N o . 1848HEAT LOSSES FROM BARE AND COVERED

WROUGHT-IRON PIPE AT TEMPERA­TURES UP TO 800 DEG. FAHR.

By R. H . H e i lm a n , P i t t s b u r g h , Pa.Junior Member

High-temperaiure superheated steam running up to 800 deg. fahr. and high- temperatwre chemical processes are being more and more widely used, and accord­ingly ihe question of heat losses from pipes under such temperature conditions is one of importance to the engineering profession.

This paper presents the findings of an experimental investigation conducted in the Mellon Institute of Industrial Research of the University of Pittsburgh. The losses from bare wrought-iron pipes have been measured for temperatures up to and including 800 deg. fahr. They have been studied carefully for pipes of various diameters, and empirical formulas are presented whereby the loss from pipes of any diameter may be readily calculated.HPHE purpose of this paper is to report some of the data obtained

recently on bare pipes operating at temperatures up to 800 deg. fahr., and to present curves and formulas which will enable the engineer to solve readily the problems usually encountered in the calculation of heat losses from bare and covered pipes.

B A R E -PIPE HEAT LOSSES2 Manufacturers of pipe coverings often are required to

guarantee that the application of a specified heat-insulating cover­ing will effect a certain percentage saving of the heat which would be lost entirely from a bare pipe. Since the bare-pipe loss is the 100 per cent value against which the losses from the covered pipe must be compared, it is essential that the loss from the bare pipe shall be known accurately.

3 Many investigators have studied the heat losses from bare pipes. Perhaps the most noteworthy of these experimentalists was the French physicist P6clet. Paulding, in his book on Steam in

Presented a t t h e S p r in g M e e tin g , A t la n ta , Ga., M a y 8 to 11, 1922, of T h e A m e r ic a n S o c ie ty o p M e c h a n i c a l E n g i n e e r s . A w a rd e d A. S. M. E. J u n io r P r iz e for t h e b e s t p a p e r d u r in g th e y e a r 1922.

299

3 0 0 H EA T LOSSES FROM BA RE P IP E AT H IG H TEM PER A TU RES

Covered and Bare Pipes, has worked out the theory of heat losses from bare pipes in the light of the researches of Peclet. However, the findings of later investigators do not support the results given by Paulding. Owing to the fact tha t P6clet’s experiments were conducted a t very low temperatures, while subsequent investigators confined themselves mostly to one pipe size only, the Mellon Insti­tute deemed it advisable to carry on the research to higher tem­peratures and to pipes of various sizes. By testing pipes of various sizes under the same condition, it was thought that more reliable data could be secured than by comparing the results of other in­vestigators on pipes of various sizes under different conditions. Accordingly, tests were made on 1-in., 3-in., and 10-in. pipe.

F i g . 1 L a b o r a t o r y a n d T e s t i n g A p p a r a t u s .

4 The method of testing was practically the same as tha t described by G. D. Bagley in his paper on Conversion of Heat Losses from Pipes and Boilers, presented before the Society in 1918, except that the pipe-covering tester had been improved. A Leeds & North- rup type K potentiometer was substituted for the milli-voltmeter, and a General Electric saturated-core-type voltage regulator and smaller thermocouples were added. Fig. 1 shows a view of the laboratory and the testing apparatus.

5 When conducting tests on bare pipes it is very desirable that

R. H. HEILMAN 3 0 1the 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-in. pipe was selected for test at the higher temperatures, as the relatively small amount of heat loss from a 1-in. pipe could not greatly affect the room temperature.

6 This pipe was run up to a temperature of 800 deg. fahr. The average room temperature throughout this test was 81 deg. fahr. and the temperature did not vary more than 1.8 deg. fahr. during its progress.

7 When the emissivity coefficient is plotted against the heat loss, it is found that the curve obtained is not a straight line, but falls off at the higher temperatures. This means that the heat loss from a bare pipe does not increase as rapidly at the higher temperatures as would be anticipated. A possible explanation for this condition is that the convection loss at the higher temperatures does not in­crease as rapidly as at the lower temperatures.

8 The first test on the 1-in. pipe was checked by a second test on another 1-in. pipe and both tests corresponded exactly at the higher temperatures.

TABLE 1 LOSSES FROM HORIZONTAL BARE-IRON STEAM PIPES From 100 Lineal Feet of Pipe per Month of 30 Days with Steam in Pipes 24 Hr. per Day. Coal a t $4.00 per Ton of 2000 Lb.

In this table coal has been figured a t $4.00 per ton of 2000 lb., 13,000 B.t.u. per lb. of coal; labor, boiler-room expense, etc., taken a t $1.00 per ton, making total value of coal fired a t $5.00 per ton. Boiler efficiency taken a t 70 per cent; air temp. 70 deg. fahr. Experimental data obtained a t the Mellon Institute.

