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Absolutemeasurementofthethermalconductivityofelectricallyconductingliquidsbythe
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J.Phys.E:Sci.Instrum.,Vol.14,1981.PrintedinGreatBritain
AbsolutemeasurementoftheofthermalelectricalIconductivity
yconductingliquidsbythetransienthotwiremethodYNagasakatandANagashimaDepartmentofMechanicalEngineering,KeioUniversity,Hiyoshi,YokohamaJapan
Received9March1981,infinalform10June1981
AbstractAnapparatusforpreciseandabsolutemeasurementofthethermalconductivityofelectricallyconductingliquidsusingthetransienthotwiremethodhasbeendeveloped.Inthepresentapparatus,ametallicwirecoatedwithathinelectricalinsulationlayerhasbeenusedasaheatingelementandaresistancethermometerinsteadofabaremetallicwire.Theeffectsonthethermalconductivitymeasurementcausedbythethininsulationlayerhasbeenanalysed.Intheanalysis,itwasfoundthattheeffectscanbenegligiblysmalliftheinstrumentisadequatelydesigned.TheusabilityofthemethodforelectricallyconductingliquidshasbeentestedtomeasurethethermalconductivityofanaqueousNaClsolutioninthetemperaturerange0to45Catatmosphericpressure.Theaccuracyofthepresentmeasurementwasestimatedtobe&OS%.
1IntroductionThetransienthotwiremethodhasbeenwidelyusedfordeterminingthethermalconductivityoffluidswithahighdegreeofaccuracy(Pittman1968,Haarman1969,Mani1971,deGrooteta11974,Castroeta11976andNagasakaandNagashima1981).Themostadvantageousfeatureofthemethodappliedtofluidsisitscapabilityofexperimentallyeliminatingconvectiveerrorandthedataobtainedwiththismethodisgenerallymorereliablethanthoseusingthesteadystatemethod.However,itisnotpossibletomeasurethethermalconductivityofelectricallyconductingfluidsusingthismethod,sinceabarethinmetallicwireisusedasanelectricalheatingelementandaresistancethermometer.Themeasuredsubstancesobtainedwiththismethodhavebeenrestrictedtoelectricallynonconductingfluidssuchasnoblegasesandorganicliquids.
There have been only a few attempts to expand the transient hotwire method to measure the electrically conducting liquids. Van der Held and van Drunen (1949) measured the thermal conductivity of some inorganic acids withalacqueredwireandthethermocoupletogetherinanarrowglasscapillary
?Present address (15 March 198114 March 1982) c/o Professor J Kestin, Division of Engineering, Brown University, Providence,RhodeIsland,RI02912USA.
Electricallyconductingliquid
Cell
Metallicwire
Figure1Electricalcombinationofthemeasuringsystem.(Inthecasewhentheordinarytransienthotwiremethodisappliedtotheelectricallyconductingliquids.)
Our past experience has shown that the last problem produces the most serious influence on the thermal con ductivity measurements. In many cases, there is a trend towards recording the higher value of the slope of voltage change against Int. Such an example of this type of measurement is found in the report by Korosi and Fabuss (1968), who meas ured the thermal conductivity of aqueous NaCl solutions using the ordinary transient hotwire method.
-
Theirdatashowthatavariationfromotherdataofuptoabout30%.
In the present paper an attempt has been made to overcome the abovementioned problems by using a metallic wire coated with a thin electrical insulation layer instead of just the bare metallic wire. The effects on the measurement caused by the thin insulation layer, (i.e. a temperature rise in the metallic wire and that on the surface of the insulation) have been analysed. A new instrument, which has been designed as a result of our analysis, has been developed. The use of this method for electrically conducting liquids is tested by measuring the thermal conductivity ofanaqueousNaCl
00223735/81/121435+06801.50
tube instead of a bare metallic wire, but the influence of an air layer and glass capillary on the temperature change were not analysed. Turnbull (1961) used a bare platinum wire for molten salts at elevated temperature (3OO2C), concluding that the current through the salts would be negligible under the experimental conditions. It seems insufficient that the con clusion of Turnbull was based on Smythes analysis (1955) which gives only the ratio of total current to the wire current. Baruel (1972) carried out measurements with an electrically uninsulated wire for acids and salt solutions by arranging the experiment in such a way that a balance was quickly established between the counterelectromotive force from polarisation and voltage applied to the cell. Baruel also considered the theoretical foundation of the modification in detail. Recently, Dietz et al (1980) modified the method for heating a bare metallic wireusingalternatingcurrentinordertoavoidthepolarisationeffectsonsurfaceofthewire.Theusabilityofthe
AC
methodhasbeendemonstratedwiththemeasurementsofwaterathighpressure.
When the ordinary transient hotwire method is applied to the electrically conducting liquids, the following problemsmayoccur.
(i)Thecurrentflowsthroughtheliquidandtheheatgenerationofthewirebecomesambiguous.
(ii)Polarisationoccursonsurfaceofthewire.(iii)Theelectricalsystemcombineswiththemetalliccellthroughtheliquidsandsmallvoltagesignalsaredistorted(figure1).
I
/
01981TheInstituteofPhysics1435
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YNagasakaandANagashima
solutioninthetemperaturerange0to45Catatmosphericpressure.
