ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT maximum velocity in an annulus appears t o shift inward from its position in fully viscous and fully turbulent flow. The amount of t h e shift may well be enough to equalize t h e skin frictions on t h e inner and outer boundaries. The exact position of t h e maximum point in transition flow is not yet known precisely. The factthat the first deviation from viscous behavior is observed a t the position of maximum local velocity does not necessarily mean t h a t initial turbulence is generated a t that point.
D,D, = diameter of pipe, ft. D, = diameter of needle, ft.
= Fanning friction factor, dimensionless = length of conduit over which pressure drop is measured,
Et.
ATRe = bulk Reynolds number for pipes =
DVp -->
P
diinerisioriless
KRet = special bulk Reynolds number for annuli 4pgo
= =
ro
= =
r
T,
= =
r2 ri
=
4R .vaT i P
-,
Ll
dimensionless pressure drop due t o fluid friction, poundals/sq. ft. radius from geometrical center to point of measurement in fluid, ft. inner radius of pipe, ft. inner radius of annular space, ft. outer radius of annular spx< radius from geometrical center'^^ edge of laminar film, ci
lb.
radius from geometrical center t o point of maximum local fluid velocity, f t . RH = hydraulic radius of t h a t portion of fluid lying between T,, and r. f t . ?2 - 7 2 =in annuli 2r = r / 2 in pipes R H p = hydraulic radius of that portion of fluid lying between r m and r2, f t . ri - r; =in annuli 2~2 = ro/2 in pipes = local fluid velocity, ft.jsec. u = local fluid velocity a t edge of laminar film, ft./sec. u, rnL
T TO TI
72
maximum local fluid velocity, ft./sec. average fts/sec. = fluid viscosity, lb./(sec.)(ft,) = fluid densit,!., lb,/cu. ft. = local shearing stress, poundals/pq. ft. = skin friction a t wall of pipe, poundalsjsq. ft. skiil friction a t core of a n n u b PoundaWsq. f t . = skin friction a t out,er boundary of annular space, poundalsjsq. ft. =
=
Literature cited
Nomenclature
fL
'
urn
=
(I) Carpenter, F. G., Colburn, AL P., Schoenborn, E. AI., and Wurster, A, Trans. Am. Inst. Chem. Engrs., 42, I65 (1946). (2) Gazely, C., J r . , P h . D . thesis, TJniversity of Delaware, 1948; Dukler. -1.E., and Bergelin, 0. P., Chem. Eng. Progr., 48, 557 (1952). IT..Phil. illaa., 7, 15 (1933). (3) Gibson, -1. (4)Knudsen, J. G., and Katz, D. L., Proc. Midwestern Conf. on Fluid Dynamics, 1st Conf., No. 2, 175 (1950). (5) Lamb. H.. "Hydrodynamics," 5th ed., p. 555, Cambridge University Press, London, 1924; Lindgren, E. R., A p p l . Sci. Resenrch, Sect. A , 4, KO.4, 313 (1954). (6) Maurer, E., 2. Phvsik. 126, 522 (1939). (7) AIelrsyn, D.. a n d Stuart, J. T., Proc. Roy. SOC.( L o n d o n ) ,208A, 517 (1951). (8) I\Iueller, A. C., Trans. Am. Inat. C h e m Engrs., 38,613 (1942). (9) Prengle, K. S.,Ph.D. dissertation in chemical engineering, Carnegie Institute of Technology, Ma37 (10) Rothfus, R.R . . LIonrad, C. C., and Senecal, T. E., ISD. EXG. CHEM.,42, 2511 (1950). (11) Rothfus, B.R.. and Prengle, R. S., Ibid., 44, 1653 (1952). (12) Schiller, L., Proc. Intern. Congr. Appl. Mech., 3rd Congr., Stockholm, 1, 226 (1930). (13) Senecal, V. E., and Rothfus, R. R . , C i ~ e m E . T I ~Progr., . 49, 533 (1953)
In
RECEITED for review July 30, 1934. ACCEPTEDNovember 8, 1964. Submitted by R . S. Prengle in partial fulfillinent of the requirements for the degree of doctor of science a t Carnegie Institute of Technology. Material supplementary t o this article has been deposited a3 Document No. 4434 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 2 5 . D. C. A copy may be secured by citing the document number and by remitting 517.50 for photoprints or R5.60 for 35-mm. microfilm. Ad\-ance payment is required. Make checks or money orders payable to Chief, Photoduplication Service, Library of Congress.
M e t a l 4 1m esistance Ther for Measuring Surface C. C. WINDING, L. TOPPER', Cornell Universify, Ifhaca,
AND
B.
v.
