September 1954
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
tions. The analysis of reflectance data versus graphite concentration for these detergents in a manner similar to the alkyl sulfate washed fabric will prove either that differences exist in the mechanism for detergency or that all four detergents act in similar manner. An increased slope for the line of regression would indicate increased surface soil removal; while a decreased slope would indicate better removal of embedded soil.
1947
Equations relating reflectance to graphite concentration for washed and unwashed fabrics were developed; high correlation coefficients indicated the reliability of these equations. Considerably more work with varying types of detergents is necessary to define the mode of soil removal. LITERATURE CITED
(1) Bacon, 0. C., and Smith, J. E., IND.ENG.CHmr., 40, 2361- 70 (1948).
SUMM4RY
A method mas devised for removal of graphite from cotton fabric so that a quantitative estimate could be made in comparison with reflectance values. The method has a i 6 . 5 % limit of accuracy based on the amount of graphite present. The Kubelka-Munk equation correlating reflectance to soil concentration on cotton fabric as proposed by Bacon and Smith has been experimentally reaffirmed. The K / S value for colloidal graphite on cotton fabric is shown to be essentially a linear function of graphite concentration.
Duncan‘, A. J., “Quality Control and Industrial Statistics,” R. D. Irwin, Inc., Chicago, 1952. (3) Harris, J. C., J. Am. Oil Chern. Soe., 29, 110-13 (1952). (4) Hart, W. J., and Compton, Jack, Teztile Research J . . 23. No. 6, 418-23 (1953).
Kubelka, P., and Munk. F., 2. tech. Phusik.. 12, 593 (1931). (6) Reich, I., Snell, F. D., and Osipow, L., IND.ENG.CHEM.,45, 137(’)
41 (1953). (7) Utermohlen, W. P.,Jr., and Wallace, E. L., Textile Research J., 17, NO. 12, 670-88 (1947). RECEIYED for review March 25. 1954.
ACCEPTED June 30, 1954.
END OF SYMPOSIUM Reprints of this symposium may be purchased for 75 cents each from the Reprint Department, .4merican Chemical Society, 1155 Sixteenth St., N.W., Washington 6, D. C.
Thermal Conductivity of Liquids J. R. WOOLF’
AND W. L. SIBBITT Purdue University, Lafayette, Ind.
A
SURVEY of the literature on the thermal conductivity of
liquids showed that experimental values had been reported for more than 130 liquids. Only for water was there sufficient agreement among several investigators to establish the values within a few per cent. The law for the conduction of heat in fluids (liquids and gases) is the same as for solids; however, under engineering conditions, it is usually impossible to eliminate the effect of convection. Some of the early experiments were probably in error because adequate precautions were not taken to eliminate or reduce the effects of convection currents. Conduction was not the sole process by which heat was transferred; consequently, reliable data on the thermal conductivities of liquids are rare, and accurate data on the temperature coefficient of thermal conductivity are especially meager. APPARATUS
A concentric cylinder apparatus, Figure 1, was selected for steady-state operation. The liquid ”as contained in the annular space between two concentric brass cylinders, which were carefully ground to uniform diameters. The inside diameter of the outer cylinder, Dz,was 1.1272 i 0.0003 inches and the outside diameter of the inside cylinder, Dl,was 0.9972 f 0.0003 inch leaving an annular space of 0.0650 inch. The inside cylinder was centered by the cover plate and by three centering screws spaced 120 degrees apart. Axially drilled holes were provided in both cylinders for the thermistors. The electrical heater was in a hole 0.5 inch in diameter in the inner cylinder. The heater was 9.5 inches long and consisted of 22 E. & S. gage Manganin wire wound on an insulated brass tube. The center 4 inches was wound a t 12 turns per inch and the remainder of each end a t 18 turns per inch to provide guard heating against end losses. The test section, L, was 1.9764 i 0.0079 inches long, as established by the location of the potential taps which were welded to the heater wire. 1
Present address, Consolidated Vultee Aircraft Gorp., Fort Worth, Tex.
