Thermal Conductivity Measurements of Viscous Liquids JAMES H. BOGGS’ AND WILlMER L. SIBBI‘M‘ Purdue University, Lufayette, Znd.
T
HIS investigation was a continuation of a research program
initiated in the Purdue Laboratories in order t o obtain reliable values of physical properties for use in various dimensionless moduli which are used in heat transfer studies (5, 8, 1 1 ) . Aqueous solutions of high viscosity are of interest in experimental heat transfer investigations because the viscosity may be increased by a hundredfold with very little change in the thermal conductivity and specific heat of the aqueous solution. Such “tailormade” solutions may be used to obtain specified boundary conditions.
wells. All of these tubes passed through mating tubes, which were welded to t h e outer cylinder cap in order t o prevent the bath liquid from leaking into the test liquid in t h e annulus. The energy was supplied t o t h e cylinder from a resistance heater made by winding Chrome1 P (30 B. & 9. gage) wire on a balsa wood core 0.75 inch in diameter. The number of turns of heater wire per inch was increased in steps from 8 turns in the center 4 inches to 11 and then t o 14 at t h e ends. This provided proper guard heating against end losses. The test heater section was determined as t h e distance between two potential taps which were spot-welded t o the heater wire on turns 1 inch apart. The energy for the resistance heater was supplied from nine 6-volt storage batteries connected in series and parallel t o give a n 18volt supply. T h e maximum current drawn from this bank of cells was about 0.25 ampere. T h e voltage regulation was excellent (deviations less than 1 part in 10,000). Figure 2 shows t h e arrangement of the bath, thermistor, Wheatstone bridge, and photocell circuit used to obtain t h e temperature control. The bath temperature was controlled to d ~ 0 . 0 0 9F. ~ by a Wheatstone bridge circuit, one leg of which was a thermistor suspended in t h e oil bath (8). An auxiliary heater was arranged t o provide most of the energy required in the bath, so t h a t the control heater provided only a small fraction of the total energy requirements.
Most thermal conductivity measurements have been made with fluids of low viscosity. Bates ( I ) measured the conductivity of some viscous silicone mixtures ranging from 0.65 to 12,500 cs. The purpose of this investigation was to measure the thermal conductivity of hydrocarbons and silicone polymers as well as viscous aqueous solutions. Solutions with viscosities as high as 60,000,000 os. were studied. APPARATUS
The experiences of other investigators were freely used in the design and operation of this equipment (6, 8, 11). Figure 1 shows the concentric cylinder apparatus which was used in this investigation. The cylinders and caps were machined of 245 aluminum. Careful polishing provided smooth surfaces for the annulus. The surfaces remained bright, although they were covered with a very thin film of oxide. The annulus was 8 inches long and 0.100 inch thick. Woolf (11) experienced many difficulties when he attempted to force viscous liquids into an annular space of 0.0650 inch. It was necessary t h a t the annular space be small enough t o prohibit convection currents when pure water was used with a temperature difference of l oF. across the space. The annular space was fixed by Teflon plugs inserted in the wall of t h e small cylinder to provide spacers. Aluminum tubes were welded to the top of the outer cylinder to provide access t o the thermistor wells. The leads for the direct current heater and for the otential taps passed through ceramic insulators inserted in stainEss steel tubes. Aluminum tubes were also welded t o t h e top of the inner cylinder to provide access t o those thermistor
Figure 2. Bath temperature control circuit
Figure 3 depicts the measuring and heater circuits. A Type K-2 (L & N)potentiometer and a Type E (L & N ) galvanometer (sensitivity o 0.49 pv. per mm.) were used t o measure t h e voltage drops t o 1 part in 10,OOO. An Eppley standard cell which had been recently calibrated served as the voltage standard. The voltage drop across t h e heater was measured and the current was obtained from the measurement of the voltage drop across the 1.0-ohm standard resistance in series with the heater. The resistances of the T y e 14A and 14B thermistors were measured with a 5-decade (]e & N ) Wheatstone bridge and a Type E (L & N ) galvanometer (sensitivity of 0.0004 @a.per mm.).
