T”“ (4)
4 measurement of the thermal conductivity of liquid has received considerable attention in the past, 75 years. may be considered the first to attempt the measureDespretz ment of this property. I n a rather crude esperiment he showed that the temperature along the axis of a cylinder filled with water followed the same law as the temperature in a cylindrical bar of small cross section. Through the years many experimenters devised various forms of apparatus to measure the thermal conductivity of liquids. Great improvement in the experimental accuracy n-as attained by the introduction of thermocouples for t,he measurement of temperature, t,he supplying of heat by elcctrical means, and the realization that in order to decrease convect,ion currents liquid layers of very small thickness should be used. Of all the unsteady-st,ate and steady-state methods cmployed by the workers in this field, three methods have given the niopt reliable results. These three are the flat. plate method, the filament met)hod, and the concentric cylinder method. In the flat plate method the liquid is contained b e t w e n two horizontalplates, the heat is supplied from above, and the temperature drop across the liquid film is measured. Since the heat supply is external t o the liquid layer, great precaut,ions are needed t o hold heat losses to a reasonable value. Also, evaporation of the test’ liquid along the periphery makes this method wireliable for studies of volatile liquids. In the filament method the lest liquid is held in a small tube having along its axis a thin mire of known resistance and temperature coefficient. Electric current is supplied to this wire and the thermal conductivity of the liquid under test is calculated from the geometry of the system and from heat input and temperature measurements. Usually tn.o tubes of different lengths are employed in order to calculate corrections due to the end losses. I n this method previous experimenters found i t difficult to determine the cell constant and t o obtain good reproducibility of results. In the concentric cylinder method the liquid is located in tjhe annulus between two cylinders, heat is supplied along the axis of the inner cylinder, and the temperature difference across the liquid layer is measured. The main objections to this method center around the difficulty in measurement of the thickness of the annulus and expected errors due to chance eccentricity of the two cylinders. Schmidt and Sellschopp ( 2 1 ) have shown that the dimensions of the annulus may be determined by means of the measurement of the electrical capacity of the cylinders with air used as the dielectric medium. It may be shown analytically (955) t h a t eccentricity as large as 10% of the annulus thickness has an insignificant effect on the test cell constant. Ordinary care in cell assembly is, therefore, sufficient to eliminate the eccentzicity of cylinders as a source of error.
outer ring of the larger cylinder and the inner ring of the smaller cylinder were grooved along their length in three places each 120 angular degrees apart. The grooved cylinders were of such dimensions as to give the groove-to-liquid surface distance of about 0.10 inch. The matching rings were then force-fittcd by cooling the inner rings in an acetone-dry ice bat’h and heating the outer rings with a gas flame. The ivhole assemblies were finally machined to the following dimensions:
APPARATUS AND EXPERIMENTAL PROCEDIJRE
DETERMINATIOY OF THE CELL COXSTANT
I n view of the above facts, the concentric cylinders were chosen for the thermal conductivity cell. The cell 1%-as constrnctcd from rods of electrolytically refined copper machined down t’o the specified dimensions. Each, the larger and the smaller cylinders enclosing the liquid space, was composed of tvm rings. The
The accuracy of the thermal conductivity measurements depends to a large extent on the accuracy of the determination of the heat transfei area and the thickness of the liquid layer. In the case oE concentric cylinders. I’ouner’s formula takes the form
1 Present address, Philadolphirt, Pa.
Pitman-Dunn
Laboratories,
Frankford
length of cylinders, 2.859 inches o.d. of the inner cylinder, 0.998 inch i.d. of t,he outer cylinder, I .030 inc1ic.s 0.d. of the outer cylinder, 2.500 incahcs The q-hiders n-ere held in place by means of Bakelite spacers for the riieasurement of the electrical capacitance and were later replaced by 0.005 inch thick PYIonel “IC” spacers for the thermal rims. Monel “K” was chosen for its low therinal conductivit,y (about 7yot h a t of copper). The Monel spacers were carefully machined mid soft-soldered t,o the cylinders. In order to fill and empty the test cell, a hole of about 0.064 inch in diameter n-as drilled through t,he outer cylinder perpendicular to the side surface and about 0.25 inch from the top of the cell. Another hole of the same diameter was drilled parallel to the cylinder axis to connect a t a right angle with the first hole. The outside outlet of the horizontal hole Tvas then closed by means of a brass plug. Finally, a 0.125-inch 0.d. silver tube was brazed to the outlet of the vertical hole. A diagram of the test cell is shown in Figure 1and a photograph of the assembled cell in Figure 2.
