. 50-85%
Magnesia No. 1. Average of 6 tests 51-85% Magnesia No. 2. Average of 6 tests 52-85% Magnesia No, 3. Average of 7 tests 53-85% Magnesia No. 4. Average of 6 tests 54-Nonpareil. Average of 6 tests 55-Carey Multi-Ply. Average of 8 tests 56-Johns-Manville Asbesto-Sponge Felted. Average tests 57-Carey Hi-Temp. Average of 7 tests 58-Watson Imperial. Average of 2 tests No. 59-Carey Carocel. Average of 6 tests No. 60-Carey Pyrex. Average of 6 tests No. 61-Carey Air Cell. Average of 9 tests No. 62-Johns-Manville Asbestocel. Average of 4 tests No. 63-Johns-Manville Asbestos Fire-Felt, 1 inch thick. Average of 2 tests No. 64-Johns-Manville Asbestos Fire-Felt, 1.5 inches thick. Average of 2 tests No. No. No. No. No. No. of 11 No. No.
g
s
'
O
0.31 100
I
200
300
400
I
500
600
I
700
TEMPERATURE, * E FIG.8-THERMAL CONDUCTIVITY
POROSITY OF PIPE COVERINGS The author has been requested to discuss the effect of voids in relation to the thermal conductivity of pipe coverings. Therefore, the porosity has been determined for one section of each of the different makes of pipe coverings tested. The apparent density and porosity were determined as follows: A sample piece of covering about 8 inches long was sawed off of the %foot section with a band saw. The sample was then weighed on a chemical balance and its apparent volume was
INDUSTRIAL AND ENGINEERING CHEMISTRY
454
determined by placing it in a battery jar of known volume. The jar was filled level full with millet seed, and the sample was then removed add the volume of millet seed remaining in the jar was measured in a graduated cylinder. The difference between the volume of the jar when empty and the volume of the millet seed gave the apparent volume of the sample. The sample was then suspended in water and allo.u.ed to soak from 24 to 48 hours or until no further change in weight was observed. The weight of the sample when suspended in water was subtracted from the original weight, which gave the loss of weight when suspended in water. The porosity of the sample was taken as equal to the original weight minus loss of weight when suspended in water divided by the original weight. I
I
0,4f00
io0
TEMPERATURE, OF.
do
~
Vol. 16, No. 5
from the measurements described above, and are also shown in Table 111. From an inspection of Table I11 and the curves of Fins. 3 and 4,it can readily be seen that the thermal conductivity of a material does not depend upon the porosity of the material alone. The term “thermal conductivity,” as applied to pipe coverings, takes into consideration the flow of heat from one surface of the material to the other surface whether the flow occurs through conduction only or through conduction, radiation, and convection. In some types of material the transfer of heat takes place mainly by conduction, while in other types the transfer results mainly from radiation and convection. Since the radiation loss is proportional to the difference of fourth powers of the absolute temperatures, it is to be expected that a covering in which the heat flow takes place mainly by radiation will show a very steep conductivity curve. The increase in heat loss due to internal convection currents will also tend to cause the conductivity curve to be steeper than for conduction only. Tests made by the National Physical Laboratorys on external convection losses from plane surfaces show that the heat loss by natural convection is proportional to the five-fourths power of the temperature rise above the ambient temperature. While this proportion may not hold true for the convection losses within a covering, it is possible that the loss due to internal convection increases a t a greater rate than the loss due to conduction. The conductivity curve for air-cell covering confirms these statements. This particular covering has the greatest porosity of any of the coverings tested, but by no means the best conductivity value, although a t the very low temperatures it shows a very low conductivity value, due mainly to the fact that the internal radiation losses for low temperatures are very small. It is also to be noted that the air-cell curve is very steep. This is probably due almost entirely to the very large air spaces that it contains. Hence the conclusion may be drawn that the conductivity curve depends probably to a great extent upon the size of the air pockets. The very approximate void thickness for the different materials is given in Table 111. These thicknesses were obtained by examination under the microscope and by calculation; they are not to be taken as the true values, which are almost impoSsible
Fro. 4-THERMAL CONDUCTIVITY
These tests will give only practical values of porosity for the different types of coverings tested, as an extremely accurate determination was not made. It has been found that the porosity of different samples of the same brand of covering tested varies as much as 5 per cent, so that it was considered impracticable to take extreme precaution, such as weighing the samples in vacuo and other refinements. TABLE 111-POROSITYAND APPARENT DENSITYOF PIPS COVERINGS Void Apparent Apparent Thickness Density Density Microns G./Cc. Lbs./Cu. Ft. 1 0.270 16.9 16.6 1 0.266 0.233 14.5 1 1 0.287 18.0 2 0.361 22.6 1 0.332 20.8 150 0.465 29.0 275 0.353 22.1 500 0.444 27.7 2300 0.430 26.9 260 0.517 32.3 4600 0.190 11.9 4400 0.219 13.1 0.647 34.2
to get for all the materials. The values are given only for the purpose of determining the relative effect of the size of the air voids upon the thermal conductivity of the covering. The air pockets in magnesia coverings are so small that they cannot be measured, even with the most sensitive micro-
The porosity values are presented in Table 111. The apparent densities of the coverings have been calculated
I Griffiths and Davies, “The Transmission of Heat by Radiation and Convection,’’ Special Reporf 9, Department of Scientific and Industrial Research, London, England.