302 HEAT

LOSSES FROM

BARE PIPE

AT HIGH

TEMPERATURES

R . H . H EILM A N 3 0 3

9 The location of the curves for the 3-in. and the 10-in. pipes was obtained by experiment at the lower temperatures, as indicated by the solid lines in Fig. 2. The values for the higher tempera­tures are the result of extending the curves parallel to the curve ob­tained for the 1-in. pipe. This procedure was necessary because of the fact that the larger pipes could not be raised to the higher

TABLE 2 HEAT LOSSES FROM HORIZONTAL BARE-IRON PIPES

temperatures without raising considerably the temperature of the room. Tests are now in progress to ascertain the loss from vertical iron pipes, and the results will be reported later.

10 In Table 1 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 deg. fahr. The loss varies from $1.32 for 100 lineal feet of §-in. pipe at 180 deg. fahr. to $297.50 for 100 lineal feet of 18-in. pipe at 664 deg. fahr. A ten-degree fahr. temperature

drop has been assumed from the steam to the outer surface of the pipe for superheated steam.

THEORY OF HEAT LOSS FROM INSULATED PIPE S11 In order to calculate the loss of heat from an insulated

pipe or boiler, it is necessary to know the total temperature drop from the pipe to the surrounding air; and to enable one to make accurate calculations it is required that the component temperature drops be known.

12 The total temperature drop from the steam inside a pipe to the outer air can be considered as made up of four components, as follows:

(a) Drop from steam to the outer surface of the pipe(b) Drop from outside surface of the pipe to inside surface

of the insulation(c) Drop from the inside surface of the insulation to the

outside surface of the insulation(d) Drop from outside surface of the insulation to the sur­

rounding air.13 The temperature drop from the steam to the outer surface

of the pipe depends upon the resistance to heat flow offered by the film at the inner surface and the resistance offered by the iron wall of the pipe.

14 This combined resistance is very low, owing to the high conductivity of the iron and the relatively high conductivity of the water film. Consequently the temperature drop is very low. No attempt has been made to measure the above temperature drop in this investigation, as it was considered to be so small as to be negligible. This drop has been measured for saturated steam by L. B. McMillan 1 and found to be a fraction of a degree. How­ever, a test conducted by Eberle2 for superheated steam shows a drop as high as 10 deg. fahr. This drop should be taken account of when making calculations for superheated steam.

15 The temperature drop from the outside surface of pipe to the inner surface of the insulation depends upon the resistance to heat flow offered by the air space between the surface of the pipe and the inner surface of the insulation. The heat flow which takes place in this case is due to radiation, conduction, and convection. Since the radiation increases as the fourth power of the absolute

1 Trans. Am. Soc. M. E., vol. 37, p. 928.a Mitt, uber Forschungs-Aibeiten auf dem Geb. des Ing., heft 78.

3 0 4 HEAT LOSSES FROM BARE PIPE AT HIGH TEMPERATURES

R. H. HEILMAN 3 0 5

temperature difference, it is to be expected that the temperature drop would tend to decrease at the higher temperatures.

16 The temperature drop from the outer surface of the pipe to the inner surface of the covering for 1-in., 3-in., and 10-in. pipe is shown in Fig. 3. These curves show that the temperature drop increases as the pipe diameter decreases. -A test was also made on a 3-in. pipe with an air space of 1.2-in. between the surface of the pipe and the insulation. By comparing this curve with the curve for an air space of 0.1 in., it is observed that the temperature drop

F i g . 3 T e m p e r a t u r e D r o p f r o m O tjter Su r f a c e o f P i p e t o I n n e r Su r f a c e o f C o v e r in g

for a 1.2-in. air space is only a few degrees more than for an air space of 0.1 in. This is probably due to the fact that for air spaces much greater than 0.2 in. convection currents are increased, thus causing an increase in heat loss.

17 Since the flow of the heat is directly proportional to the cross-sectional area, and inversely proportional to the length of the path, it is obvious that the presence of a 1.2-in. air space between the surface of the 3-in. pipe and the inner surface of the insulation will cause an increase in the total amount of heat lost from the sur­face of the pipe, provided, of course, the air space is not as good an insulator as the covering itself. In this case the insulating value of commercial coverings is many times greater than the insulating value of the air space.

18 The results of this test show that an air space of over 0.25 in. is of little use as an insulator on flat surfaces at high temperatures, and that this air space is of little value as a protection to the cover­ing from the effects of the high temperatures. This test also demon­strates that coverings should be kept as close as possible to cylindrical surfaces, because the insertion of an air space of approximately 0.1 in. between the pipe and insulation actually increases the overall loss. An examination of Fig. 3 shows that the temperature drop for a 0.1-in. air space is approximately equal to that for 0.1 in. of com­mercial insulations, so that this temperature drop can be neglected in calculations and the pipe covering considered as fitting close to the pipe with the pipe temperature and the temperature at the outer surface of the covering as the temperatures bounding the covering.