BAUS2
N. Y.
A
CCURATE average surface temperatures ate frequently required in heat transfer investigations. LIeasurement of true surface temperature is particularly necessary in determining film coefficients when the driving force is very small. For horizontal tubular exchangers where condensation or boiling occurs, surface temperatures generally vary both longitudinally and around t h e circumference, as vel1 as a i t h tube position in t h e bundle. I n such a case, point values of surface temperature may be inadequate for t h e calculation of film coefficients. Nuclear boiling and dropwise condensation further reduce t h e accuracy of point values because of temperature variations a t t h e surface. Two techniques now in use for measuring true surface temperatures are radiation pyrometry and t h e optical methods of E. Schmidt (schlieren photography) and R. B. Kennard (interferom1 3
Present address, The Johns Hopkins University, Baltimore 18, Md. Present address, E. I. du Pont de Kernours & Go., Inc., Wilmington,
Del.
386
eters
etry) These method.: require that the observer see the surface and so they are not applicable to many heat transfer studies. Colburn and Hougen (6) have reviewed the conventional methods for surface temperature measurements. Most of them involve the use of embedded wire thermocouples which measure point values and are seldom positioned exactly at the surface. Flow patterns are frequently disturbed, and heat may be conducted t o or from t h e junction by lead wires. Different methods of inetalling the thermocouples do not give consistent results. Surfaces, such as condensers, which have a wide variatioii in temperatures, require the installation of many thermocouples t o obtain a useful average value. Bendersky (4)used a nickel film deposited 011 a steel probe as a thermocouple. Xear the turn of the century, Callendar suggested that the average temperature of a metal tube might be derived from a measurement of its electrical resistance. Jeffrey ( 7 ) reexamined this proposal and %-asable to derive a relation between
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 3
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT the average surface temperature of a thin-walled tube and the average bulk temperature indicated by resistance measurements. The main disadvantage of his method is the need for an expensive Kelvin double bridge to measure the resistance of a tube of ordinary dimensions. Baker and Tsao ( 2 ) used this technique to measure the heat transfer coefficients for condensing mixed vapors which were immiscible in the liquid phase. They employed both a 20-gageJ 5/8-inch and a 20-gageJ 1-inch copper tube with total resistances of 400 and 650 microhms, respectively. Their results were in general agreement with those of other investigators using more conventional methods. The development of the evaporation method for depositing thin metal films suggested a novel method for the measurement of surface temperatures. Thin, uniform metal films deposited on nonconducting substrates by vacuum evaporation may be used as resistance thermometers to measure surface temperatures. Baus (3) has shown that such films measure average surface temperatures. These films, usually less than 1000 A. in thickness, have negligible thermal resistance and capacity, so that the measured temperature should be identical with that of the interface of fluid and solid. For the same reasons, the film responds quickly to changes in fluid temperatures. There is no disturbance of the flow of heat or fluid over a tube coated with an evaporated metal film, nor is the topography of the surface affected. Changes in the emissivity of the surface and the interfacial tension of the solid and fluid may occur, but in many instances these effects are unimportant. The effect of heat conduction by lead wires is negligible, since temperature measurement is spread over a large surface and not located a t a single point. The resistance of the film can be controlled so that the measurement is easilv made and negligible heat is generated in the film by the passage of the meamring current. Once calibrated, electrically stable film resistance thermometers should be capable of good precision. F i l m suitable for surface resistance thermometry should be resistant to corrosion and abrasion and electrically stable (resistance of a given film dependent only on temperaturej, and they should have high temperature coefficients of resistance. Published work on the properties of evaporated metal films, although considerable, is often contradictory, and little attention has been given to those metals which are best suited for this application. Carefully controlled conditions are used to deposit uniform metal fllms on nonconducting substrates
In the work reported in this paper carefully controlled conditions were used to evaporate chromium, nickel, Inconel, silver, aluminum, and germanium. Some of the films were protected by films of calcium fluoride, magnesium fluoride, or silicon monoxide deposited by vacuum evaporation in the same vacuum system that was used for the metalizing process. Glass and quartz plates (Pyrex Brand No. 7740, Vycor Brand No. 790, crown glass and quartz obtained from Gencral Electric Co ), 2 X 1 X inches, with ground and polished surfaces were used as substrates for the metal films. Electrical contact with the films was made by copper wires soldered to heavy fired-on platinum layers (Figure I), which were coated and fired on the glass plates for I/z inch a t both ends before the metal films were deposited. The platinum lacquer used in the firing process was Platinum Paste No. 14, a product of Hanovia Chemical and Manufacturing Co. Thermometer, used for heat transfer measurements, was prepared with a different lacquer (Figuie 7 ) . The evaporations were done in a chamber made from a borosilicate glass tee-tube equipped with ground joints a t the open ends. Through the two straight-run openings, tungsten electrodes entered the chamber; the third opening was connected to a cold trap and mercury diffusion pump. Exhaustion of the chamber to a vacuum of 10-6 mm. of mercury (measured with a McLeod gage) was possible. An attempt was made to maintain a similar environment in the evaporator for successive evaporations. March 1955
The technique of the evaporation was essentially that recommended by Strong (9). The metal being evaporated was heated until its vapor pressure reached approximately 10-2 mm. of mercury. The heat for the evaporation was supplied by the ohmic heating of a tungsten filament. Materials which were available in wire form were wrapped on 0.020-inch tungsten wires and twisted into helical coils; the others were evaporated from a conical tungsten wire basket. These filaments were jointed by brass connectors to the tungsten electrodes.