MATERIAL 8 5 7 Magnesia No. 1 Magnesia No. 2 Magnesia No. 3 86 Magnesia No. 4 Nan areil Hi-gemp Asbesto-Sponge Felted Multi-Ply Imperial Carocel Pyrex Air Cell Asbestocel Fire-Felt, 1.5 inches thick
qj
Porosity 84.3 84.7 83.4 83.4 81.2 81.1 65.6 75.7 69.1 73.4 61.7 88.9 87.3 67.3
....
FIQ. 6-CANVAS
SURaACE LOSS CURVSS
INDUSTRIAL A N D ENGINEERING CHEMIXTRY
May, 1924
scope, as they have been found to have a diameter of less than 1 micron. The nature of the material in the covering will also affect the thermal conductivity. Some substances are composed
r
I
TEMPERATURE DIFFERENC€,~F, PIPETO R&M
FIG.&-HEAT
LOSS THROUGH
MULTI-PLY C O V E R I N G 1 INCH
TRICK
of a highly reflecting medium which tends to reflect the heat back into the covering, thus more readily preventing its escape. The shape of the air pockets probably has some effect upon the conductivity of the covering. Some materials are composed of very minute crystals, and these prong-shaped crystals no doubt tend to diminish the heat flow by conduction on account of the very small area of contact that they present. They also tend to decrease the loss by radiation and convection. Considerable time has been spent in trying to analyze the results shown in Table I11 and Figs. 3 and 4,in the hope that a general law might be derived from the test results obtained in this investigation. However, it has been found that the variables are too many and too complicated to permit of applying even an empirical equation to the findings.
455
The heat emitted from the surface of the insulation depends upon the heat conveyed through the body of the insulation, as all the heat transmitted through the insulation naturally has to go from the surface of the insulation to the surrounding air. Therefore, if the heat loss law from the surface of the insulation can be determined and expressed as a function of the temperature difference, it will enable one to determine the heat loss through a given insulation if the temperature difference between the surface and the surrounding air is known; or, vice versa, if the heat loss is known, the temperature difference, and hence the surface temperature of the insulation, can be readily calculated. In order to calculate accurately the loss of heat through a given insulation from the thermal conductivity of the insulation, it is absolutely necessary that the temperature of the outer and inner surfaces be known. Commercial steam pipe coverings are almost invariably covered with a canvas jacket. Since pipe coverings are always cylindrical in shape, it is only necessary to determine the heat loss per unit area of surface and the temperature difference between the surface and the surrounding air for Arious diameter coverings, to formulate the canvas surface loss law, as mentioned above. Accordingly, temperature measurements were taken in a great number of tests of pipe coverings on 1, 3, and 10-inch pipes used in determining the bare pipe losses. The average outer diameters of the coverings tested on the three different pipe sizes were 3.1, 9.5, and 17.2 inches. The results of these tests are shown in Fig. 5 . I n order to simplify the calculations necessary to determine the loss of heat through coverings of various diameters, a general equation for the three curves has been derived. I n this equation Td = temperatye difference between canvas surface and room, F. h = total B. t. u. loss per hour per square foot of canvas surface D = outer surface diameter, in inches 272.512 Td = (3) 564 Do.'g 564 Td or h= (4) (272.5 - Td)
'+
HEATLOSSES FROM CANVAS SURFACE OF PIPECOVERINGS From a theoretical consideration of the subject it is clear that, in order to have a transfer of heat from a pipe line through the insulation on the line and to the surrounding air, it is necessary that a temperature difference exist between the inner and outer surfaces of the insulation and also between the outer surface of the insulation and the surrounding air. The temperature difference between the inner and outer surfaces of the covering depends upon the thermal conductivity of the covering, thickness, shape factor, etc. The temperature difference between the outer surface of the insulation and the surrounding air depends upon the amount of heat emitted by radiation and air contact. This, in turn, is dependent upon the nature of the surface of the outer covering, the shape of the insulating body, the excess of its temperature over that to which radiation takesplace, and the absolute value of the temperature of these bodies.