1 Present address, Oklahoma Institute of Technology, Oklahoma A. and M. College, Stillwater, Okla.
289
INDUSTRIAL AND ENGINEERING CHEMISTRY
290
Vol. 47, N o . 2
where R 16 calculated at either 7’1or T 2 f ~ o mEquation 1. Thi+ equation can he used to approximate the temperature differrnc.1 hetn-ern the t a o thermistors if it ih moclifid H S follow.::
In 1,l~uittioii3 the bath temperature, 2’h (ahout 0.W‘ 14’. less). has 1)een substihted for t,emperature l’z. The resulting error was in the fourth decimal place arid could be neglected. Correction for the drop in temperature in t8hemetal between the therniidor well^ amounted to ahout 1 .?yofor water arid water Polutioiis mid 0,5y0for all other ruw. IZath te~nperatiireaIVWY ot)t,aiiii~iwith precision rnel.t.ur?-iii-Rlarl.: thprmonieters.
.,L# ‘I -
7//F*N/5.W
EXPERIRZEN’IAL PKOCR1)IiRE
/9* 7~K&mIsroE
Figure 3. Measurement aiid direct current heater circuit
The therinist,or probes, lvhich were used for the nieasurerileIlt of the temperature drop across the liquid layer, were a,Qsenibledin 18-inch lengt,hs of thin-walled stainless steel tubing (0.125 inch in outside diameter). A tcrminal block was fastened to {,he upper end of the tube. Two Manganin wires were passed through ceramic insulators in the tube t o the thermistor a t the lower end, The thermistor hcad cstmded about 0.25 inch from ~ in the tube the lower end of the tube. Thc thermistor w a sealed with Sauereisen cement. Finally, the lower end of t,he probe was dipped i n G.E. lxlliitlg varnish and haked in R furnace at 300” F.
The c:ylindi~rswere cleaned thorougfsl>. will1 suitable solvents I)efore each run The usual fill ng protwiu-ro was to evacuate t,he aniiulns for several hours anti then t f i ~ J I P I IH stopcorlr to t81ie test liquid reservoir. Thc liq\iitl filled t h e evacuated annulus from the hottom through H J-*h:iI:td tulw welded to the hottoin cap of the outer cylinder. For liquids (11’ high viscosity this procedu1.r w : not ~ feasible. The OLW iiqtiids were heat,ed to 275” V. : i i i d then poured into t.hv Iiirgv ri4iiirier; the inner cylinder
‘IXZIPEH ATCR E IIIFFER ENCE
T h e relation h e t w r ~ r temprmturr ~~ and rf t h w n ~ i ~ tii; o rgk.rn .:)k
(2)
In
=
H (2’ - T o ) TT,
(I!
The constant, 13 actually i;i a func.tion of temperature; however. the variation is only 0.1% per 9 ” F. and thus may he cousidered constant over the tcmperature range of 1.5” F. used in each experiment. Equatio~iI rim be used to derive the following equation for the temperatuw tiiff errncr
-
70
80
SO
1
100 110 120 I30 TEMPERATURE O F :
_--
140
150
160
170
200
220
240
260
.070 .069 .06 6
,960
1 7 ---1_L_C 1
IC)% .94C
-
I
I
I---/
Y
A
.066
.065 ~
,064
Figure
60
80
100
V - INDEPO
140 160 180 TEMPERATURE * E
I20
6. Thermal
conductivity polymers
oT
hydrocarhoii
INDUSTRIAL AND ENGINEERING CHEMISTRY
February 1955
waa then pushed into i t forcing the liquid up around the inner cylinder. The top cap was then bolted into place and the annulus was completely full. The test instrument was then placed in the bath and the leads were connected. The proper current was passed through the heater to give approximately a 1' to 1.4' F. temperature difference. When steady state was obtained, as indicated by the constant resistance reading of the thermistor in the inner cylinder wall, the reading of that thermistor was taken. I t wm then moved to the outer cylinder well and thence to the bath, where readings were taken. Potential drops were measured and the run was completed by reading the bath temperature. The entire series of memurements was then repeated.
291
contained the liquid sample tended to cancel out. It was possible to reproduce values on pure liquids within less than 0.5% scatter a t a constant bath temperature. A brief compilation of recommended values of thermal conductivity of pure water is presented in Table I (10).
Table 1. Thermal Conductivity of Water Thermal Conductivity K*,
Temperature,
E'.
B.t.u./(Hr.)(Ft.)(O
60
h.)