19 The temperature drop from the inside surface of the insu­lation to the outside surface of the insulation depends upon the resistance to heat flow offered by the insulation itself. Heat is transmitted through the insulation by means of radiation, conduc­tion and convection. The relative amount of each of these three factors depends entirely upon the construction of the insulating material.

20 The amount of heat transmitted through the insulation and the temperature drop from the inner to the outer surface de­termine what is generally called the absolute conductivity of the insulation. However, this does not give the true absolute conduc­tivity of the insulation, but gives what may be called the mean absolute conductivity. The true absolute conductivity for an insu­lating material, say, 1 in. in thickness can be represented by a curve. The absolute conductivity for a given material increases as the temperature increases, and therefore the absolute-conductivity curve depends upon the thickness of the covering and also upon the curvature of the covering.

21 The drop in temperature, or the temperature-gradient curve through the insulation, then depends upon the thickness of the covering and the curvature. In a cylindrical covering the resistance to heat flow diminishes as the outer surface is approached, the temperature drop becomes less, and the gradient curve is bowed downward if the curvature alone is taken into consideration. How­ever, the absolute conductivity decreases as the outer surface is neared, with a consequent bowing up of the gradient curve, and the two tend to counteract each other, so that the temperature-gradient curve may be bowed either up or down or be a straight line, depend­

3 0 6 HEAT LOSSES FROM BARE PIPE AT HIGH TEMPERATURES

B . H. HEILMAN 3 0 7

ing upon the curvature of the cylinder. The temperature-gradient curve for a flat surface should bow up.

22 It is highly desirable that tests should be conducted on commercial steam-pipe coverings of different thicknesses and at different temperatures, in order to obtain mean absolute-conductivity curves for the different thicknesses.

23 The temperature drop from the outer surface of the insula­tion to 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 body, the shape of the body, the excess of its temperature over that of objects to which radiation takes place, and the absolute value of the temperature of these bodies. Commercial steam-pipe coverings are invariably covered with a canvas jacket. From the above-mentioned facts it is obvious that the loss from a canvas surface at a given temperature is independent of what is under the canvas, so that, if the canvas-loss law can be ascertained, this law may be applied to the loss from steam-pipe coverings and thus the temperature of the outer surface of the insu­lation can be determined. In making calculations of heat loss through an insulation, it is absolutely necessary to know the temperatures at the inner and outer surfaces.

24 P6clet made a careful study of the heat emissivity from various surfaces, canvas surfaces included. As mentioned, however^ his experiments were conducted at relatively low temperatures. McMillan made a study of the heat emissivity from a canvas surface in his study t>f commercial steam-pipe coverings, but he confined his experiments to one pipe size only. Nevertheless, McMillan’s results in the form of a curve present a readier means of calculating the losses from steam-pipe coverings than do P6clet’s, whose observa­tions, while taking all the variables into consideration, are in too complicated a form to provide a ready means of calculation.

25 Since McMillan’s canvas-surface-loss curve was obtained from experiments on one pipe size only, this curve can be used in making calculations on coverings of a diameter approximately the diameter of the coverings tested. In order to be able to calculate the loss of heat from pipe coverings of any diameter, it has been necessary to obtain the canvas-surface-loss curves for various diameters. Accordingly, coverings were tested on the 1-in., 3-in., and 10-in. pipes used in determining the bare-pipe losses. The average outer diameters of the coverings used were 3.1 in., 9.5 in. and 17.2 in. The results of these tests are shown in Fig. 4.

3 0 8 HEAT LOSSES FROM BARE PIPE AT HIGH TEMPERATURES

26 In order to simplify the calculations necessary to determine the loss of heat through coverings of various diameters, the equations of the three curves shown in Fig. 4 have been derived. In these equations—

F ig 4 C a n v a s-S u r f a c e - L o ss C u r v e s

which is approximately accurate for diameters up to 2 ft.27 It is believed that these curves are fairly accurate, inasmuch

as they were obtained from the results of numerous tests on different materials.

28 Thermocouples were used in determining the canvas tem­peratures. During this investigation, it was found that the couple,

R . H . HEIL.MAN 3 0 9when 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. From a theoretical consideration of the question, it can be shown that the minimum distance to which the thermocouple can be placed under the canvas is reached when the temperature of the thermocouple wires, a short distance from the junction, is the same as the temperature at 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

29 A covering 2 in. thick, assumed as having a mean absolute- conductivity coefficient of 0.56, is placed on a 4j-in. outside-diameter i pipe maintained at a temperature of 400 deg. fahr. The tempera­ture of the surrounding air is 70 deg. fahr. Determine the heat flow ln B.t.u. per hour per sq. ft. of pipe surface.