The cell was suspended in a thermostated bath of 14-gallon capacity, which was provided with a 0.25-hp. stirrer, a cooling coil, and an auxiliary heater which operated continuously. The “on-off” thermostat control operated a second heater which maintained the bath temperature constant to 0.0036’ F. The bath and controls have been described (14). The direct current power for the test section was supplied by a Model E-12-50 Sorenson voltage regulator. The electric circuit is shown in Figure 2. The test heater current was regulated by a slide-wire rheostat and measured by determining the potential drop across a laboratory standard I-ohm resistor. A Leeds and Northrup Type K-2 potentiometer was used for measuring the potential drops across the standard resistor and the heater test section. The resistances of the thermistors were measured with a Leeds and Northrup five-dial Wheatstone bridge. A Leeds and Northrup Type 2430-D galvanometer was used with the bridge and potent iomet er . Western Electric Type 14A thermistors, thermally sensitive resistors developed by the Bell Telephone Laboratories (5, IO), were used to measure temperature differences. T F i r high temperature coefficient of resistivity (about 2.2% per F. a t 86” F.) made it possible to detect temperature changes of 0.002’ F. with a five-dial bridge. EXPERIMENTAL PROCEDURE
The cell was cleaned with metal polish and solvents before each filling. The distilled water n-as boiled for a t least 2 hours before filling the cell, which had been evacuated overnight. This was necessary in order to prevent gas from being liberated on the metal surfaces when the temperature was increased. These extreme precautions were not necessary with the other liquids The liquids filled the space from the bottom, as they were forced in through a small tube which passed through the outlet in the cover plate. The cell was then placed in the bath and the test current adjusted to give the approximate temperature differential desired.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1948
The resistances of the thermistors were recorded when steadystate conditions were attained as evidenced by the stabilization of the thermistor resistances. Then the potential drops across the standard rwistor and the heater test section were recorded.
TW
Vol. 46, No. 9
I n another series of experiinent,s the values of At n-ere varied; however, the influence of radiation could not be detected. Therefore, in the work reported in this paper, no corrections were made for radiation. CONVECTION. The effect oi heat transfer by convection could be very large. The work of M u l l and Reiher (f6)and Beckmann ( 6 ) ,fuither interpreted by Jakob (19); w m used to estimate the effect of convection. A4ccordingto their results, when the product of A'p7 and ~YG? is less than 1000, the error in k which results from the assumption that t,he heat transfer is all by conduction is less than 2%. Thie critical value of the ( N P ,N G ~group ) in) creases as the temperature is increased. The (Npr N G ? products for the liquids a t t,he highest temperature are given in Tablc I. I n order to satisfy this criterion it is necwsary to use a very thin liquid layer and a small temperature difference of the order of 1" F. Analytical corrections Tvere not made, as they would he only crude approximations.
Cs
Figure 1. Test Cell CS. H. IC. LS.
Centering screw Heater Inner cylinder Liquid space OC. Outer cylinder T W . Thermistor well PT. Potential taps
y y
Figure 2. Both t,hermist'ors were removed from their wells and placed d i r e d y in the bath. The bath temperature was then increased to the temperat,ure which had been previously measured in the thermistor PT-ell of the outer cylinder. The resistance of the thermistor from the inner cylinder \vas measured. Then the temperature of the bath was measured with a calibrated precision mercury-in-glass thermometer. Thu?, in effect, the thermistors were calibrated each time they viere used. These precautions were taken because of the lack of experience TTith these elemcnt,s. The temperature differentials were then calculated. The physical measurements of t,he system, the heating poser, and the temperature differential were the only dat,a necessary for the calculation of the t,hermal conductivity.
Schematic Diagram of Electric Circuit
AM. G.
Ammeter Galvanometer Potentiometer RS. Rotart switch SR. Standard resistor SWR. Slide wire rheostat T. Thermibtor TH. Test heater Voltage regulator and pnwer supply VR. WB. Wheatstone bridge W C R . Water-cooled rheostat
P.
SHAPEFACTOR, 8. The use of Equation 1 impliej that the heat flows by conduction only through the test length of the liquid in the symmetrical annulus. If these conditions are satisfied, then
ACCURACY OF &lEASCRERlENTS
This primary or absolute instrument did not require calibration. The measurements were made under steady-state conditions, where the following equation approximated the heat flow relations: q = S ~ ALt L
(1)
RdDIATION. First, it v a s necessary to make the measurements in euch a manner that the heat flop- through the liquid as only by conduction. The effect of heat transfer by radiation through a liquid from one cylinder to the other was small; approximate calculations indicated that the corrections were less t 8 h m0.2%. The data obtained in the Purdue laboratory on Fater in a tarnished brass inst,rument and in a polished aluminum instrument were identical (within the limits of precision of the measurements).
Corrections aere made for changes in heater and annulus length with temperature. Temperature had no appreciable effect on the width of the annular space. The length of the heater section between the potential taps was measured by means of a cathetometer to within 0.4%. End losses through the heater core and cylinders are inherent in this type of apparatus. -4 number of heaters were constructed and tested. The temperature distributions along the axes of the heaters and cylinders were measured a3 a function of the liquid in the annulus and the temperature drop across the liquid layer. This particular heater had an isothermal region more than 3 inches long.
September 1954
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
6
1949
0
E
E 0
E -7
5:
OX
TEMPERATURE TEMPERATURE,
OF.