Figure
1.
Construction of metal-film thermometer
resistance
In order of application: 1. Six layers of flred-on Hanovia Platinum Paste No. 14, (electrical resistance between ends of film is less than 0.1 ohm) 2. Metal fllm deposited by vacuum evaporation 3.
4.
5.
Clamps, 0.030-inch beryllium copper Copper wire, 1 8 B. & S. gage, soldered to platinum and to clamp Copper wires leading to Wheatstone bridge, soldered to clamp
The blank glass plates were washed with an abrasive soap, rinsed in distilled water, and dried a t 200" C. Cellulose tape (Scotch tape) was used to mask the central 1-inch square of one face of the slide, while the exposed 1 X '/z inch rectangles a t both ends were painted with platinum lacquer (Figure 1). Just enough platinum was applied to make the coating level out smoothly. After the coating had dried, the tape was carefully removed and the slide was placed in an electric muffle furnace. A firing temperature of 550" C. was used for crown glass; the other glasses were heated to 650" C. This temperature was approached slowly and maintained for 10 minutes. The slide was allowed to cool in the furnace to about 250" C. and was cooled in theiroom. This procedure was repeated until six successive layers had been deposited. The resistance between opposite ends of the platinum bands was always less than 0.1 ohm. The plates were then cleaned rigorously. They were scoured with a dilute suspension of scouring powder (Bon-Ami), rinsed successively with water, acetone, a silicate detergent, and with boiling distilled water. After they were dried in air, they were mounted in the plate holder. During all of these operations, slides were clamped with forceps on a part of the platinized area that would not receive evaporated metal. The final cleaning was effected by quickly passing the tip of the flame from a gas-air torch over the surface of the glass. The plate and plate holder were then placed in the evaporator, and the system was assembled, sealed, and evacuated. The heating current for the evaporation was controlled by a water-cooled rheostat, which was in series with a direct current ammeter. When the vacuum had attained its ultimate value the flow of the rheostat cooling water was started, the desired filament terminals were selected, and the current was turned on and slowly increased until the filament was hot enough so that the attached metal had a vapor pressure of about 10-2 mm. of mercury. Observation with an optical pyrometer of the metal to be evaporated was sometimes helpful, but usually it was sufficient to watch for the gradual darkening of the glass slide and of the unshielded part of the evaporator. After the metal had been deposited, the current was reduced and then turned
INDUSTRIAL AND ENGINEERING CHEMISTRY
387
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT loo
60
1 1
I
i
lLEaxIl
n as no evidence t h a t the electrical properties
of otherwise similar films were affected by the nature of the substrate when Pyrex Brand Yo. 7740 and Vycor Brand No. 790 glass, or fused quartz, xere uqed; nor did protective mineral coatings change the resistance or temperaturc coefficient appreciably. There is evidence ( I S ) that any chemical bonding between metal films and glass is through unshared electrons of oxygen atoms. This is in agreement with the observation that the solder and platinum films 1% ere very easily removed from glass substrates, while chromium, with its considerable affinity for oxygen, formed a very tenacious deposit. The chromium films could not be scratched with a knife, and were very resistant to corrosion .!.qua regia dissolved chromium films a t a rate equivalent to a reduction in thickness of only 10 A. per hour. Sickel films had moderate resistance t o abrasion and a resistance to chemical attack comparable with that of the hulk metal. The Inconel films wcre cqual to those of niclrcl in electrical Etability arid in resistance to attack and abrasion, but their temperature coefficients n ere small. For transmission of nreater than 5%.-, t h e relationship betwecn light transmission and film thickiiess is Patisfa.ctorily expressed by Lambert's law, Film thickness T~~~ calculated from the loss in filanlent neight during evaporation. For chromium films, t h e coefficient of correlation O n a Lambert's law plot was 0.98 (Figure 2; left). This correlation is also suitable for nickel films (Figure 2, right). The resistance of evaporated metal films is always higher than T o d d be predict'ed from the properties of the bulk metal, and the ratio of the resistivity of a thin film t o that in the bulk condition depends on the metal and the film thickness, This ratio can assume very high values (150 for chromium and nickel) when the thickness is less than 100 A. Silver and Inconel are more nearly normal; t h e resistivit,y ratio varies from a value of 4 when the film t,hickness is 100 9.t,o 1.2 a t 1000 A. Figure 3 presents
