I A . DUSTRIAL AXD EXGINEERING C H E - I S T R Y
522
hydroxide forms in the presence of moisture, and the tin is left in the form of sponge. I n dry air the alloy tarnishes only superficially with a coating which seems to be a mixture of the oxide and carbonate. Table I11 gives some corrosion data for an alloy containing 18 per cent strontium. Table 111-Rate
of Corrosion of 18 Per C e n t Strontium-82 Per C e n t T i n Alloy a t Z O O C. IN AIR SATDWITH
EXPOSURE WATERVAPOR
IN DRYAIR
Days 10 20 30 40 50
Gain in weight Gram per sq cm. 0 07 0 18 0 31 0 45 0 62
Gain in weight. Gram per sq cm. 0 0013 0 0024 0 0033 0 0048 0 0051
60 85
0.85 1.42
0,0060 0.0081
I N WATER Hydrogen evolved per sq cm. surface
Hours 10 24 34 46 58 65
Cc. 52 106 154 202 264 Completely disintegrated
Vol. 22, No. 5
All the chill-cast alloys containing more than 12 per cent strontium were practically non-malleable and non-ductile. Alloys containing from 12 to 18 per cent strontium were coarsely crystalline, as shown by the fracture, and the alloys still higher in strontium were about as brittle as glass. Strontium-tin alloys might be used as de-oxidizing agents for bronze, or they could be used to introduce tin and strontium into many other alloys if this were found to be desirable. Literature Cited (1) (2) (3) (4) (5) (6) (7)
Donski, 2 anorg Chem., 67, 213 (1908) Grube, I b t d . , 46, 76 (1905). Jellinek and Wolff,I b i d , 146, 329 (1925). King and Clark, J . A m . Chem. Soc., 61, 1709 (1929). Ray, Metals and Alloys, 1, 112 (1929). Ray and Thompson, Ibzd , 1, 314 (1929) Tammann, “Textbook of Metallography,” p. 228, Chemical Catalog, 1925.
Studies in Heat Transmission’ I-Measurement of Fluid and Surface Temperatures A. P. Colburnl and 0. A. Hougen DEPARTMENT
OF
CHEMICAL ENGINEERING. UNIVERSITY OF WISCONSIN, MADISON, WIS
The accuracy of experimental data on heat transmission depends upon exact measurements of temperatures of surfaces and fluid streams. The serious errors introduced by improper use of thermocouples are demonstrated. Methods are given for the following temperature measurements with thermocouples: ( 1 ) Measurement of the average temperature of a given cross section of a fluid stream or of a given surface area by a single observation by means of a special multiplejunction thermocouple. (2) An accurate method of measuring surface temperatures of metals. This method consists in imbedding the
wires in a narrow slot in the metal surface in a line of zero temperature gradient for a distance of about 1 inch in each direction from the junction. The junction is soldered in place and made flush with outer surface of metal. The rest of the couple in the groove is packed flush with surface with glycerol-litharge cement providing excellent thermal contact but poor electrical contact except at the junction. (3) Method of minimizing temperature fluctuations of couples in fluid streams so as to facilitate readings. A review and criticism of previous methods are given.
I
will be the average of the individual circuit e. m. f.’s. If the resistances are not the same, the individual temperatures will be weighted by the relative conductances of the junction circuits in determining the reading of the single wires. A proof of these statements follows. The relation of the e. m. f . of the single wires to.the e. m. f .’s of the individual thermocouples can be shown theoretically from Kirchoff’s laws. Let the individual junctions and wires be represented by sources of e. m. f . (el, e2, . . . e,) and by electrical conductances (e1, c2, . . . en). (Figure 1) By Kirchoff’s first law the total e. m. f., E, across the main wires bears the following relationship t o the individual e. m. f.’s, where il, i2, , , i, are the currents flowing in the individual circuits:
N DETERMINING the heat-transmission coefficients of
the various fluid films in an experimental tubular gas condenser, a preliminary study was made of the technic of temperature measurements in such a heat exchanger. For convenience and precision thermocouples were used which required special arrangements for the following conditions: (1) to measure the average temperature of an area over a given cross section of a fluid stream or over a given surface; ( 2 ) to measure the temperatures of surfaces; and (3) to minimize the fluctuations of thermocouple temperatures which would prevent precise balancing of the potentiometer. Measurement of Average Temperature of Areas
To measure the average temperature of fluid streams and of surfaces a multiple-junction single thermocouple was devised. This consists essentially of several very short thermocouples connected in parallel to a common pair of thermocouple wires. These short branch thermocouples are all of equal length (3 or 4 inches), just long enough t o reach the common thermocouple wires. If the resistance in each small branch circuit is the same the e. m. f. indicated by the common wires Received February 10, 1930. Abstracted from a forthcoming bulletin of the Chemical Engineering Department of the University of Wisconsin. Present 2 Fellow in Chemical Engineering, University of Wisconsin. address, Experimental Station, E. I. du Pout de Nemours & Company, Wilmington, Del. 1
E
= el
E
= e2
- il -
or E
c1
= el
c1
-
il
GI’ a2
- -,
or E cz = e2 c2 - i~
61
E = e,,
=
5 or E
c,, = e,, c,, -
i,
cn’
By summing up the (n) equations for the (n) junctions and by Kirchoff’s second law, placing it + i * . . . . +in = 0
+.