30 The heat flow through a cylinder is given by the equation:

where T2 is the temperature at the outer surface of the covering. To obtain T2, knowing only T\, the pipe temperature and Ts, the room temperature, it is necessary to change the form of the equa­tion so as to include Td. The equation for Td, as developed from experimental results, is

h = B.t.u. loss per hour per sq. ft. of canvas surface K = mean absolute conductivity of insulation n = radius of inner surface of insulation, inches r2 = radius of outer surface of insulation, in inches

Td = temperature difference between outer surface of insulation and room, deg. fahr,

junction temperature.SAM PLE CALCULATIONS

whence

in which

3 1 0 HEAT LOSSES FBOM BABE P IP E AT HIGH TEMPERATUR

DISCUSSIONB . N . B ro id o . The author states that the temperature drop

between the steam and the wall of the pipe is very low, that it has been found to be, for saturated steam, a fraction of a degree, and with superheated steam, in accordance with tests by Eberle in Munich, only 10 deg. This is misleading, as it might give the reader the impression that the temperature between the super­heated steam and the wall of a bare pipe is only 10 deg. As a matter of fact, Table 3, which shows the result of the tests with superheated steam in covered and bare pipes, shows a temperature difference at a velocity of the steam of about 30 ft. per sec., and, at a pressure of 98 lb., of as high as 110 deg.

Of particular interest is column 6 of the table, which shows the heat transfer from the steam to the metallic wall per sq. ft. and

DISCTJSSIQN 3 1 1

1 deg. temperature difference. The lowest is 15.4 B.t.u. at 30 ft. velocity; the highest, 36 B.t.u. at a velocity of about 98.5 ft.; while the same heat transfer for saturated steam is over 400 B.t.u. This shows the difference in the heat transfer from the steam to the pipe between superheated and saturated steam.

It is true that this difference is of less importance for a covered pipe, and the better the insulating quality of the covering, the less important is this difference. There is, however, no covering which is a perfect insulator, and there are a great many power plants where the piping is very poorly covered, so that the property of superheated steam of not readily giving up its heat is advan­tageously utilized, and in many cases, especially with long pipe lines, the saving due to elimination of radiation losses in itself warrants installation of a superheater.

With the exception of the Munich tests, no others have been made, to the knowledge of the writer, to show the difference in radiation losses from pipe lines, between saturated and superheated steam, due to the fact that it is very difficult to measure the radia­tion losses of saturated steam. With superheated steam, the radiation losses are expressed in the temperature drop of steam, while with saturated steam, no temperature drop occurs, arid a part of the steam is condensed, and there are no means to com­pletely separate the water from the steam. Practice has shown, however, that there is considerable reduction in the radiation losses in a pipe line carrying superheated steam, as compared with one with saturated steam.

In the table of losses from bare iron steam pipes, the author makes the same error as many of the pipe-covering manufacturers in giving the pounds of pressure of the steam and the superheat in degrees fahrenheit, corresponding to the total temperature, which gives the impression that the tests were made with superheated steam actually flowing through the pipe, while as a matter of fact these tests are made with electrically heated pipe. • The radiation losses as well as the temperature of the wall, if superheated steam of the given temperature and superheat were flowing through the pipe, would be considerably less.

Another point which should not be neglected, but which is not mentioned, however, is the influence of the velocity and moisture contents of the air. The author properly states that when con­ducting tests on pipes, it is very desirable that the room tempera­

3 1 2 HEAT LOSSES FROM BARE PIPE AT HIGH TEMPERATURES

ture remain constant. In order to have a constant temperature, the air in the room is kept as still as possible, which to a certain extent defeats the purpose of the tests, as in practice, air is always moving more or less, and the results are quite different. Any engineer operating a saturated engine, especially with a long outside pipe line, notices the difference in the moisture of the steam in a good clear day, or a stormy day.

The Munich tests, to which the author refers, and with which the writer is quite familiar, were also made in a closed laboratory, and Eberle had recognized and admitted that the temperature differ­ence between the steam and the wall, even with a covered pipe, increases considerably with the increased velocity of the air.

Particularly in discussing the heat exchange between the canvas surface and the air, the velocity and moisture of the air should not be neglected.

L. L. B a r r e t t . The bare-pipe-loss curves and the canvas- surface-loss curves given in Figs. 2 and 4 represent a notable ad­

DISCUSSIQN 3 1 3

vance in the investigation of these subjects, and the author is to be congratulated on the results attained. Where results on different pipe sizes are obtained by the same investigator, these results are preferable to results obtained by other investigators each working on a single pipe size, as variables other than the one being con­sidered are less likely to be present. By comparison of Figs. 2 and 4, it is noted that the heat loss per square foot per hour at 100 degrees temperature difference is greater from the 3.1-in. O.D. and 9.5-in. O.D. canvas-covered pipes than from the 3-in. and 10-in. bare iron pipes. This is at variance with previous results, which showed that the losses from bare pipes were greater than those from canvas-covered surfaces. The difference is understood to be accounted for by the fact that the author used thermocouples to obtain the canvas surface temperature whereas previous experi­menters have used thermometers for the purpose.