a 0.I
FIG.
J I J / 100 200 390 400 500 600 T E M P E R A T U R ED I F F E R E N C L , O F , PIPE TO ROOM 7-HFtAT L O S S THRQWQH MULTPPLY COVEFXNG 1.6 INCHES
700
THICK
INDUSTRIAL A N D ENGINEERING CHEMISTRY
456
It is believed that these curves and equations are fairly accurate, as they were obtained from the results of a very large number of tests on different materials. The equations are approximately accurate for diameters up to 2 feet. Thermocouples were used in determining the canvas temperatures. During this investigation it was found that the couple, when just inserted under the canvas, would invariably read low. This difficulty was overcome by inserting it under the canvas for a distance of several inches, this distance depending upon the size of the couple and the temperature of the covering. The minimum distance to which the thermocouple can be placed under the canvas and still record the correct temperature is reached when the
I
I
I
I
100
200
300
400
TEMPERATURE DIFFERENCE,OF., FIG.8-HEAT
I
1
500 600 PIPE TO ROOM
J
700
when Td = 40' F., room temperature = 70' P., steam temperature = 470' F., and pipe covering is 2 inches thick. (D = 9.56 inches.)
From Equation 4 It=
Example-Find the heat loss per square foot of pipe surface and efficiency of installation for 5-inch pipe (5.56 inches 0. d.),
564 X 40 (272.5 40) = 60.5 B. t. u. per square foot of
-
canvas surface per hour 9 56 60.5 X - = 104 B. t. u. per square foot of pipe surface 5.56 per hour From Table I1 the loss from a 5-inch bare pipe at 400' F. temperature difference = 3.90 X 400 = 1560 B. t. u. per square foot of pipe surface per hour. 1560 - 104 = The efficiency of the installation, then, is 1560 93.5 per cent.
A number of investigators have studied the heat losses from flat and curved surfaces, but none has been able satisfactorily to derive a general equation for the loss from flat surfaces, since the loss of heat per unit area from flat surfaces varies greatly with the size and position of the body. As shown by Langmuir,g the loss from the surface in a horizontal position is entirely different from that for the same surface in a vertical position. Moreover, the loss is different for the same flat surface facing downward from that when facing upward. To enable one to arrive at an approximate flat-surface temperature, it is suggested that Equation 3 be used, assuming D to be a 30-inch diameter pipe. It is to be understood that this will give only approximate results for flat surfaces. It is not based on any flat-surface loss determinations by the author, but is suggested only until something more definite is developed.
LOSS THROUGH MULTI-PLY C O V E R I N G 2 I N C H E S THICK
temperature of the thermocouple wires a short distance from the junction is the same as the temperature a t the junction. When this condition is reached, there is no flow of heat from the junction to the wires, and consequently no lowering of the junction temperature. The canvas surface loss equations are especially valuable to the engineer who wishes to determine the approximate heat loss from pipe covering already in service and without interruption of the steam service. Simply by taking the temperature under the canvas jacket, the temperature of the surrounding air, and the steam temperature, he can check up the efficiency of a commercialinstallation by comparing the loss through his pipe coverings with the loss from bare pipe shown in Figs. 1 and 2, Tables I and 11,or Equations 1and 2. I n order to secure fairly accurate results, it is necessary that the steam be flowing through the line at a fairly constant temperature for a period of 8 to 20 hours, depending upon the thickness of the covering, pipe diameter, etc. A place in the line should be selected where the pipe is in a horizontal position with as little as possible draft of air blowing over it, and the canvas covering should be clean and unpainted. If the canvas covering is painted, it should be removed and a clean white canvas jacket should be stretched over the insulation until after the test has been completed. Fine wire thermocouples should be used, if possible, and the couples inserted at least 2 inches under the canvas, care being taken not to imbed the thermocouples in the insulating material. An average of the temperature a t the top and bottom of the pipe covering must be taken. Small cylindrical bulb thermometers can be used, but they are not SO accurate as thermocouples.