Regulat,ed direct current was mpplied to a closely wound Sichrome wire heater located along the axis of the test, cell. The temperature level and the temperature difference across the liquid layer were measured nit11 selected No. 30 B. &. S. gage enameled copper-constant,an thermocouples. Both the heat input. and the thermocouple voltages were measured by means of a Leeds R: Sorthrup K-2 potentiometer uvith a galvanometer and a, lampand-scale system sensitive to 0.05 microvolt per millimeter of scale. T o measure the voltage and ciirrent input to the heater, a voltage divider and a standard I-ohm resistance were also required. The tent cell fitted into a hollow copper cylinder bolted to the bott,om of’ the constant temperatiire bath vessel. I n this manner the test cell never came into direct contact with the bath liquid. Transformer oil was used as the bath liquid because of its low vapor pressure and viscosity in the temperature range of thj, study. The bath t,emperatixe aa.s held constant to within 0.002” c.
Arsenal,
1100
INDUSTRIAL AND ENGINEERING CHEMISTRY
lune 1956
The length, L , and one of the radii may be easily measured with a micrometer, The logarithmic term requires more precise methods of measurement as the ratio rC/n is very nearly equal t o unity. The formula for the electrical capacitance of two concentric cylinders is analogous to that for the thermal conductivity. Capacitance measurements can, therefore, give the value of the ratio of the radii of the two cylinders.
1
BRASS ADAPTER
THERMOCOUPLE WELLS
1101
cell cylinders. The thermal conductivity of air is known with sufficient accuracy for this purpose as its value is about only one tenth of the thermal conductivity of the liquids studied. The heat losses were determined a t the temperature levels of 30°,60", and 90" C., for temperature differences from 0.4' to 4.2" C. From the data thus obtained and the values of the thermal conductivity a t the three temperature levels, calculations of the heat losses were performed and applied as corrections t o the heat input to the cell to all runs with liquids Since the air and all the liquids studied are transparent to radiation a t and below the highest temperature of this investigation, heat losses determined in the calibration rims with air as the test fluid also included any radiation effects. The heat input corrections included the correction for the resistance of the heater leads, which also was delermined experimentally. CHOICE O F LIQUIDS FOR STUDY
I
d
RASS PLUG
i
Y
i i
/
i (3
ANNULUS
In spite of the fact that in the past 50 years many liquids have Iwen investigated, thcre remains ti large group of liquids whosc thermal conductivity was never even cursorily examined. This holdfi t,rue especially for liquids whirh only recently became of
/
I
i i
i "'p9I L .
.460"&.600"-
Figure 1.
-,750" -
Diagram of the test cell
The necessary measurements were made with a General Radio
Co. capacitance bridge and a standard 1000 f i p farad variable air condenser. The end effects were calculated n-ith the aid of wellknown numerical and graphical methods ('7, 2 9 ) . The reproducibility of the capacitance measurements was better than the accuracy of the instruments (0.1%). Uncertainties in the calculation of t h e end losses can be shown t o decrease the over-all accuracy by less than 0.1%. The value obtained for the cell constant, B, was consequently known with an accuracy better than 0.2%. The use of the above equation is based on the assumption of two isothermal surfaces maintained at At temperature difference. Temperature traverses made along the thermocouple wells to within 0.25 inch from either end of the test cell showed no detectable decrease in At other than random variations attributed to slight irregularities in the dimensions of the cylinders. The temperature difference as measured wit)h thermocouples was corrected for the temperature drop across the metal enclosing the test liquid. The magnitude of the temperature difference varied from 1.2' C. for water to 4.0° C . for the least conductive liquid of this study. The dimensions of the thermocouple wells were kept small enough to prevent significant distortions of the temperature distribution in the walls of the test cell. The error in the measurement of heat input, y, was smaller than 0.1%. CALIBRATION O F THE TEST CELL
The heat losses from the test cell were determined by direct calibration of the apparatus, using dry air as the fluid between the
Figure 2.