The author’s statement in Par. 18 that a 0.1-in. air space be­tween the pipe and insulation increases the overall loss does not appear to be borne out by his further statement that the tempera­ture drop for a 0.1-in. air space is approximately equal to that of 0.1 in. of insulation. If it is true that 0.1-in. air space is equivalent to 0.1 in. additional insulation, the overall loss is decreased by the use of the air space, assuming that there is no heat loss through the joints of the covering. However, the author’s conclusion that coverings should be kept as close as possible to cylindrical surfaces is true for the reason that in commercial installations where cover­ings are not carefully sealed an air space will allow the circulation of convection currents along the pipe and the heated air will escape through the joints in the covering.

The curve for 1-in. pipe in this figure seems too far removed from the other curves for consistency. The matter can be investi­gated on the basis of the author’s statement that the temperature drop through a 0.1-in. air space is approximately equal to that through 0.1 in. of insulation. The temperature drop through the first 0.1 in. of covering on a 1-in. pipe, assuming a standard thick 85 per cent magnesia covering and a temperature difference between pipe and room of 370 deg., figures out as 49 deg. which is one-third less than the corresponding ordinate on the author’s curve for the 1-in. pipe. The temperature drops through the first 0.1 in. of in­sulation on 3-in. and 10-in. pipes figure out greater than the cor­responding ordinates of the author’s curves for these pipe sizes.

This makes it appear that the ordinates of the curve for 1-in. pipe are too great. Imperfect sealing of the ends or joint of the cover­ing tested, thus allowing air infiltration, would account for the results obtained.

It is unfortunate that the author gives the impression in Par. 20 that conductivity is in some way related to the curvature of the covering. The definition of the thermal conductivity of a material is that it is the quantity of heat transmitted in unit time through unit area of a plate of unit thickness having unit difference of temperature between its faces. The proper conception of con­ductivity is therefore a conception of heat flow in one direction between two parallel planes. It is a specific property of the ma­terial and is independent of its shape. When heat flows through a material having curved surfaces, such as the insulating covering on a pipe, the increase of heat flow is accounted for by the increasing area of the path through which the heat may flow. The con­ductivity of the material, however, remains the same. In solving a problem of the heat flow through a pipe covering the correction for curvature is readily made, thus making it unnecessary to intro­duce the idea of curvature into the conception of conductivity.

In Par. 22, the author gives his ideas as to the direction in which future experimental work should proceed. This is a most important subject as manufacturers and users of insulations are constantly demanding more accurate data on conditions which are not directly covered by experimental research. To meet this de­mand various refinements in calculating processes have been intro­duced. One of these refinements which was introduced by G. D. Bagley,1 was the plotting of conductivity curves as a function of the temperature difference of the two surfaces of the insulation. The author of the present paper apparently has in mind, in Par. 22, the plotting of some such curves for commercial pipe coverings, although he does not state whether these curves are to be plotted as a function of temperature difference or not. He also mentions plotting them for different thicknesses of covering. It therefore is desirable that this process of plotting conductivity as a function of temperature difference be examined to see whether it affords a rational basis for the calculations of heat losses. If at the same time we can find a method which eliminates the necessity for

1 Conservation of Heat Losses from Pipes and Boilers, T r a n s ., vol. 40, 1918, p. 667.

3 1 4 HEAT LOSSES PROM BARE PIPE AT HIGH TEMPERATURES

DISCUSSION 3 1 5

plotting conductivity curves for every thickness of covering we shall have simplified matters considerably. Now we do know that con­ductivities change with temperature. If we are to accept Bagley’s method, we must agree that the conductivity of a plate of material the two faces of which are at temperatures 200 and 100 deg. fahr. is the same as the conductivity of a plate of the same material the two faces of which are at temperatures of 600 and 500 deg. fahr. This does not seem logical and' causes us to examine again the question of what conductivity is. We know that the conductivity of a substance is determined by the physical and chemical nature of the substance and that its physical and chemical nature is de­pendent upon its temperature and not upon a difference of tempera­ture. The thermal conductivities of the metals and of some of the electric insulators have been determined by Lees, Hornbeck, and other physicists, all of whom have expressed the conductivities they obtained as conductivities at certain temperatures. Now if by experiment we establish our curve of conductivity as a function of the temperature (not temperature difference) and we find this curve to be approximately a straight line between the temperatures corresponding to the temperatures on the two surfaces of an in­sulating covering, we have the elegant and useful relationship that 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. The proof of this proposi­tion is given by Hering.1 In order that the proposition may be true, it is unnecessary that the conductivity be proportional to the absolute temperature as was assumed by Hering, but only that it be a linear function of the temperature such as k = aT -|- b, where k is the conductivity, T the temperature, and a and b are constants.