Vol. 16, No. 5
CALCULATION OF HEATLOSSESTHROUGH COVERINGS The theoretical calculation of heat losses through coverings on flat and curved surfaces is somewhat difficult, inasmuch as the emissivity factors for various surfaces are not the same. This fact causes a variation in the surface temperatures for a given rate of loss. I n order to determine the 0.6
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1 FIG. H HEAT Loss
8
T DIFFCRENCE,,'E, ~ ~ PIPE ~ TO ROOM ~ ~
THROUGH
~
MULTI-PLY COVERING 3 INCHES THICK
heat loss through the material, it is necessary to know the temperatures at the inner and outer surfaces and the conductivity of the material at the mean temperature between the two surfaces. Probably the simplest procedure for calculating the loss through a covering is to make an assumption of the outer surface temperature, then from the conductivity curve to determine the conductivity of the material 9
Trans. A m . Eleclrochem. Soc., 28, 299 (1913).
~
INDUSTRIAL A N D ENGINEERING CHEMISTRY
May, 1924
at the mean of the surface temperature assumed and the inner surface temperature. The loss through the covering should then be calculated for the assumed outcr surface temperature, and this loss should be checked against the loss as obtained from the surface loss curve or equation. If the two losses do not check, the assumed outer surface temperature must be changed according to the indications of the calculation and the process repeated until the two losses or the outer surface temperatures check. At first this may seem to be a very tedious method, but with the aid of a slide rule and Table IV one will find that the loss through single and compound sections can be accurately calculated in a very short time.
face loss equation. A variation of several degrees in the surface temperature will cause only a slight variation in the conductivity value. Therefore, a canvas surface temperature of 129.6" F. is next assumed. The mean temperature, then, is 249.8' F. and the conductivity is 0.590, while the temperature difference between the inner and outer surface is 240.4' F. h = 590 1.24 240'4, = 114.5B. t. u.
Checking again,
272.5 X 114.5 = 59.70 F. 114.5 408 This indicated that 114.5 B. t. u. is the correct loss per square foot of outer surface. The loss per square foot of pipe surface 2 75 is 114.5 X = 180B.t.u.perhour. 1.75
Td =
TABLE IV-VALUES
L
D Inches 3.00 3.25 3.50 3.75 4.00 4.25 4.50
0'
+
-
0.6 L 0
457
I IO0
I
I 200
I
oa
300
I 500
I 600
I
700
TEMPERATURED ~ OF, PIPE To ~ ROOM ~ FIG.IO-HEAT Loss THROUGH MULTI-PLYCOVERING 4 INCHESTHICK
I n the case of a cylindrical surface having a single thickness of insulation applied to it, the quantity of heat conducted per unit of time per unit of area of outer surface is given by the equation h = K(Ti - Tz) 72
loge
72
-
(5)
71
in which
h = B. t. u. loss per hour per square foot of outer surface 2; = temperature of inner surface of covering TZ = temperature of outer surface of covering rx = radius of inner surface of covering r2 = radius of outer surface of covering
564 DO.10
458 451 445 439 433 428 423
D 1nch 5.0 5.5 6.0 6.5
7.0 7.5 8.0
564 D e s F Inches 8.5 415 408 9.0 9.5 401 10.0 395 390 10.5 11.0 385 380 11.5
OF
564 n -0.19
564
fi Inches 375 371 367 364 361 357 354
12.0 12.5 13.0 14.0 15.0 16.0 17.0
564 go.'S
351 349 346 341 337. 333 329
D Inches 18.0 19.0 20.0 21.0 22.0 23.0 24.0
564 P . 1 0