Substrate Pyrex Brand No. 7740 Q Vycor Brand No. 790 9 Quartz d Vycor Brand No. 7 9 0 with MgFz coating 57 Quartz with MgFz coating +
Y
off. If a protective coating m s to be deposited on the met,al film, the new filament terminals were connected and the heating process JTas conducted in a similar manner. The part oi the plat,inized surface of the slide Rrhich had not heen coated Iyith evaporat,ed metal vas tinned lyith a 90:10 alloy of tin and antimony, This solder, melting at 2430 c.,perIllitted testing of the film a,t temperatures about 70" 6,higher than lT,l-ouldhave been possible Tvith conventional solders, The light translnission of the film lneasured, and clips of 0,030-i~1ch beryllium copper strip were slipped over the untiniied platilium and tightly closed. Each of the clips (Figure 1) carried three soldered copper mires, two of them lead .iT-ires for the hiidge, and t h e third a short \Tire soldered to the adjacent tinned platinum band. The film n-as connected into the modified Wheatstone bridge circuit of \Tenner and 10' Smith ( l a ) , which compensated for the resistance of t h e lead wires. The films were heat-treated, either isothermally in an electric muffle furnace at 200' C., d or in a cyclic fashion from room temperature Lo t o 170" C. by an infrared lamp operated intermittently by a timing switch. The electrical resistance of unannealed films drifts upward isothermally, but annealing at higher temperatures than those of subsequent use may reduce the drift.
I
II4
8
t
IO'
w v)
g 0
10
Electrical stability is critical property in selection ob metal film for resistance thermometry I
The requirement of electrical stability was found t o be critical in determining which metals were suitable for temperature measurements. Of t h e metals tested, chromium, nickel, and t h e alloy, Inconel, produced films that were satisfactory. Chromium was the only metal t h a t yielded completely stable films. The crown glass, which has a much higher temperature coefficient of expansion and adsorbs and evolves larger amounts of gas, was found to be an unsatisfactory substrate, but there
3 88
THICKNESS,PNGSTROM UNITS
NICKEL
CHROMIUM
Figure 3.
Effect
of film
thickness on electrical resistance
So bstrate Pyrex Btand No. 7740 0 Vycor Brand No. 790 d Vycor Brand No. 790 with CaF2 coating )Q: Vycor Brand No. 790 wi!h MgFz coating 8 Quartz (? Crown glass - Computed values based on resistivity of bulk metal f
--
~
INDUSTRIAL AND ENGINEERING CHEMISTRY
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ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
THICKNESS, ANOSTROM UNITS
CHROMIUM
NICKEL
Fiaure 4. Effect of film thickness on temDerature coefficient of resistance at 20' C. Substrate + Pyrex Brand No. 7740 C, Vycor Brand No. 790 KJ' Vycor Brand No. 790 CaFz coating ,M Vycor Brand No. 790 with MgFz coating 0 Quartz Crown giass
0
comparisons for chromium and nickel films between the observed specific resistances (at 20' C.) and those computed from the resistivities of the bulk metal. The specific resistance is defined in this usage as the resistance of a film 1 X 1 inches square, measured between opposite edges. The experimental and computed curves are essentially parallel when the film thickness exceeds about 200 A. When the films are thinner, the observed specific resistance rises far more rapidly than would be predicted by the assumption of a constant resistivity for the film The temperature coefficients of resistivity of evaporated films of a metal diminish with decreasing thickness (Figure 4) and may, as they do for chromium, pass through zero and become negative for thinner films. Many workers have observed this phenomenon, and several theories have been proposed to explain it (1). The variation in temperature coefficient (and in resistivity) with thickness is due to a decrease both in the rate of change of electronic free path with temperature (11) and in the electronic free path. Several nonelectronic phenomena may also figure in the anomalous behavior of metal films: ( I ) differential expansion of film and substrate, (2) pressure a t the interface of the film due to the release of adsorbed or dissolved gases, (3) surface tension, (4)crystal orientation and growth by atomic migration, and ( 5 ) abnormal crystalline forms of the metal existing in thin films. Topper (10)has presented a more complete review of these effects. Figure 5 shows the rise in resistance of an Inconel film approximately 600 A. thick after it is heated in air a t 200" C. Theresistance of all films was increased by heat treating. Only those films that eventually reached a constant resistance during the initial