There is reason to believe that the conductivity curves of com­mercial insulating coverings when plotted against temperature will approximate sufficiently to straight lines to permit advantage being taken of the relationship referred to. The German physicist Nusselt2 gives curves of conductivity as a function of temperature in Fig. 9. The curve for asbestos is a straight line between 200 and 600 deg. cent., while that for burned kieselguhr is a straight line from 0 to 450 deg. cent., and the curves for the other substances tested could be approximated by straight lines. The present knowl­

1 Trans. Am. Electrochemical Soc., vol. X X I, p. 520.2 Zeitschrijt der Vereines Deutcher Ingenieure, p. 1006, vel. 52.

edge of the relationship of conductivity and temperature has been summarized as follows by Pierce and Wilson: 1 “ Most experi­menters have been able to reproduce mathematically the results of their work on thermal conductivities by assuming that the con­ductivity is a linear function of the temperature.”

There is therefore some ground for the conclusion that if we are to refine the methods for the computation of heat losses by taking into consideration the effect of temperature on conductivity, we should reject the conception of conductivity being dependent upon temperature difference and should establish instead the curves of conductivity as a function of temperature. In the experimental work incident to the establishing of these curves, it is desirable that the differences of temperature used should be comparatively small and that the mean temperature of the substance under test should be ascertained by means of temperature measurements at both surfaces. In order to keep the temperature difference between the two surfaces low when investigating the conductivity at the higher temperatures, it will be desirable to place an outer insulating covering over that which is being tested, as this will cut down the temperature drop in the covering under test. After such a curve is established, it is only necessary to enter the curve with the mean temperature of the two surfaces of an insulation to ascertain the equivalent conductivity of the insulation for use in the current formulae. This process is applicable whatever the thickness of the insulation, so that it becomes unnecessary to establish conductivity curves for each thickness of covering as outlined by the author in Par. 22. The result is to simplify greatly the experimental work required and to put the computation of heat losses on a more rational basis. Inasmuch as the author has not established con­ductivities in the experiments reported in this paper the suggestion here advanced does not detract in any way from the excellent results which have been accomplished.

L. B. M c M il l a n . This paper is a timely contribution on a very important subject. It is of special interest to note that the author’s results on losses per square foot of surface on various sizes of bare pipe show how very much small differences between the large and small pipes than those given by Paulding. For example, Paulding’s curve for 16-in. pipe falls below the author’s curve for

1 Amer. Acad. Arts & Sciences, Proc., vol. 34, p. 24.

3 1 6 HEAT LOSSES PROM BARE PIPE AT HIGH TEMPERATURES

DISCUSSION 3 1 7

18-in. pipe, while Paulding’s curve for -|-in. pipe is considerably above the author’s curve for that size. Paulding’s curves show that at 500 deg. temperature difference the loss from a 16-in. pipe is 25 per cent less per square foot than from the same area of J-in. pipe, while under the same conditions the author shows that the difference is only about half as great as Paulding’s curves would indicate.

The writer is of the opinion that the author’s curves are the more nearly correct in this respect, because, while it is certain that there is a tendency for the rate of heat loss to be higher on the smaller pipes than it is on the larger ones, this difference is not as great as it is often assumed to be. Furthermore, the difference between rates of losses from small and large pipes are small com­pared with those caused by varying rates of air circulation on the same pipe. In other words, while pipe size may account for a varia­tion of 15 or 20 per cent, difference in air circulation may cause a variation of upwards of 100 per cent.

It will be noted that the author’s curves are based on tests of three pipes of different size, and that the other five curves were obtained by interpolation and extrapolation. An explanation of how this was done would be of interest. This is particularly im­portant, in view of the fact that the author’s curves differ con­siderably in slope from those of Paulding arid other recent investi­gators. In this connection, referring to Par. 8, it would be of interest to know if the slope of the curve from the second test was the same as that from the first. It is stated that the tests checked exactly the same at high temperatures, but it is not stated whether or not there was any variation at low temperatures.

Referring to Par. 15, the temperature drop does not depend only on resistance of the air space. It depends also on the amount of heat flowing across the air space and out from the insulation, just as voltage drop depends upon the electrical current, as well as resistance. Therefore, since temperature drop is equal to the product of thermal resistance (expressed in proper units) and heat flow, it is not clear that the temperature drop should decrease at the higher temperatures, as stated in this paragraph. While the resistance decreases at high temperatures, the heat flow in­creases, and if it increases more rapidly than the resistance de­creases, the temperature drops at the higher temperatures should continue to increase in spite of the decrease in resistance.

Therefore, some other explanation of the lower temperature drops at higher temperatures may be required. One such possible explanation might be increased air leakage into and out of the air space at high temperatures.

Some such explanation is required for the curve for 1-in. pipe, because it is hardly possible that the insulating value of a 0.1-in. air space on a 1-in. pipe would be equal to one-third of the total insulating value of the insulation, unless that insulation were very inefficient. In order to check this point the kind and thickness of the insulation should be given.