325 322 319 316 313 310 308
This method of calculating gives results that are strictly accurate. In most cases, however, where extreme accuracy is not necessary, the loss of heat through any of the insulations tested in this investigation, for any thickness of covering and for any temperatures generally used in engineering practice can be obtained from Table V and Figs. 6 to 10, inclusive.10 In these curves the unit loss through 1, 1.5, 2, 3, and 4-inch thick Multi-Ply is given for temperature differences up to 700" F. The loss through other thicknesses can be~ obtained~ from the~ curves by ~ ~ interpolation, ~ and the loss a t somewhat higher temperatures can be obtained by extending the curves. TABLEV-PIPE COVERING FACTORS -Temperature Difference, Pipe to Airlooo 200' 300' 400' 500° 600° 700" TYPE OF COVERING F . F . F . F . F . F . F . 1.045 1.025 85y0 Magnesia No. 1 1.082 1.060 85% Magnesia No. 2 1.040 1.019 850/,Magnesia No. 3 1.082 1.056 85'$$, Magnesia No. 4 1.220 1.196 Nonpareil 1.014 1.010 Asbesto-Sponge Felted 1.115 1.085 Hi-Temp 1.360 1.345 Imperial . Carocel 1.166 1.160 Pyrex
. . . . . .. . .
Air Cell .~..
Asbestocel Fire-Felt, 1 inch thick Fire-Felt, 1.5 inches thic:k
..... ..... ..... .....
1.877 1.840 1.761 1.722
The process involved will be illustrated by an example: It is desired to calculate the heat flow in B. t. u. per hour per square foot of pipe surface through a Carocel covering 1 inch thick on a 3-inch pipe (3.5 inches 0. d,). The temperature of the pipe is 370' F., and the room temperature is 70" F. First, a canvas temperature of, say, 136' F., is assumed. 370 136 The mean temperature of the covering is then equal to 2 or 253' 17. From Fig. 4 the conductivity of Carocel a t 253' F. 2 75 = is found to be 0.592. The value of 72 X log. 2 or 2.75 log. rl 1.15 1.24, and the temperature difference between the inner and outer surface of the covering = 370 136 = 234' F. . then h = 0'5921.24 234 = 111.6B.t.u. This value is substituted in the surface loss equation as follows: 272.5 X 111.6 Td = 564 111.6 + 95Td = 272.5 X 111.6 = 58.70 F. 111.6 4- 408 This corresponds to a surface temperature of 128.7" F. It will generally be found that the correct surface temperature is very near the first temperature calculated from the sur-
+
+-
-
Table V gives the factor by which the loss through MultiPly covering must be multiplied to give the loss through any of the coverings tested. For example, the loss through the Carocel installation previously solved can be obtained very readily from Fig. 6 and Table V, as follows: The loss through Multi-Ply covering 1 inch thick on 3-inch pipe a t 300" F. temperature difference is 0.454. The factor for Carocel a t 300" F. temperature difference is 1.333; then the heat loss through Carocel is 0.454 X 1.333 X 300 = 181.5 B. t. u. per square foot of pipe surface per hour. This value checks very closely with the value of 180, previously obtained, and for most engineering purposes the values by the last method will be sufficiently accurate.
The determination of heat transmission through compound sections is more difficult than the calculations for single sections. The labor involved in making the calculations increases as the number of sections is increased. 10 The curves in Figs, 6 to 10,inclusive, are based on 1 square foot of covering and the curves for the various diameters are nominal and not actual diameters.