the following equation results:
I Y D USTRIAL A V D ENGI-VEERISG CHEMISTRY
May, 1930
+
+ . . + E c,, = el c1 + e2 cz + . . + e, c,, el + e? cz + . . . . + e,, cn E = c 1 + cz + . . . . +
E cl E cz Solving for E:
CI
Cn
This equation states that E is the average of el, e2, . e,, weighted by the conductances, cl, c2, . . cn. If the conductances of the individual circuits are equal: E =
el
+ e2 + . . . + e, n
The above relationship was checked expeiimentally by the use of a double-junction copper-constantan thermocouple and two mater baths at different known temperatures. When both junctions were in the same bath, the resultant e. m. f . n a s the same as that of an ordinary single-junction thermocouple. When the two junctions were in different baths, the resultant reading was almost exactly the average temperature of the two baths as determined separately by the double junction or by single thermocouples, as shown by Table I. T o test the applicability of the multiple-junction thermocouples to the measurement of surface temperatures, the effect of an electrical connection of low resistance between the two individual junctions mas determined. The junctions of the double-junction thermocouple mere connected by a piece of heavy iron wire and again immersed in the two baths. The resultant reading again agreed well with the average temperature of the baths, as shown by Table I. T a b l e I-Test of D o u b l e - J u n c t i o n T h e r m o c o u p l e (The tx.0 hot junctions are represented by symbols A and I'OSITIOX
A B
2644
B
4""
ks where k , = thermal conductivity of wires k , = thermal conductivity of surface d = diameter of wires h = heat-transmission coefficient from wires to surrounding medium
Surface temperatures of a steam drum were measured with copper-constantan thermocouples soldered directly to the surface and with the mires extending perpendicularly into the air. This arrangement showed a n error of 2 per cent in temperature measurement. The heat-transmission cocfficient for natural convection from wires to air is very small
B)
1048 4192 2625
A
temperature gradient from the surface to the medium. Kusselt (G) showed that the error is a function of the term:
M2 crowolts
A and B in bath (1) A and B in bath (2)
(Checked by single couple) (Checked by single couple) Average in bath (11, B in bath ( 2 ) in bath ( l ) ,A in bath (2) Average . JUNCTIOUS A A U D B C O U N E C T E D B Y HEAVY IRON in bath ( l ) ,B i n bath (2) in bath (11, A in bath (2) Average
523
2616 2630 WlRE
2660
2600 2630
Thus for a difference of 130" F. in temperature of the two baths, the deviation of the double-junction reading from the average of the two single e. m. f.'s corresponded to only 0.6" F. The error in the case of theconnected junctionswas only 1.2OF. For small temperature differences between the junctions an excellent average value should therefore be obtained. This type of thermocouple was used only for measuring the average temperature of areas where differences of only a few degrees prevailed. Measurement of Surface Temperatures
The modern trend of the experimental determination of heat-transmission coefficients of separate films has required accurate methods for the measurement of surface temperatures. Measurements by means of a thermocouple may be subject to serious errors, depending upon the method of attaching the junction to the surface. Errors may be introduced by the conduction of heat along the wires to or from the junction, or the location of the couple on the surface may act as an insulator and thus change the normal temperature a t that position. The latter condition disallows the use of insulation over the junction and adjoining area to minimize the heat conduction along the wires. Where the thermocouple wires extend directly out from the surface, the magnitude of the error in the temperature of the junction due t o conduction of heat along the wires depends upon the diameter of the wire, the thermal conductivities of the metal surfaces and the wires, the heat-transmission coefficients from the wires to the surrounding medium, and the
Figure 1