Figure 4. Thermal Conductivity of Carbon Tetrachloride
OF,
Figure 3. Thermal Conductivity of Water
li'or most liquids, the end losses were estimated by making runs a t several temperature differences and extrapolating the thermal conductivity to the zero temperature differential. In most cases the corrections were negligible. The maximum correction was 1.5%, corresponding to a temperature dMerentia1 of about 5' F. This experimental correction also accounted for the influence of convection. Calculations indicated that the effect of eccentricity of the heater cylinder could be appreciable. A series of conductivity measurements was made with various amounts of eccentricity. The effects on the k values were not measurable until an easily detectable degree of eccentricity was produced; consequently corrections were not necessary, RATEOF HEATFLOW, q. The rate of heat flow was determined from measurements of the current through the heater and of the potential drop across the heater test section. A laboratory standard 1-ohm (&O.Ol%) resistor in series with the heater w a used to determine the current flow The accuracy of the rate of heat flow determination was limited by the voltage regulation of the power supply. The regulation was to only 0.25%. TEMPER4TURE DIFFERENCE, A t L , The thermistor elements were small beads of oxides. The bead and leads were coated with glass to form a probe about 2.5 inches long. The thermistors were prcaged in the furnace for 70 days a t 390' F. in order to improve their stability. -4current of 0.15 ma was passed through the thcrmistors during the aging period. The resistance of the thermistors were then measured a t the ice point by means of a five-dial Wheatstone bridge (bridge accuracy of &0,05% iO.005 ohm). The thermistors Rere then ready for use Because of the high resistance of the thermistor elements, a srnall current will cause an appreciable amount of internal heating. The elements can be damaged by currents in excess of 0.2 ma.; therefore a current-sensitive galvanometer was used with the
TABLE I. PRODUCT OY GRASHOF'S A N D PRANDTL'S MODULI Liquid Water Dowtherm A Dowtherm E Carbon tetrachloride Chloroform Glycerol Ethylene glycol Propylene lycol Tricuoroetghylene Circo XXX oil Olive oil Aroclor 1248 Aroclor 1254
t,
0
F.
212 300 300 155 124
NP~NG~ 111 212 920
1300 1360
25
50
75
100 125 I50 175 200 225 250 275 TEMPERATURE, "F.
3CO
Figure 5. Thermal Conductirity of Ethylene Glycol
Wheatstone bridge. About 0.035 mw. was dissipated in the thermistor, The dissipation constant in still oil was ca. 2 mw. per O F.; therefore, the difference between the temperature of the thermistor and its surroundings was of the order of 0.018" F. As the thermistor currents were maintained approximately constant, this difference should have remained constant enough not to affect the temperature measurements more than 0.0018" F. The thermistors were calibrated each time they were used and their resistance values a t the ice point were periodically checked The thermistor constant, B, was calculated from Equation 3 and the uncorrected temperature differential was obtained from Equation 4
(3) (4)
The measured temperature drop took place partially in the brass cylinder walls and partially across the liquid layer; therefore corrections were necessary. The corrections were greatest for water-about .2%-as the thermal conductivity of water wae four or five times larger than that of organic liquids. Depending upon the temperature level, the accuracy of the determination of a temperature difference of 1' F. was 0.5% or better.
0.8 203 59 1400
300
158 250 250
40 14.9 215 102
At AtL
kL + G
xa
(5)
L
13ased upon these assumptions and experiments, the calculated maximum error is 1.85% (see Equations 6 and 7). However, this
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Vol. 46, No. 9
I
I-"
110
sb
''45
/5
Id0
'
I
I25
150
li5
TEMPERATURE,
v 2h5
2A
'
I
250
275
OF.
Figure 6 . Thermal Conductivity of Propylene Glycol
TEMPERATURE,
OF.
Figure 9. Thermal Conductivity of Glycerol, U.S.P.
25
50
75
100
125
150
175
200 225 250 275
TEMPERATURE,
300
OF.
Figure 10. Thermal Conductivity of Olive Oil
TEMPERATURE, "F.
Figure 7. Thermal Conductivity of Trichloroethylene 85
80,
,
,
,
,
I
,
I
,
1
,
,
i
8d 75 70 65 60
TEMPERATURE,
55 25 OF.
Figure 8. Thermal Conductivity of Chloroform
analysis neglects the influence of gas bubbles and sample purity. Gas bubbles tend to give low values of k for water. The purity of the hgdroscopic liquids may vary slightly during an experiment. Therefore, the maximum error in these data is probably less than 2.5%.
= 0.50
f 0.40
+ 0.50 f 0.45 = 1..85%
DISCUSSION OF RESULTS
With the exception of vater, materials of commercial grade were used in this investigation. Kater was tested first, because Its thermal conductivity is known within about 14%. These data for water agree with those of Timrot and Vargaftik within the accuracy of tjhe measurements (Figure 3). For purposes of comparison, selected groups of data from the literature are presented in Table 11. I n general, only data points with measurement errors of less t