Test cell assembly
c:oiiiiiiercial irnportjaiic:cB. In addition to watcr, which was used as i t means of comparison with the results of other investigat,ors, ethylene glycol, diethylene glycol, and some of their ethers werc chosen for this study. This series of liquids is growing in iinportance as antifreezes, plasticizers, solvents in lacquer and thinner formulations, mutual solvents for coupling immiscible liquids used in the preparation of soluble oils, cutting oils, dry-cleaning soaps, and leather compositions, to mention only a few of a long list of uses. In addition, these liquids are two groups of conipounds of close chemical resemblance. The thermal conductivity data should prove of sonie value not only in the heat transfer field but also in future correlations when more information on their other properties is obtained. In-
INDUSTRIAL AND ENGINEERING CHEMISTRY
1102 Table I.
Experimental Values of Thermal Conductivity -
Ethylene g l ~ c o l Diethylene glycol Ethylene glycol monolnetli) 1 ctlirr Ethylene glycol monoethyl ctlior Xthylene glycol mono-n-butyl cther Ethylene glycol Iiiono-n-hexyl ethcr Ethylene glycol niono-2-ethylbutyl ether Ethylene glycol inonophenyl e t h ~ r Ethylene glycol diethyl ether Ethylene glycol dibutyl ether Diethylene glycol inonomethyl ethcr Diethylene glycol monoethyl e t h e r Diet.hylene glycol mono-n-butyl ether D i e t h y l m e glycol diethyl ether Diethylene glycol dibutyl ether a
149.9 150,O 150.6 149.6 62,I 62.6 62,2 50.0 49 8 50.0 45 7 45 7 45 8 41.3
...
41.3 38.7 38.7 37 8 37.4 36.3 36,5 40.4 40.4 34.7
156.9 157,O 157.8 157.3 62.6 62,s 62.8 50.7 5O,3
50.4 44.11 44 3 44.2 40.36 39.8) 39.8 39,Q' 37.4 37.4 36.1 36.0 35.2 35.2 40.1 40.1 32.6 33.0
33.2 33.2 44.2 44.0 40.2 40.0 38.5 38.6 36.0 38.9 36.3 34.8 34.7
31.2 31.4 43.2 43.2 39.0 38.9 37.2 37.4 33.7 34.0 33.9 33.2 33.2
162:4
ldi:7 63.2 63.2 63.3 51.1 50.7 50.7 42 fl 42.7 42.7 38.3
...
38.4 36.0 36.0 34.8 34.8 34.1 34.1 39.6 39.6 30.4 30.5
29 3 29 3 42.3 42.2 37.5 37 6 36.3 36.3
Val. 48, No. 6
least twice a t half-hour intervals. Thc bath temperat,ure IV:M then raised or lowered to the next level and after the steady statc was again reached the measurements were made as above. -\ run x i s considered completed when sufficient data were obtained a t the three temperatures, 30°, BO", and 90" C. A t least two separatc runs were made with each purified liquid and an additional run with the industrial grade material (n-ith the except,ion of ethylene glycol, diethylene glycol, and water. The glycols of high quality m-ere available in the laboratory and, thcrefore, did not require further purification. Distilled water was considcrcd sufficiently pure). I n most instances the results oht>ainedwith purified materials mere lower than the values obtained with ind u ~ t r i a grade l liquids, the difference being of the order of 1 to 2'70. RESULTS
?'hc experimental values of the thermal conductivity of I h c , liquids studied are shown in Table I. They were obtained noar t,he indicatcd temperatures and adjusted t o 30", BO", and 90' C. by means of t)he correlating equations. Their probable error is cstimated as O.Syc. In Figure 3 the data of thermal conductivity of TTater are compared with those of Bates and Hazzard ( I ) , Bridgman (a),Davis (5),Dick ( 6 ) , Frontasiev (Q), Hutchingon ( I O ) , Jakob ( I I ) , K a y and Higgins ( I S ) , Nulriyama and Yoshizawa ( I f i ) , Schmidt ( d o ) , Schmidt and Sellschopp ( $ I ) , Smith ( a d ) , Timrot and Trargaftik ( 2 6 ) ,and Weishaupt (18).
,..
...
32.1 32.4 32.3
.4t 50' C .
I
dustrial grade liquids were purchased from the Carbide and Carhon Chemical Corp. and purified by means of fractional distillation using a packed column equivalent to 35 theoretical plates. The column was operated a t a reflux ratio of a t least ten to one. Only a small middle cut was used for the thermal conductivity runs. The absence of impurities was indicated by agreement of thc specific gravity with the values reported by the manufacturer for the pure liquids. The purified liquids were stored in a diy atmosphere until needed.
. .. .. .