heat treatment were considered usable. Steady and intermittent heating were equally effective when the comparison mas based on maintaining the peak temperature for the same length of time. The resistance of unstable films increased irreversibly either on extended standing a t constant temperature, or after cyclic heating through a temperature range. Marked changes in the resistance of unstable films occurred when they were heated to a temperature near or above the highest in their history. Every film had to be calibrated individually to establish its stability. In general, the thicker films were inherently more stable, and stability was enhanced by the deposition of protective mineral coatings on chromium and nickel films. The chromiuni film used in the heat transfer study of this work increased in resistance over a 2-year period to an extent equivalent to a calibration error of only 1' C. March 1955
It is desirable to use different metals for evaporated metal-film resistance .thermometers, depending on whether the temperature rneasurements are to be static (periodic observations over a long time) or dynamic (a few measurements during a short time interval, requiring greater accuracy). Films combining high sensitivity and complete stability have not been developed. Chromium films should be used for the static tests and nickel films are acceptable for the dynamic measurements. The stability requirements for dynamic tests are more modest because the plots of resistance against temperature remain parallel even though the absolute resistance drifts. It is essential, however, that the drift be slow enough so that a calibration is valid during the time used for a set of measurements. Technique is used to determine film coefficients for condensing organic vapors
In order to test the effectiveness of evaporated metal films for heat transfer investigations, surface temperatures and heat transfer coefficients for condensing organic vapors were determined. The apparatus developed for this purpose, shown in Figure 8, consisted essentially of a kettle, entrained liquid separator, condenser, electrical resistance measuring circuit, and piping. The measuring tube (Figure 7) vas inserted in the main vapor chamber. Liquids were vaporized in a small electrically heated kettle of about 1-gallon workin capacity. The heat input to the kettle was controlled by a lfariac adjustment of the applied voltage. Vapors from the kettle passed through an entrainment separator, consisting of two concentrically mounted steel pipes, before they were admitted to one end of the main condenser.
TIME, HWRS
Figure 5. Aging of Inconel film in air bath at
200" c.
The main condenser consisted of a horizontal cylindrical shell, 12 inches long and 8 inches in diameter. Condensation took place on the 0.586-inch (outside diameter) tube mounted axially in the center of the condenser. The condensate from the center 6-inch section (area of sensitive evaporated film) drained into a trough terminating with knife edges on each end. The liquid from the trough flowed through a liquid seal into a small glass condenser where it was cooled before the volume was recorded. Atmospheric pressure was maintained in the condenser by bleeding off vapor through a '/*-inch line to two small glass condensers where it refluxed and flowed back to the kettle A 1-foot length of I-inch glass tubing filled with calcium chloride and mounted above the reflux condensers protected the apparatus from moisture. Make-up liquid was introduced to the bottom of the kettle by gravity feed from a 5-gallon tank. The condenser was provided with a drain for any condensation that took place on the tube outside the trough section or on the
INDUSTRIAL AND ENGINEERING CHEMISTRY
389
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT temperature was considerably less in the second method, checks could be obtained by either met,hod, verifying the fact that the filin measured average surface temperat,ures. Although the dopes of the plot's of Figure 8 vary between -0.18 and -0.31, the average i8 close to the Xusselt prediction of -0.25. TTit,h one or two exceptions, the vapors mith the loivest purity have the least negative slope. Similar types of compounds have approximately the same slope. Of the purer vapors, benzene and toluene are the only notable exceptions to this rule. Discrepancies between the theoretical Nusselt equation and experixentnl data can be partially explained both by certain effects n-hich were li,'s origiriitl work and errors inherent t o some experimental techniques. The foilon-ing factors qualitativpll- increase t'ir Susselt, coefficient:
C' 1 J
Figure 6. Kettle
F.
8.
Entrainment s e w r a t o r
G. Feed tank
Condenser
H.
D.
Condensate cooler Reflux condenser
'. J.
K. 1.
Drying tube
C.
E.