0.3397 0.3532 0.3641 0.3733 0.3810 0.3861 0.3905
80 100
120 140 160 180
ANALYSIS OF DATA
The equation for conduction of heat through a concentric cylindrical shell in a radial direction can be derived from the equation of Biot and Fourier. Rearrangement of the equation gives the following:
(4)
The equation holds for radial heat flow only; preliminary tests indicated that these conditions were obtained for the test section. All the energy added in the test section was assumed to pass through the test section. The use of Equation 4 implies that convection does not occur. Results of experimentation by Beckmann (8),Jacob (3) and Mull and Reiher (4)show that the error due to convective losses will be less than 2% if the product of the Prandtl modulu~and the Grashof modulus is less than 1000. In these experiments the maximum value of this product was 400 for pure wfater; for the other compounds it was very small The maximum value of the product for the silicones was only 5.7. Thus the heat transfer by convection was negligible. Woolf ( 1 1 ) gave a detailed discussion of the accuracy of measurements with this type of instrument. RESULTS
The data are presented in Figures 4 through 10. The data for aqueous solutions are reported as ratios of thermal conductivities K / K * , where K is the conductivity of the solution and K* is the conductivity of pure water a t the same temperature. The errors in the primary or absolute values were estimated to be less than The secondary measurements were of much higher accuracy than the absolute measurements, as the errors in the determination of the length and diameters of the space which
Aqueous gelatin (USP) solutions with up to 10% gelatin (by weight) were tested. Gelatin lowered the thermal conductivity by about 0.5% for each weight per cent of gelatin in the water, as shown in Figure 4. Methocel (Dow methylcellulose, technical grade) produced about the same decrease in thermal conductivity as shown in Figure 5. The 10% (Methocel, by weight) solution had a viscosity of 2600 cs. at 68' F. and formed a gel at 104" F. Kelcosol (sodium alginatc, a water-soluble, colloidal carbohydrate), Hercules cellulose gum (Type 70 High, sodium carboxymethylcellulose), and ACCO acrylic polymer (medium viscosity 201, a modified sodium polyacrylate) in aqueous solutions of 2000 to 10,000 cs. all had nearly the same thermal conductivity as pure water. A maximum decrease of 1% was observed. In addition t o checking the operation of the instrument with pure water as a test fluid, olive oil was also used. The data are presented in Table 11. The thermal conductivity of olive oil is approximately one fourth as large as that for water. The experimental data which have been reported in the literature are not in agreement for fluids in this range of thermal conductivity (6, 7 ) . Olive oil is not rewmmended as a calibrating liquid for secondary instruments, because some surface phenomena exist between certain metals and olive oil. I n some cases a measurable difference was observed between brands of olive oil. I n spite of these objectionable features, olive oil appeared to be the most suitable liquid. These data (Table 11) are about 1% lower than the values reported by Davis ( 6 ) , and about 2% lower than the values reported by Kaye and Higgins (6) and by Woolf (11). Davis used a platinum heater wire in a silver tube. His results ,092 ,091
.oao *OS3
,089 .088
991
.089 ,085
,087 Y
cL. 5+
,085
'12'
I
,083
*
SO81
,084
De 3 .082
.081 .080
.079 *OT980
100
120
140
160
180
TEMPERATURE
200 220
240 260
E
Figure 7. Thermal conductivity of General Electric silicones Viscosity at
looo F.
A 78 VISCOSITY
-
CENTISTOKES AT 100%
Figure 8. Thermal conductivity as a function of viscosity for General Electric silicone fluids SF-96 series
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
292 ,091
.OW
,089
.OB8 .OS7
Y
.084
.cia3 .052
100
120
140 160 180 TEMPERATURE
'F.
200 220
240
Vol. 47, No. 2
Seven different General Electric silicone fluids were studied. The data are presented in Figures 7 and 8. These fluids nxre essentially pure dimethyl silicone polymers of varying molecular weight distributions. The physical properties are presented in Table IV. Figure 8 shows that the thernial conductivity for the SF-96 series increases with the viscosity. For the lower viscosity nieiiibers of this series the plot of thermal conductivity us. viscosity (at a given temperature) results in an approxiinately straight line. Figure 7 shows that the thermal coriductivit,y of t'he high viscosity fluids is not a sensitixye function of viscosity. This is in agreement with the results reported by Bates ( 1 ) . The General Electric and Dow Corning fluids are similar, but apparently there are no equivalent fluids in these two series. Figure 9 compares the authors' data for DC-200 (500,000-cs.) fluid with the data reported by Bates ( 1 )for DC-200 (12,500-cs.). The 12,500-cs. fluid was the inost viscous fluid thfit Bates used. Sakiadis and Coates rate his data as good iestirnatcd csperimental errors of less than 1 1 2 % )
Figure 9. Thermal conductivity of Dow Corning silicone fluids Type DC-200 T'iscosit) at 77' F.
