INDUSTRIAL AND ENGINEERING CHEMISTRY
2566
separately. The method is especially useful for materials which cannot be held a t elevated temperatures for extended periods of time, aiid may be adaptable to pasty and granular materials. ‘The method as described is suited only t o materials of low thermal conductivity. Experimental data are given for three types of plastic materials and for a double-base rocket propellant.
n r
ACKNOWLEDGMENT
Y
The assistance of J. H. Kiegand, Rocket Department, U. S. Naval Ordnance Test Station, is gratefully acknowledged.
A b
= an exponent defined in the text;
C,
slope of the log 1’-0 curve, hr. -l heat capacity at constant pressure (B.t.u.)/(lb.-” F.) = base of natural logarithm = surface heat transfer coefficient (B.t.u.)/(hour-sq. foot-
e h
graphically, it is the
=
F:)
notation of Bessel function Bessel function of first kind and zero order of z J l ( z )= Bessel function of first kind, first order of 5 = thermal conductivity (B.t.u.-foot)/(hour-sq. foot-’ I?.) I; L I D = length to diameter ratio, dimensionless = resistivity rat,io = k / ( h rqn),dimensionless rii
J
= J o ( z )=
rnl
t ti to
a 6
XV
= a constant defined in text; in Figure 3 it is the intercept a t 6 = 0 of the tangent to the st,raight port,ion of the
log Y-0 curve, dimensionless
position ratio = r / r m , dimensionless radial dist’ance from center of cylinder, feet radial distance from center of cylinder to outer surface of specimen, feet; numerically equal to radius of cylinder, feet = temperature a t point T and a t time e, O F. = initial uniform temaerature of cylinder, F. = ambient temperature during heating or cooling of specimen, O F. = temperature difference ratio = ( t o - t ) / ( t , - t i ) , dimensionless = thermal diffusivity k/(pC,), (sq. feetlhour) = symbol denoting partial differentiation = heating or cooIing time, hours = v positive root of xJ1(x) = ( h ~ m / k ) J(x) , = density of specimen (lb.)/(cu. foot) = = =
e
N OIMEN C LATUKE
Vol. 46, No. 12
P
LITER4TURE CITED
Am. SOC.Testing Materials, Philadelphia, Method C 17i-4.5, Ball, C. O., Bull. Natl. Research Council, 7, no^ 37 (1923-24). Jacob, Max, “Heat Transfer,” Val. I, pp. 276, 276, Sew York. John Wiley & Sons, 1949. AToAdams, W.H., “Heat Transmission,” 2nd ed., pp. 36, 200, New York, JIcGraw-Hill Book Co., 1942. Manufacturing Chemists’ Association, Washington, D. C.,
“Technical Data on Plastics,” pp, 73, 112, 1952. Olson, F. C. W., and Schulte, 0. T., IND. ENG.CWEM., 34, 874 (1942). RECEITED for reviexy February 27, 1954,
ACCEPTED August 16, 1954
Thermal Conductivities of Liquid Silicon Compounds A. C. JENKINS Linde Air Products Company, Dicision of Union Carbide k Carbon Corp., Tonazcanda, S. Y .
A. J. REID Carbide & Carbon Chemicals Co., Diuision of Union Carbide k Carbon Corp., South Charleston, W . Vu.
T
HE direct measurement of the thermal conductivity of
liquids is difficult. However, extensive and precise measureinents have been made by Bates and associates who have determined nhernial conductivities of water ( 1), mixtures of water and glycerol ( 2 ) , chlorinated hydrocarbons ( b ) , and alcohols and glycols (3). Data on the thermal conductivities of a number of silicon compounds were required as a help in making plant design calculations. For this purpose a method of making the measurements rapidly with a precision of 5% or bett,er )vas sought. An apparatus and method were developed to fill these requirements. APPARATUS AND XIETIIOD
The apparatus shown in Figure 1 makes use of t v o glass vessels. The inner one is maintained a t a fixed temperature (50” C.) by circulation of water through it from a constant temperature bath of large volume. This inner vessel is suspended in a second glass container which holds the 60-inl. saniple. The hottom of the outer glass vessel (containing the sample) is ground flat, arid cenirnt,ed to it are two 3-inch diameter borosilicate glass disks, each */r-inch thick. The Burface of the upper disk i E grooved to hold a copper-constantan thermocouple called t,he intermediate thermocouple. The lower disk ie cemented to the copper bottom of a metal container suspended in a larger galvanized iron container partially filled with ice and water, with a slab of ice in cont’actwith the copper.