compared with the thermal conductivity of the wires, so that if the leads pass out into a medium in which they have a high heat-transmission coefficient, such a s cooling water or condensing vapors, the error will be much larger. Some investigators have minimized this error by carefully peening the wires into holes in the surface, thus avoiding a n increase in the area of surface at the junction of the thermocouple. Even in this arrangement any measurements made where the leads passed directly into a highly conducting medium must be in error. Many data of heat-transmission coefficients are unreliable because the surface temperatures used in the calculations were incorrectly measured. PREVIOUS AlmHoDs-Because of the importance of an accurate knowledge of surface temperatures for determining the heat-transmission coefficients of film and the thermal conductivities of solids, many methods of measurement have been suggested. Among the first to publish surface-temperature measurements in heat-transmission investigations were Stanton (11) and later Soennecken (IO), who used extensometers to indicate tube temperatures. These methods require frequent difficult calibrations and only determine the average temperature of the entire tube. Jordan 13) and later Kebster (12) brought thermocouples out from the surface in small tubes attached to the surface. Such attachments change the surface temperature, since the presence of the tubes changes the flow of heat from the surface. Rietschell (9) supported the thermocouples for measurement of surface temperatures in rather long grooves on the inside of the pipe. The wires near the junctions were kept in good thermal contact wit11 the surface by being packed in the grooves with a litharge-glycerol cement. At the end of the groove away from the junction the wires were led through a hole in the pipe to the outside. Such a system will give accurate results only if the wires are electrically insulated near the junction.
524
INDUSTRIAL A N D ENGINEERIAVG CHEMISTRY
Kreisinger and Barkley (5) attempted to correct for conduction of heat to the junction by measuring the surface temperature with thermocouples of different sizes. By plotting observed temperatures against diameters of the wires, they expected to be able t o extrapolate t o zero diameter and then obtain the correct value for the temperature. Unfortunately one of their smaller wires broke before they obtained satisfactory results. This method may be accurate if the different junctions are attached a t positions of exactly the qame temperature, but is inconvenient since it requires additional thermocouples of different sizes. A test made by the writers with thermocouples of three sizes showed this method to be difficult of application, since the presence of different amounts of solder on the different junctions would throw off the extrapolated value. Reiher ( 8 ) used a method similar to that of Rietschell. He introduced the wires into small grooves parallel to the axis of the pipe and extended these grooves from the junction t o the end of the tube. The junctions were soldered in small depressions and smoothed over. The groove was covered with cement so as not t o alter the surface conditions. King and Blackie ( 4 ) imbedded thermocouples in small copper disks, which were then pressed against the surface. This is similar to the surface temperature elements of Hencky ( 2 ) , in which the wires are contained in a spiral groove of a copper disk. This method should be good if care is taken to see that the wires are in good thermal contact with the disk but electrically insulated from it, and that the disk is in very good thermal contact with the surface-a condition which is difficult to obtain. Bayer and Buss (1) developed a portable thermocouple consisting of a thermocouple junction held against the surface and compensated against heat losses by means of a small electric heating element. This couple cannot be used when the surface is cooler than the medium next to it, and cannot be kept in place on the surface more than momentarily or it will act as an insulator for heat transmission and thereby change the surface temperature from its normal value. Othmer and Coats (7) used an electrodeposition method in which one wire was of the same metal as the surface and was attached directly to it, and the other wire was looped around the pipe a t the desired position and then covered by an electrodeposited layer of metal of the same composition as this wire. The claim for this method was of providing a comparatively broad interface for one junction of the couple. This broad interface, however, acts as a large number of junctions conneded in parallel. It was previously shown, in discussing the theory of multiple-junction couples, that the e. m. f . indicated by the resultant leads is the average of the individual e. m. f.’s weighted as the conductances of their separate circuits. Thus the interface just a t the position where the wire enters the deposited metal will have an enormous conductance, and the resultant e. m. f. will be practically that of this relatively small area. The temperature a t this small interface will be affected by heat conduction alolig the wire unless the