Steam Pressure g a g e Steam contraller
P,
Heat exchanger Cooling water M. Orifice N. Cooling water 0. Condensate receiver Q. Thermometers
walls. A shield above the tube and trough prevented the collection of any extraneous condensate from above. Two glass windows were provided on each side of the condenser to permit observation. The 0.586-inch (outside dianiet,er) measuring tube was held in place by packing glands coupled to a 3/4-inch cooling water line. A calibrated t'hermometer, graduated to 0.1" C., was mounted horizontally on the condenser and submerged in the vapor space to the 20' C. mark. Fluctuations in cooling water velocity through the condenser \yere minimized by the installation of a pressure regulating valve upstream from the condenser. The temperature of the viater was controlled by adjusting steam pressure in a small Ross heat exchanger through which t,he cooling mater flowed. Flow rates of the water \wre measured a t a 3/16-inch calibrated orifice immediately downstream from the heat exchanger, and t,his orifice, together with several bends in the line, produced sufficient mixing to ensure a constant temperature cross section when the water reached the measuring condenser. Two glass therrnonieters in the inlet and outlet' &earns to the condenser provided checks on t.he cooling vater temperature. Experimental results show satisfactory correlation with theoretical coefficients
Roughness of condenbing surface Impure vapors Unsaturated vapors Noncondensable gases Thermal resistanre of gas liquid interface Subcooling of condensate Blanketing of the lover portions of the condenser tube
Some of these effects can be corrected quantitatively xhile others are obviously negligible. Discussions of these influences are given by Baus ($1, Peck and Reddie ( 8 ) ,and Colburn (6).
$7 Figure 7.
v
(2)
I
, ' I
'J (3)
Construction of resistance thermometer for heat transfer measurements
I n order of application:
1.
2. 3. 4.
5.
Heat transfer coefficients for the conden-ation of 14 organic vapors are shown in Figure 8. Coefficients calculated from the Nusselt equation are also plotted for compounds whose thermal conductivities have been reported. Continuous film condensation was obtained in all cases. Additional data are given by Baus (3). Two methods were employed to control the temperature drop across the condensing film. I n one, the water flow through the condenser was regulated to control both the water-film resistance and the temperature driving force. For the second method, the teniperature of t h e cooling water entering the condenser was controlled to limit the over-all At. High water velocities could be ufied t o limit t h e cooling water rise through the condenser tube to less than 2" C. Although the gradient of the outer surface
390
Effect3 that lower the Susselt coefficient are:
Apparatus for measuring heat transfer coefficients for condensing films
A.
A noncontinuous condensate filrn Temperature variation of the outer tube surface Acceleration oi the condensate iiln Vapor velocity Turbulence in filin flow Convection of heat in film
Six layers of fired-on l i q u i d Bright Platinum (electrical resistance between ends of film less than 0.1 ohm) Chromium film deposited b y vacuum evaporation Relatively heavy layer of evaporated chromium Clamps of spring brass Copper wires, 2 2 B. & 5. gage, soldered to platinum and clamped a t three points around periphery of tube
The blanketing of the lower part of the tube by a heavier layer of condensate than is allowed for by the Xusselt equation is believed to have an important effect on film coefficients foi condenser tubes of the size employed in this study. The blanlieting layer of condensate is caused by surface tension forces which prevent drainage of the liquid in t h e manner assumed by Xusselt. Although the Xussclt equation predicts zero resistance for a discontinued heat flux, the residual condensate film on the surface of the tube has a finite thickness and therefore thermal 1 esistancc. Yormally, compounds with a high suirace tension
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47,No. 3
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT 700
e00 500
c’
5
8
700 600
#A
300
m
Y
In
400
f
5
$
film for conden2n,g organic vapors
-Experimental - - - -Calculated from Nurselt equation
300 P50
200
150
A t,’F
will be retained in the larger amounts and the films provide greater resistance to the flow of heat. Since surface tension is capable of holding only a specified weight of liquid on the tube, the effective area of the blanketing layer should be less for large tubes. For liquids that wet the tube surface, the degree of blanketing is independent of interfacial tension between the condensate and the tube wall. There are other effects associated with the static thickness of liquid due to surface tension forces. For example, addition of a slightly greater amount of liquid to the tube causes an uneven distribution along the bottom surface. This slight initial addition does not cause liquid to drip from the tube, but rather produces points along the bottom where the liquid accumulates in small “bulges.” The heavier weight of liquid tends to reduce the thickness of previous static film about the side and upper surfaces of the tube, accumulating a greater proportion of the blanketing layer a t the bottom of the tube. With water and a 15-mm. borosilicate tube, the bulge was observed to cover approximately all of the lower quadrant of the tube surface. A t reasonable drainage rates, a sufficient number of droplets were present to cause heavy thicknesses over better than 10% of the surface of the tube. Opposing the blanketing effect, surface tension of the condensate also acts to increase the heat transfer coefficient by introducing nonlaminar motion to the flowing film. At the moment drops actually separate from the liquid surface, the condensate film a t the bottom is extended to its maximum thickness. Surface tension forces reacting to cause the rapid return of the film to its normal rounded surface produce momentary movement of liquid back up the walls of the tube. This upflow of liquid is presumed to cause some accelerated motion in the condensate flow. For water dripping from a 15-mm. borosilicate tube, ripples are visible on the surface of liquid remaining on the tube as far as halfway up the side of the tube just after the drop separates. The disturbance to the normal flow of condensate causes a corresponding higher rate of heat transfer. It has been