There is a constant temperature differential of 50” C. between the upper surface of the liquid sample and the bottom of the lower glass disk. Since the thermal conductivity of the glass is constant a t constant t,emperature, the teniperat,ure of the upper surface of the upper glass disk is a function of the thermal conductivity of the particular liquid being investigat’ed. Care niuqt be exercised to ensure a constant liquid sample thickness and to avoid disturbing the saiiiple during measurements. X st,eady state is usually reached in about 2 hours. The apparatus was calibrated by determining the electromotive force values of the intermediate therniocouple for several liquids of kn0T-n t,hernial conductivity. The values used are those determined by Bates (1, 3). T h e same value for ethylene g1;Vcol has recently been reported by Van der Held and associates (6)> whose results on water also agree closely with those of Bates.
Calibrating Liquids Water Aqueous solution of ethvlene glycol, 32.1y0 by weight Aqueous solution of eth$lene glycol. 61 . S % b y weight Ethylene glycol, 9 9 . 9 % Butanol
Thermal Conductivity. Cal./(Sec.) (Sq Cm.) (‘ C.,’Cm.) 16.02 x 10-4 11.61 X 1 0 - 6 iJ.04 X 10-1 6 . 6 1 X 10-* 3 . M X 10-4
The calibration curve for t,he particular apparatus used is shown in Figure 2. The thermal conductivity may he expressed as a function of the electromotive force of the intermediate thermocouple by the equation y = a9
.2 c
December 1954
2567
INDUSTRIAL AND ENGINEERING CHEMISTRY
T h e equation derived from the water and ethylene glycol solutions by the method of least squares was
+ 2.542 log&
log,, X = log,, 1.445 X
where X is the thermal conductivity in cal./(sec.)(sq. cm.) ( " C./cm.), E is the thermocouple reading in millivolts. The curve shown in Figure 2 represents the equation; the points shown are the actual experimental values. The butanol point, which was not used in deriving the equation, falls on the curve. As an additional check, the thermal conductivity of C.P. carbon
TO CONSTANT TEMPERATURE BATH
STAINLESS ST BRASS SUPPORTING RINGS
Figure 2. CEMENT
Calibration Curve for Thermal Conductivity Apparatus
GALVANIZE0 IRON CONTAINER
RESULTS THERMOCOUPLE JUNCTION COPPER BOTT INTERMEOIATE THERMOCOUPLE
ICE IN WATER
The thermal conductivities of 23 silicon compounds determined by the method described are given in Table I. T h e tempeiatures represent the Incan between the temperature of the upper and lower surfaces of the sample. One measurement was made on each sample. However, the apparatus was checked with butanol and carbon tetrachloride several times and completely recalibrated once during the measurements. Indications were that the results were reproducible to approximately 5%. ACKNOWLEDGMENT
tetrachloride was measured. Values from 3.7 X 10-4 to 3.9 X lo-* a t 32" C. were obtained. Bates ( 4 ) reports 3.7 X at 30" C., but states that because of the general characteristics of the chlorinated hydrocarbons and their low thermal conductivities, the precision of the data (about 2%) is not as high as that of his earlier work. The boiling range of the sample which he used was 76.2"to 77.0" C. Our agreement with his data indicates that the method is Satisfactory when the highest precision is not required. T h e apparatus is limited, however, in temperature range, and a further limitation may be imposed by the volatility of the material being tested.
The sample of butanol used in this work wa3 specially purified material supplied by the Carbide & Carbon Chemicals Co. The writers acknowledge the assistance of F. 8. DiPaolo in the assembly and calibration of the apparatus and of G. F. Chambers in making the measurements. LITERATURE CITED
(1) Bates, 0. K., IND. EKG.CHEM.,25, 431 (1933). ( 2 ) Ibid., 28, 494 (1936).
(3) Bates, 0. K., and Hazzard, G., Ibid., 37, 193 (1945). G., Ibid., 33, 375 (1941). ( 5 ) Van der Held, E. F. AI., Hardebol, J., and Kalshoven, J., Phqsmk, 19, No. 3, 208 (1953). (4) Rates, 0. K., Haezard, G., and Palmer,
RECEIVED for review M a y 28, 1954.
TABLE I. THERMAL CONDUCTIVITIES OF LIQUID SILICOS COMPOUNDS
Av. Tzmp,
C.
32 31 31 31 31 31 32 32 31 32 32 32 32 32 32 31 31 32 32 32 32 32 32
Thermal
Conductivity,
Cal./(Sec.) (Sq.
Cm.)(" C./Cm.) 2.9 x 2.7 x 2.7 x 2.5 x 2.6 x 2.4 x 3.2 X 3.1 X 2.7 x 2.9 x 3.0 X 3.7 x 3.1 x 2.9 x 3.4 x 2.5 X 2.7 X 3.0 x 2.9 x 3.3 x 3.0 x 3.1 x 3.7 x
10-4 10-4 10-4 10-4
10-4 10-4 10-4 10-4 10-4
10-4 10-4
10-4 10-4
10-4 10-4
lo-: 10-
10-4
10-4
10-4 10-4
10-4 10-4
ACCEPTEDAugust 18, 1!154,