,
INDUSTRIAL A N D ENGINEERING CHEMISTRY
458
The equation for compound sections on a cylindrical surface in terms of heat loss per square foot of outer surface is Ti
h =
rs log, K1
2 r1
-
re log,
Tz rg
-
rs log,
(6)
2
Heat Transmission in an Inclined Rapid Circulation Type Vacuum Evaporator'
r3
r2
+ T f 7
By D. J. Van Marle
The various steps involved in the solution of a problem of this type will be illustrated by an example. It is desired to calculate the heat flow in B. t. u. per hour per square foot of pipe surface through a compound insulation on an 8-inch pipe consisting of a first layer of Hi-Temp 1.5 inches thick, and a second layer of 85% Magnesia No. 1, 2 inches thick. The temperature of the pipe is 800' F., and the room temperature is 70' F. First, a canvas temperature of 120' F. is assumed. The total drop in temperature through the two coverings then is 800' 120" = 680' F. The next step is to assume the temperature drop through each insulation, in order to determine the conductivity value to use. No rule can be given for the first assumption, but it will be found that the second assumption can be calculated fairly closely. It is known from Fig. 3 that the drop through Hi-Temp should be less than the drop through Magnesia, so there is first assumed a drop of 300' F. through Hi-Temp and a drop of 380' F. through Magnesia. The temperature between the Hi-Temp and the Magnesia covering then is 800' - 300' = 500' F. The mean temperature of Hi-Temp is 8ooo + 5000 = 650" F. 2 and from Fig. 3, K1 = 0.676. The mean temperature of Magnesia is 5000 + l 2 O o = 310' F., and & = 0.509. 2 Now 71 = 4.3125 r2 = 5.8125 t'8 = 7.8125 73
Vol. 16, No. 5
BUFFALO FOUNDRY & MACHINE Co., BIJFFALO, N. Y.
T
HE evaporator is of the rapid circulation type with inclined steam chest. Its body is cylindrical in shape, with conical bottom. T o this bottom the steam chest and downtake are bolted, inclined a t an angle of 45 degrees. At the lower end they are connected by a casting which forms the liquor space. The liquor enters the top of the liquor space, boils up through the tubes, strikes a baffle plate in the vapor body, and returns through the downtake. Steam enters through one of two inlet openings, one near the top and one near the bottom of the steam chest. Condensed steam is removed by means of a wet vacuum pump. At first an attempt was made to remove noncondensable gases from the steam chest through this same pump, but this proved unsatisfactory. With the steam entering a t the bottom of the steam chest, air removal was apparently incomplete, resulting in greatly reduced heat transmission. By carefully venting the steam chest directly into the vapor body, better andmore consistent results were obtained. Fig. 1 shows the arrangement of the evaporator with the exception of the upper steam inlet and the corresponding air vent a t the other end of the steam chest.
log, rz - = 2.33 71
ra log,
2
= 2.31
r2
Substituting the values obtained above in Equation 3, so0 - 120 680 h = 2 33 2.31 - 3.45 4.54 =85.1B.t.u* __ 0.676 + 0 x 9 Substituting this value in the surface loss equation, there is obtained 272.5 X 85.1 = 55.3 Td = A64 85.1 15,6°.'8 This indicates that 50' F. temperature difference first chosen was too low, and there is next assumed a temperature difference of 55' F. or a canvas temperature of 125' F., since the canvas temperature will generally be fairly close to the canvas temperature first obtained by substituting in the surface loss equation. The temperature drop through Hi-Temp for the foregoing calculation was approximately 3.45 X 85.1, or 293.5" F., while the temperature drop through Magnesia was approximately 4.54 X 85.1, or 386.5' F. Since there has been assumed a canvas temperature increase of 5" F., there will be assumed a corresponding decrease in the drop through the coveing. or the temperature drop throughoHi-Temp as 292' F. and the drop through Magnesia as 383 F., with the temperature between the Hi-Temp and Magnesia covering as 508' "F. 800' 508" The mean temperature of Hi-Temp then is "
+
v'
+-
+ 4
654' F., and
= 0.677.
The mean temperature of the Magnesia covering is 5080 4- 12" = 216.5' F., and KZ = 0.512. 2 675 Then h= = 85.5 B. t. U. 2.33 2.31 0.678 + 0.512 Checking again for the canvas temDerature difference. 272.5 X 85.5 = 55.40 F, Td = 85.5 335 This value checks very well with the last value of 55" F. assumed, and the heat loss is 85.5 E. t. u. The total heat loss per square foot of pipe surface per hour is, then. 8.55 X 7'8125 = 154.8B. t. u. 4.3125 -
K1
I
+
-
FIG.1-INCLINED RAPID CIRCULATION TYPEEVAPORATOR
It is realized that this method of venting causes a slight increase in the heat transmission, but this is estimated to be well within the experimental error of the tests as a whole. The heating surface consists of seven 3-inch 0 . d., 1Pgage copper 1
Received January 19, 1924.