a:
March 1955
further postulated that this effect is more pronounced for liquids of high surface tension, since they bound back with a greater force and stronger accelerated flow. The surface tension of the condensate, therefore, acts both to increase and decrease the heat transfer coefficient. The retarded condensate drainage due to su face tension forces causes a blanketing layer along the bottom of the tube, which results in a lower value for the measured heat transfer coefficient. The greater the surface tension of the condensate the more serious will be the blanketing and the lower the coeficient. On the other hand surface tension causes oscillations in the film on separation of droplets from the tube. The greater the surface tension the more extensive should be the acceleration with a higher rate of heat transfer from the induced convection. Both effects become more severe for smaller tube sizes. Since all of the measured coefficients in this work are below the Nusselt value, it is assumed that the effect of the blanketing layer is predominate for a 0.586-inch tube.
Conclusions
-4novel method of measuring average surface temperature has been investigated and applied to the determination of film coefficients for condensing vapors. As might be expected, the electriral stability of evaporated metal films is a critical property, but careful preparation and calibration permits their use with fair accuracy over a limited temperature range. On the basis of work reported in this paper the useful range of temperatures should be restricted, probably from room temperature to 200’ C. It is hoped that additional work will extend this range, but it is probably not possible to approach the range and accuracy of standard resistance thermometers. However, the fact that this method is free of many of the errors inherent in other methods of measuring surface temperatures and the average values of surface temperature rather than point values are desired in most heat transfer studies may more than offset the inaccuracy of absolute values. Also, many experimental techniques permit easy and frequent calibration a t single values of temperature, which appears to be all that would be necessary to obtain good accuracy, since for any given film under fixed conditions, it is the total resistance that varies with time while the temperature coefficient remains constant within the limits of accuracy of the experimental methods so far employed. Perhaps the greatest advantage of the method described in this paper arises from the fact that film thicknesses can be reduced to the range of molecular dimensions-many orders of magnitude
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ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT less than is possible with alternate methods. This makes it possible to investigat,e true surface temperatures of glass and quartz substrates. The authors are of t'he opinion that' the method will not prove to be applicable to other electrically nonconductive substrates, since any materials having vapor pressures greater than glass or likely to release gases during the deposition of the films markedly increase the electrical instability of the films. Another adrant,age resuking from the negligible thickness of the films in their effectively zero heat capacity, which should permit sufficiently accurate measurements of transient fluctuat,ions of surface temperat,ure. It should be possible to apply this method to the determination of thermal conductivities and work along this line is in progrese. If such films are applied to either side or incorporated in sandwichlike constructions of material of known thermal conductivit,ics, such as quartz, it should be possible to use one film as a source of heat and another for surface temperature measurements. If this can be done, a relatively simple heat met'er could be made that should prove very useful in many heat transfer studies. Acknowledgrnenf
Grateful acknowledgment is made to the Eastmsn Kodak Co. and to The Texas Co. for financial aid received under their fellowship programs.
Heat Transfer Design Data
Literature cited (1) Appleyard, E. T. S.,Proc. P h y s . Suc. (London). 49, S o . 274, 124 (1937). (2) Baker, E. M., and Tsao, V.,Trans. Am. Inst. Citem. Engrs., 36, 531 (1940); IND. ENG.CHEM., 32, 1115 (1940). (3) Baus, B. V., P h . D . thesis, Cornell University, Ithaca, S . Y., 1960. (4) Bendersky, David, Mech. Eng., 75, 117 (1953). (5) Colburn, A. P., Inst. M e c h . Engrs. ( L o n d o n ) , Proc. 164, 445 (1951). ( 0 ) Colburn, A. P., and Hougen, 0.A , , IND.EXG.CHEX..22, 5 2 2 (1930). (7) Jeffrey,J. O . , Cornell Unireraity, Eng. Expt. Sta., Bull. 21, 1930 ( 8 ) Peck, R. E.. and Reddie, W. A., ITD. E m . CIAEM., 43, 2926 (1951). (9) Strong, J., "Procedures in Experimental Physics," PrenticeHall, Xew York, 1941. (10) Topper. L., Ph.D. thesis, Cornell Uniyersity, Ithaca, ! i Y. ., 1952. (11) Weale, R. A., PTOC. Phgs. SOC.( L o n d o a ) ,62A, 135 (1949). (13) Wenner, F., a n d Smith, A , , S a t l . Bur. Standards (U.S.),Sci. Paper 481, 1942. (13) Williams, R.C., and Backus, R. C., cJ. AppZ. Phys., 20, 98 (1949). RECEIVED for review May 18, 1954.