were rated as good (errors of less than A127,) by S:Llii:did and Coates (6). Kaye and Higgins used a flat plate (aluminum) type appaxatus with temperature differences of about 8" F. Their data were rated as average (errors greater than =k12%) by Sakiadis and Coates (6). Woolf used Pompeian brand olive oil in a brass concentric cylinder instrument. The various sarnples of Conti brand olive oil had identical physical properties and the oil remained stable during storage for over a period of one year. Table 11. Thcrmial Conductility of Olive Oil (US€', Conti Brand) Temyeratule, 79.6 101.5 109.6 146.9
60 70
Thermal Conductivity, B t u /(H1.)(Ft.)(' F.) 0.0951 0.0941 0.0933 0 0922
F.
90
100
110
120
1:
'E
Figure 10. Thermal conductivit! ~f solution of cellulose acetate (5y0 by weight) in acetone (98%) and water (2G&.7,)
I
Three hydrocarbon polymers-Orenete polybutene (KO 32), Indepol polybutene (H-300), and Esso Vistanex ( L M k a 1 1 had therinal conductivities of about 0.066 B.t.u./(hour) (foot) ( O I$'.) and positive temperature coefficients as shown in Figure 6 The physical properties were incasured in the Purdue laboratory and are given in Table 111.
80
TEMPERATURE
Figure 10 compares the authors' values for the thermal conductivity of cellulose acetate solution (50/, by weight) in a solution of acetone (98%) and water (2%) TTith the thermal conduct,ivity of pure acetone. Riedel used a concentric cylinder, a concentric sphere, and a flat plate apparatus to make his mcasurenients and he covered a temperature range from 112' to 122' F. ( 6 ) . Sakiadis and Coates rate Riedel's data ns very good (errors of less than +5%).
-
Table 111. Physical Properties of Viscous Polymers Viscosity" cs., 790 F: Fluid Orenete polybutene KO. 32 64,000 70,000 Indepol polybutene H-300 64,000,000 Esso Vistanex Lbl 405,000 Dow Corning silicone DC-200 (500,000 cs. a t 77' F.) Measured i n falling ball viscometer.
Density, G./Cc. 790 F.' 0.897 0.902
Specific Heat, B.t.u.,/(Lb.)(' F.), 750 F.
0.911
0.978
ACKNOWLEDGMENT
0.4ii8
0.479 0.473 0.377
Thaiiks are extended to the International Business Machine Co. for t,he €el!ow-ahipand to the various c,onipaniesthat furnished
the liquids. KQlIENCLATURE
Physical Properties of Silicone Fluids [General Electric Type SF-96 and experimental fluids (9)I
Table IV.
Fluid SF-96(40) SF-96(100) SF-96(300) SP-96(1000) 201-17-763 201-17-764 201-17-765
Viscosity, Cs., 100° F. 40 100
300 1,000 28,160 56,640 102,400
Maximum Pour Point,
F.
- 65 -6 3 -57 - 57
Specific Gravity,
Refractive Index, 68/68O F. 77" F. 0,964 1,4022 1.4030 0.965 1.4034 0.967 1 4036 0.989
Specific Heat 80' F. B.i.u.1 (Lb.)(' F.) 0 374 0 370 0 366 0 352
B
D1 Dn IC L
= therniistor constant, absolute temperature = out,side diameter of inner cylinder, 1.2965 It 0.0002 inch = inside diameter of out,er cylinder, 1.4969 =k 0.0003 inch = thermal conductivity, B.t.u./(hour)(foot)(' P.) = length of test section, 1.000 i: 0.0025 inch
ratc of heat flow, B.t.u. per hour resistance, ohms ice point temperature, ' R. T, temperature in inner wall, R. 2'2 = temperature in outer wall, I