In this connection, it may be stated that the kind and thick­nesses of insulation should be given for each of the curves, for the thicker the insulation the lower will be the temperature drop through the air space.

The writer has made tests to check the author’s results on temperature drop across 0.1-in. air .spaces on 1-in. and 3-in. pipes. In these tests standard thick 85 per cent magnesia was applied in such manner as to provide air spaces of a uniform thickness of 0.1 in. around the entire circumference of the pipe. At a tem­perature difference between pipe and room of 235 deg. fahr. the temperature drop across the 0.1-in. air space on 3-in. pipe was11 deg., which checks within 3 deg. of the author’s curve for 3-in. pipe. However, at a temperature difference of 242 deg. fahr. be­tween pipe and room the temperature drop across the 0.1-in. air space on 1-in, pipe was only 19 deg., while the author’s curve for this size of pipe at the same temperature difference showed a temperature drop across the 0.1-in. of about 56 deg. Therefore, it would seem, as pointed out above, that the high values of tem­perature drop shown by the author’s curve for 1-in. pipe must be accounted for by some factor other than the normal temperature drop across the air space.

It is not clear on what the .conclusion in Par. 18 regarding the value of air space above 0.25 in. on flat surfaces is based, as the paper contains no record of results accomplished by various thicknesses of air space on flat surfaces.

The statements in the last two sentences in Par. 18 seem directly contradictory. If it is true that a 0.1-in. air space has the same resistance as 0.1 in. of insulation, then the heat transmission with the 0.1-in. air space would be less than without it, because surely the transmission through 1.1 in. insulation would be less than

3 1 8 HEAT LOSSES FROM BARE PIPE AT HIGH TEMPERATURES

DISCUSSION 3 1 9

that through 1 in., all other conditions being equal. Due to prac­tical considerations, the writer does not advocate applying insula­tion over such air space, but the author’s conclusion would seem to indicate that such a procedure would give slightly higher effi­ciency. He has shown that an air space as large as 1 in. increases the loss of a 3-in. pipe, due to the increased area, but that the small air space is just as good as that much additional insulation. It would be interesting to know just what thickness of air space would give the minimum loss, but this would be different for all different pipe sizes, increasing as pipe size increased, and in view, of the practical difficulties in the way of applying insulation in this manner, it is doubtful if tests to determine this would be of prac­tical value.

The first sentence in Par. 19 is open to the same comment as that made in connection with Par. 13, viz.: that temperature drop through the insulation depends upon the product of resistance, and heat flow, and not on the resistance alone.

Referring to Par. 20, the absolute conductivity of the material is a specific property of the material, just as density and specific heat are specific properties. Therefore, it is not dependent upon the size or shape any more than the density or specific heat is dependent upon these conditions. However, it does vary at different temperatures, but the effect of this variation may be determined without making tests on all thicknesses and all pipe sizes, as sug­gested by the author.

In this connection, the writer feels that Mr. Barrett’s discussion has clarified the situation very materially. The use of what Mr. Barrett terms “ equivalent conductivity ” which is the absolute conductivity at the arithmetic mean of the temperature at the two surfaces of the insulation is far simpler than the determination of conductivity by tests of all thicknesses of insulation on all sizes of pipes. Mr. Barrett has shown that the proposed method may be proven to be mathematically correct where the absolute conductivity curve with respect to temperature is a straight line and the writer believes that such curves for most efficient insulating materials are either straight lines or vary slightly from straight lines.

The curves showing losses from canvas-covered surfaces of various dimensions are of considerable interest. However, the sur­face resistance for an efficient insulation 1 in. or greater in thick­

ness is usually less than one-quarter of the total resistance. There­fore, small variations in surface resistance will have little effect on the total result. Furthermore, small changes in air circulation will have much greater effect on surface resistance than will differ­ence in pipe sizes.

The writer would like to ask the author what curve he would use for flat surfaces? It is evident that if the general equa­tion [4], is applied to a flat surface, the temperature difference will be 272.5 deg., regardless of all other conditions. This is obviously impossible, therefore, it is doubtful if the author’s general equationcan be used very much beyond the limits of his actual experiments.1

T h e A u t h o r . The main object of this paper has been to present some of the latest findings on bare and covered pipes operating at the higher temperatures and to give empirical formulas developed from the results, which would enable engineers to solve more readily heat insulating problems. It is to be understood that lack of space has prevented elaborate details concerning funda­mental data, all of which have been covered fairly well by other investigators.

However, since some of these points have been brought out in the discussion, the author will reply as briefly as possible to the most important questions.

Referring to the temperature drop from the outer surface of the pipe to the inner surface of the insulation, which has been discussed by Messrs. Barrett and McMillan, the results of these tests indicate that ordinarily the drop through a 0.1-in air space, or the space between the pipe and the inner surface of commercial insulations, is equal to the temperature drop through 0.1 in. of insulation, or the temperature drop is approximately the same as would be obtained if the insulation could be made to fit absolutely tight to the surface of the pipe. This depends upon the thickness of the insulation, the size of the pipe, temperature, etc. For strictly accurate calculations this temperature drop should be taken into account, especially for pipes 1 in. in diameter or less.