electrically deposited layer is quite thick. Thus this method is of but little advantage, and furthermore is impractical for most equipment owing to difficulties of electroplating on large tubes and the restriction of the choice of tubes or thermocouple wires. PROPOSED &~ETHOD---FrOmthe above review it is seen that the two best methods of surface-temperature measurement so far proposed are of imbedding the wires in the surfaces for some distance back from the junctions with good thermal contact and electrical insulation or, where this is impossible, to use the extrapolation method with thermocouples of different. sizes of wires, For the present investigations on heat transmission of condensing steam, great care was necessary in the
Vol. 22, No. 5
measurement of surface temperatures, since the thermoelements passed into condeniing steam, which has an enormous heat-transmission coefficient. The thermocouples were placed in annular slots around the vertical pipe which were about ‘/32 inch wide and deep. The wires were extended about an inch from the junction in opposite directions. The junctions were soldered in place so that the solder was flush with the outer surface and the rest of the couples were packed in the slot with a glycerol-litharge cement flush with the pipe surface. Thus the wires were in fair thermal contact with the metal of the pipe, but electrically insulated from it everywhere except a t the junction. Some question may be raised as to the degree of thermal contact attained with the glycerollitharge cement around the rubber-covered wires. Practically, this is not important as long as the top of the groove is flush with the pipe surface and the groove is narrow. This type of couple was tested on a steam drum and found to agree m-ith the exact surface temperature as calculated for conditions of knonn heat flow through the metal. The surface couples used for heat-transmission investigations were of the multiplejunction type with four hot junctions for each area. These were located a t points on the surface of the pipe on the same horizontal plane but a t angles of 90 degrees apart, thereby measuring the average pipe temperature a t any section. Very consistent results were obtained in practical use, which further verified both the method of fastening to the surface and the use as multiple-junction thermocouples. Minimizing Fluctuations of Thermocouple Temperatures Two methods were found to minimize fluctuations of thermocouple e. m. f.’s in fluid streams where efforts are made t o maintain constant temperatures. Where temperatures fluctuate greatly, the balancing of a precision potentiometer is difficult or impossible. Air mas bubbled into a narrownecked flask filled with boiling water and an ordinary thermocouple in the neck was found to fluctuate widely. Two methods which decreased this variation were the application of a thin covering of cotton gauze and enclosing the junction and wires near it by a closely fitting thick-walled copper tube. Since the air-steam mixture was saturated, the gauze covering became saturated also and then was slow t o change in temperature because of its high heat capacity. The copper tube also acted as a heat reservoir to keep the junction from following momentary changes in the temperature of the gas. I n both methods the covering was extended over the wires near the junction, so there would be no heat conduction along the wires to the junction. The wires were electrically insulated from the copper tube a t all places except a t the junction-a very necessary condition as the wires would follow temperature fluctuations and tend to conduct heat to or away from the junction unless this precaution is taken. The method of gauze covering was found advantageous for all couples located in streams of liquids or saturated gases. Literature Cited (1) Bayer and Buss, IND. E N G . CHEM.,18,728
(1926).
(2) Hencky, Handbuch der Physik, Geiger und Scheel, 11, 147 (1927). (3) Jordan, Proc. Inst. M e c h . Eng. (London), 4, 1317 (1909). (4) King and Blackie, J . Sci. Znstrumenls, 2, 260 (1926). ( 5 ) Kreisinger and Barkley. Bur. Mines, Tech. P a p e r 114 (1915). ( 6 ) Nusselt, Mtll. Forsch. A r b . , Heft 6 3 , 26 (1909). (7) Othmer and Coats, IND. E ~ GCHEM., . 20, 124 (1928). (8) Reiher, Mill. Forsch. A r b . , Heft 269 (1925). (9) Rietschell, Mitt. der Prufdngsanstaltung fur Heiz und Luftungseinrichtungen der koniglichen technischen Hochschule Berlin, Heft 3
(1910). (10) Soennecken, M i l l . Forsch. A r b . , Heft 108-9, 33 (1912). (11) Stanton, T m n s . R o y . SOC.L o n d o n , 190-A,67 (1897). (12) Webster, T r a m . Inst. Eng. Shipbuilders Scotland, 57, 58 (1913).