EXPERIMENTAL PROCEDURE
-
iift,er a series of preliminary runs, the following procedure TWS employed for the entire series of tests. The cell was evacuated and rinsed several times with the commercial grade of the material to be testled. The cell filling consisted of connecting a glass tube t o the brass joint of t,he silver tubing, filling this glass t,rihr with about 10 ml. of liquid, and applying vacuum int'ermittently frorii above the liquid level until there was no liquid level risc n-ith tlici lowering of pressurc. All glassware which came directly in contact with t,he liquid n-as Tvashed, rimed n i t h distillcd ivatcr, and clricd a t 110" C. .-2fter filling the cell wit,h liqiiid, thc silver titbin:: ont,lets werc covered with ground glass caps, thc c d l heatrlr w a s put in place, the leads mere connected to the power supply lincl, and t,he top and bott,om of the cell were insulated with wool yarn. The test cell was subsequently placed inside the hollomcopper cylinder located in t,he center of the oil bath nnd covered with a wooden disk to prevrnt ronvectioii c.iirrent,s n.hove the, cell assembly. The heat ?tipply to thc rrll \ v w tlicri Ciiriietl o i i . The whole system was then permitted 1 o tmnic t o 31 c~atly$ 1 :rt n-hich required almit 2 hoiirs. The measurements of voltage and cwrent, input to t,he twt, cell, as well as the thermocouple volt,agcs, were then made \\.ilk1 the potentiometer. The instrument readings werc repeated a t (1.
"
e*
0
"
130 40
0
TEMPE R A T U RE, Figure 3 .
80 OC.
Recent (lata on therrnal conductivity of watcr 0
0
I'rcvious investigators Present authors
The method ol least squares applied to the experiment,al data i'ho\vs that t>he temperatjive dependence of the t'liermal contlnctivity of all liqliitls with the exception of water c a n be ex-
pressed with adeqimte precision by means of a linear equation. Table I1 gives the values of constants k o and a of the equation
h- = ka(l
+ at) x 10-6 cal./(scc.)(cm.)(' C.)
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1956
Table 11. Values of Constants in the Least Squares Equation k
-
ka(1
+ at) X
10-6 cal./(sec.)(cm.)(O C.)
Name
ka 61.75 49.52 47.26 42.80 40.05 38.80 37.56 40.79 37.07 35.25 45.05 41.44 39.66 38.00 35.85
Ethylene glycol Diethylene glycol Ethylene glycol monomethyl ether Ethylene glycol monoethyl ether Ethylene glycol mono-n-butyl ether Ethylene glycol mono-n-hexyl ether Etbilene glycol mono-2-ethylbutyl ether Ethylene glycol monophenyl ether Ethylene glycol diethyl ether Ethylene glycol dibutyl ether Diethylene glycol monomethyl ether Diethylene glycol monoethyl ether Diet,hylene glycol mono-n-butyl ether Diethylene glycol diethyl ether Diethylene glycol dibutyl ether
a X 106
26 30
- 108
-116 -111 -115 - 103 31 197 - 188 69 104 96 176
---
k = 141.2(1
The thermal conductivity of water and the glycols calculiitrcl by means of Weber’s (27’) equation was within 10% of the experimental value. Poorer agreement r a s obtained for these three liquids using the equations of Smith (25,24) and Palmer ( 1 7 ) . A much better correlation was obt,ained when t,he thermal conductivity of all the liquids studied was plotted versus the ratio of the hydroxyl group weight to t,hc molecular weight. The average and the maximum deviations from thc least squares linr were 3.8 and 9.6y0, respectively. While such a correlation mag not have any theoretical significance, i t shows clearly the contribution of the hydroxyl groups to the over-all value of the thermal conductivity of a particular liquid. NOMENCLATURE
-111
The conductivity of water was correlated with temperature by means of a second degree equation,
+ 0.002321 - 0.0000072t2) X
10-6 cal./(sec.)(cm.)(’ C . )
B = cell constant, em. -1 k = thermal conductivity, cal./sec.-cm.-” C. L = length of test layer, cm. p = heat input, cal./sec. T, = inner radius of the test annulus, cm. r2 = outer radius of the test annulus, em. At = temperature difference across the liquid layer,
O
C.