The drop in temperature at the higher temperatures, as shown in Fig. 3, can be attributed mainly to increased radiation loss, since the radiation loss increases more rapidly than the heat flow in­creases. This drop in temperature will vary und^r different con­ditions of temperature, thickness of air space, diameter of cylinder,

3 2 0 HEAT LOSSES FROM BARE PIPE AT HIGH TEMPERATURES

DISCUSSION 3 2 1

etc. In general, it may be said that the results of these tests on cylindrical surfaces compare favorably with the results obtained by the Bureau of Standards on flat surfaces.

The statement is not made in Par. 20 that the absolute con­ductivity depends upon the thickness and curvature of the covering. It is stated that the absolute conductivity curve depends upon the thickness and curvature of the covering.

If the temperature gradient curve from the inner to the outer surface of the insulation is obtained as the author has done by measuring the temperature at successive points out through the covering, and the flow of heat is obtained at the same time, the true absolute conductivity of the insulation at any radius or tempera­ture can be calculated readily from the relation that the flow of heat H through unit area per unit of time is equal to the con­ductivity K multiplied by the temperature gradient, or H = K ~ -dr

It will be found upon plotting the absolute conductivity of the insulation so obtained against the distance from the inner surface of the covering that the resulting absolute conductivity curve will vary with the thickness and curvature of the insulation. These variations cause considerable difficulty in solving heat-flow problems.

In order to obtain more ready means of calculating heat-flow problems, the author has suggested in Par. 22 that tests should be conducted to obtain a mean conductivity coefficient for different thickness of coverings. This mean conductivity coefficient is the mean of the conductivities at different points through the radius of the covering as obtained from the temperature gradient curve. However, it is not necessary to determine the temperature gradient curve in order to determine the mean conductivity coefficient for the different thicknesses. This can be determined by the relationthat

n loge n_

nwhere K, the mean conductivity coefficient for the temperature range of the covering, is plotted against the mean temperature be­tween the inner surface and the outer surface of the covering.

The use of what Mr. Barrett terms “ equivalent conductivity ” reduces the amount of experimental work considerably, as the absolute conductivity at any temperature can be obtained

from the experimentally determined temperature gradient curve, although it will be very difficult to determine the correct tem­perature gradient curve for some materials.

In order that the “ equivalent conductivity ” theory be correct, it is necessary that the conductivity be a linear function of the temperature. While this is true for most of the materials, great care should be taken that the law is not applied to materials which do not obey this law. In materials in which the flow of heat takes place mainly by conduction, the conductivity is a linear function of the temperature, but there are some materials in which the flow of heat takes place largely by radiation and convection currents. In these materials the conductivity coefficient which embraces the flow of heat by radiation, conduction, and convection, will not always follow a straight-line law.

In reply to Mr. McMillan’s discussion of the bare-pipe-loss curves, the slope of the curve for the two tests on the 1-in. pipe was the same. A short time after this paper was prepared, a check test was run on the 3-in. pipe at a temperature of 762 deg. fahr. with the room temperature at 85.6 deg. fahr. The B.t.u. loss at this temperature, or 676.4 deg. fahr. temperature difference, was 6.51. If a correction is made for a room temperature of 81 deg. fahr., it will be found that this point falls almost exactly on the extended curve for the 3-in. pipe, thus indicating that the curves for the different diameter pipes are parallel throughout.

The general equation [4] is approximately accurate for diam­eters up to 2 ft., as stated in Par. 26.

The loss of heat per unit area from flat surfaces varies greatly with the size and position of the body. The loss from the surface in a horizontal position is entirely different for the same surface in a vertical position. Also, the loss is different for the same flat surface facing downward than for it facing upward.

For these reasons, it is unreasonable to expect that the curves for cylindrical surfaces could be extended to include flat surfaces. To express accurately the surface loss law from flat surfaces would probably require at least three rather complicated equations.

In regard to Mr. Broido’s discussion, the loss of heat from the surface of bare pipes is absolutely independent of the nature of the steam in the pipes. The loss depends only on the tempera­ture difference between the pipe surface and the surrounding air, the temperature of the air or surrounding objects, the nature of the pipe surface, diameter, position, etc.

3 2 2 HEAT LOSSES FROM BARE PIPE AT HIGH TEMPERATURES

DISCUSSION 3 2 3

The temperature drop from the steam to the outer surface of the pipe for superheated steam varies greatly under different con­ditions. In calculating the bare-pipe-loss table for the super­heated steam, a drop of 10 deg. fahr. was assumed. Under certain conditions, the drop would probably be less than this, while in other conditions the drop would probably be much greater, as mentioned by Mr. Broido.