ACCrPTEO
October 8, 1934.
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...
Inclined Falling Films LEO GARWIN'
AND
EMERSON W. KELLY,
JR.~
Oklahoma A. & M . College, Stillwofer, Okla.
P
RESENT-DSY commercial falling film heat cschange equipment is generally of two types-the trombone cooler, in which the liquid in film form f l o m dovn the outside surface of horizontal tubes in a bank ( I , I J ) , and the vertical yetted-wall heater or cooler, in which the liquid film flows down along the inside (or sometimes the outside) surface of a vert,ical tube. The well-known ammonia cooler and the recently developed sulfuric acid concentrator (4)are examples of the latter. A vertical tube film evaporator which utilizes rotating blades to induce turbulence in the film is commercially available ( 1 4 ) . The main objective of the falling film cooler is to obtain a high rate of heat transmission with a low water consumption. Advantages over the conventional tube and shell exchanger reside in the fact that, with the trombone cooler, no shell is required, giving a lower initial cost, per square foot. Also, higher coefficients are obtained n-ith film coolers, resulting in lower heat transfer requirements and further reducing the investment. Lower maintenance costs arc achievcd because of t,he ready accessibility of the tubes for cleaning; no removal of heads is required. Finally, large overloads can be handled by pumping more cooling water, with very little increase in pressure. Where evaporation takes place under vacuum as in sulfuric acid concentration, pressure drop becomes an important consideration, and the film-type heater offers a decided advantage in this respect. Too, the high fluid velocity in the falling film not only provides high heat transfer coefficients but, also reduces the residence time, so crit,ical with heat-sensitive materials. McAdams and coworkers studied the heating of n-ater in turbulent flow in a falling film vertical tubular heater (19). Data for the viscous region have been obtained by Bays and McAdams ((7). 1 Present address, Kerr-McGee Oil Industries, Inc., Oklahoma City, Okla. 2 Present address, D o u Chemical Co., Texss Dirisioii, Freeport, Tex.
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The earlier literature on the hydrodynamics of mater flowing horizontally in liquid layer form under isothermal conditions has been reviened by Cooper and coworkers ( 6 ) . Later measurements of the thickness of vertical liquid films in the viscous range have been reported by ICirkbiide (10) and by Friedman arid Miller (8). Recently, Dukler and Bergelin ( 7 ) used a capacitance technique for making such measurements in the vijcous and low turbulent ranges. Chew ( 6 ) , using an optical procedure, obtained viscous range data for several angles of inclination. There may be inetances where head room limitations make the use of a vertical falling film heater impractical, and mhere inclination of the film heater would eliminate this difficulty. Data are lacking, however, on the effect of such inclination on the heat transfer coefficient. I t was for the purpose of establishing this relationship that this study n-as undertaken. The work is limited to the case of water flowing in the turbulent range. Studies are made on flat plate aver wide range of angles of inclination and flow rates
A flat plate, 8 inches wide, 30 inches long, and 3/4 inch thick, \\as used in this study. The angle of inclination of the plate vas capable of adjustment over the entire range (Figure 1). The plate was made of half-hard engravers brass (61.5% copper, 37% zinc, 1.5% lead), with a thermal conductivity of 68 B.t.u. per (hour)(foot)(O F.) a t 68" F. (2). Flanged to the underside of the plate was a steam chest. The width of the heating surface proper was 6a/4 inches. To measure the temperature drop across the flowing liquid film, four 24-gage co per constantan thermocouples were located approximately inch below the top surface of the plate at various points along the liquid flow path. These couples were located approximately 2 inches from the eides of the plate, as shown in Figure 2. For each couple, R 0.1-inch hole was drilled into the plate from the side for a distance of approximately 1 3 / p inches. Another hole was drilled from the top surface of the
INDUSTRIAL AND ENGINEERIRG CHEMISTRY
Vol. 47, No. 3