LITERATURE CITED
DISCUSSION
The data for the thermal conductivity of water fall well within the range of recent investigations. They agree particularly well with the results of Schmidt and Sellschopp ( S I ) , Timrot and Vargaftik (d6), Kaye and Higgins (IS),and Dick (6). The results for ethylene glycol do not show such good agreement with other experimenters’ values, with the exception of the values reported by Fritz (8) and Riedel (19). The negative temperature coefficient of 0.26% found by Bates and Hazzard ( I ) is larger than for many nonpolar liquids and, therefore, does not agree with expectation. The data of Kraus (16) indicate that there exists a minimum value of thermal conductivity in the temperature range between 30” and 60” C., two of the three temperature levels of this study. As this particular temperature interval was not further investigated by the authors, such a departure from linearity would not have been detected. It should be added t h a t Kraus’ results were not independent of the spacing between the two horizontal plates of his apparatus, being about 7% higher for an increase in spacing from 0.016 t o 0.057 inch, a result quite unexpected from the experience of other workers using flat plate apparatus. The agreement of diethylene glycol data with those reported by Fritz (8) is within the experimental error of this study. No extensive comparison of the experimental data with those calculated by means of several theoretical and empirical equations could be made because of lack of data on other properties of the liquids investigated needed for such a study. The equation of Rao (18), which presupposes that the liquid state resembles more closely the solid than the gaseous state in its thermal behavior, mas found completely useless for the prediction of the thermal conductivity. The equations of Bridgman (Z), Kardos (li?),Kincaid and Eyring ( I 4 ) , Eisenschitz ( 6 ) , and Yang (30) could not be testcd a t all.
1103
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
(11) (12) (13)
Bates, 0. K., Haazard, G., IND. ENG.CHEM.37, 193-5 (1945). Bridgman, P. W., Proc. Am. Acad. Arts Sei. 59, 141 (1923). Davis, A. H., Phil. Mag. 47, 972 (1924). Despretz, Al., Pogg. Ann. 46, 340 (1839). Dick, M. F., doctoral dissertation, University of Michigan, 1950. Eisenschitz, R., Proc. R o y . Soc. 59, 1030 (1947). Emmons, H. W., Trans. Am. SOC.Mech. Engrs. 65, 607 (1943). Fritz, W., in F. Henning’s “Warmetechnische Richtwerte,” pp. 81, 82, VDI-Verlag GMBH, Berlin, 1938. Frontasiev, V. P., Zhur. Phys. Chem. (U.S.S.R.) 20, 91 (1946). Hutchinson, E., Trans. Faraday SOC.41, 87 (1945). Jakob, M,, Ann. Physik 63, 637 (1920). Kardos, A., Forsch. Gebiete Ingenieurw. 5, 14 (1934). Kaye, G. W. C., Higgins, W. F., Proc. Roy. Soc. A117, 459
(1928). (14) Kincaid, J. F., Eyring, H., J . Chem. Phys. 6, 622 (1938). (15) Kraus, W., 2. Angew. Phys. 1, 173 (1948). (16) Kukiyama, S.,Yoshiaawa, Y., J . Soc. Mech. Engrs. (Japan) 27, 347 (542-4) (1934). (17) Palmer, G., IND. ENG.CHEM.40, 39 (1948). (18) Rao, hl.,I n d i a n J . Phys. 16, 161 (1942). (19) Riedel, L., Forsch. Gebiete Ingenieurw. 1 1 , 340 (1940). (20) Schmidt, E., Mitt. Forsch. Warmesch. No. 5 (1924). (21) Schmidt, E., Sellschopp, W.. Forsch. Gebiete Ingenieurw. 3 , 277 (1932). (22) Smith, J. F. D., IND. EXG.CHEM. 22, 1246 (1930). (23) Ibid., 23, 416 (1931). (24) Smith, J. F. D., Trans. Am. SOC.Mech. Engrs. 58, 719 (1936). (25) Smythe, Wm. R., “Static and Dynamic Electricity,” p. 7 6 , McGraw-Hill, New York, 1939. (26) Tinirot, D. L., Vargaftik, N. B., J . Tech. Phys. (U.S.S.R.) 10, 1063 (1940). (27) Weber, H. F., W’ied. A n n . 10, 103 (1880). (28) Weishaupt, J., Forsch. Gebiete Ingenieurw. 1 1 , 20 (1940). (29) Worthing. A. G., Geffner, J., ”Treatment of Experimental Data,” p. 92, Wiley, New York, 1943. (30) Yang, L. PI., Nature 161, 523 (1948). RECEIVXD f o r review December 13, 1954.
ACCEPTEDJ a n u a r y 25, 1966. Division of Industrial and Engineering Chemistry, 122nd Meeting, ACS, Atlantic City, N. J., SeI)tember 19.52.