2EffectsofaninsulationlayeronthemeasurementIntheordinarytransienthotwiremethod,therehasbeenanumberofstudiesconcerningthistheory(Healyeta11976andCastroeta11976)andtheprincipleofthemeasurementiswellknown.Inthissection,wehavediscussedonlytheproblemswhichariseduetotheuseofinsulatedwire.
2.1EfectsofaninsulationlayeronthetemperatiireriseofmetallicwireThecoordinatesystemwhichdescribestheinsulatedwireisshowninfigure2.ThebasicproblemsaregovernedbythefollowingFourierequations:
auT1a+
1
aarl1
ahrlrarK~
__rl
O
-
iscalculated.Thenthethermalconductivityisdeterminedby
1436
atnri2X1
Wherehisthethermalconductivity,
K
the thermal diffusivity, r the radial coordinate measured from the centre of the wire, q theheatgenerationperunitlengthofthewire,
Yi
the radius of the metallic wire and ro the radius of the insulated wire. The suffixesdenoteeachmaterialaccordingtofigure2.Theinitialconditionandboundaryconditionsare:
hTi
=
hTz
=
AT3
hl__he__
t
-
r1ri2hl
-
ThermalConductivityofconductingliquid7
2.2 Effects of an insulation layer on the reference temperature When the initial temperature of the liquid is Th, the temperaturetowhichthemeasuredthermalconductivityrefersTrisdefinedas(Pittman1968):
indicateWhere
t1
the times at the start and end of the run, respectively. In the case of an insulated wire, AT in equation(16)isreplacedbyatemperatureriseonthesurfaceoftheinsulation.
AT2(r0,t)
2.3EffectsofthermalcontactresistancebetweenthemetallicwireandinsulationlayerThethermalcontactresistancebetweenthemetallicwireandinsulationlayer,owingtodifferenceofthethermalexpansioncoefficientineachlayer,existstosomeextent.Inthiscase,boundaryconditionequation(5)isreplacedbythefollowingequation:
4[In4K3t+l
{!i2('
Equation(17)isalsorewrittenusingconstantsDandE:
Here, R indicates the thermal contact resistance per unit length. An approximate solution can be obtained, in a mannersimilartoderivingequation(I3),toyield
ATI=~~?[Int+A+
ridKZ
(20) where A, B and C represent the same constants in equation(14),andh=27rriR.
2.4EffectsoffinitelengthofthewireItisnotpossibletopredicttheerrorduetothefinitelengthofthewireanalytically.So,itisadoptedpracticallytocompensatefortheeffectsexperimentally.Therearetwosuchmethods:theshortandlongwiremethod,andthepotentialleadsmethod.Inusingtheinsulatedwire,itseemsverydifficulttechnicallytoadoptthelatermethod.Therefore,inthepresentapparatus,theshortandlongwiremethodhasbeenemployed.AdetailedanalysisexplainingthispointisdescribedinthereportproducedbyKestinandWakeham(1978).
3Experimentalapparatus3.1InsulatedwireThecrosssectionoftheinsulatedwireinthepresentapparatus,whichwasoriginallyusedasaresistancethermometer,is
4rA3ro2Ct4
~2KI,
ri2
A2
AIro1
8
ATdro,t)=
47rA3
"
and
-
12
In+2A2
(K2KI)
rf+2/\3
x
[.I2(K2Kl)
+
'02(K3K2)
27rAlr=(ATiAT2)
+BInt+C+
(+&+:)I)II7t2
[..(If2KI)
+Tr=TI)
+[A
T(t1)
+AT(t2)I.(16)
A2A1A3A2
aATi1
arR
2A3
dK
-
rih
h
dG
]In
23z)j'r=ri.(19)
(17)
(18)
Figure3Crosssectionoftheinsulatedwire.1,Platinumwire2,polyesterlayer.
shown in figure 3. Thin platinum wire, 40 pm in diameter 1, is coated with a polyester 2 electrical insulation layer 7.5 pm in thickness. As shown in figure 3, the platinum wire almost makes a concentric circle with the insulation layer and the change in the diameter of the wire and the thickness of the polyester along the longitudinal direction is 40 pm f 1.5 % and 7.5 pm k 20%, respectively. The polyester insulation has good resistance against many chemical reagents and solvents, and also, has good physical and electrical properties (electrical resistivity of IOl7 !2 mm at 25C). This insulatedwirecanbeusedtotemperaturesupto150C.
3.2HotwirecellFigure4showsthehotwirecellassembly.Thecellisdesignedforhighpressuremeasurementoperatingupto50MPa,withthetemperaturerangeupto150C.Twocellsofthistype,differingonlyintheirlength,havebeenconstructedthelengthsofthewiresareabout200"(resistanceisabout15
s2 at OOC) and 100 mm respectively. In constructing the cell the polyester layer of each end of wire 5 is melted away with HzS04 and connected to platinum pins with a diameter of 500 pm. The pins are soldered to copper rod 9 insulated with a silicon tube. The soldered pins and inside portion of terminal 1 are painted with thin silicon rubber for insulation. These vessels were immersed in a liquid thermostatic bath at a stable controlled temperature of k 0.05 K.Thetemperatureofthebathwasmeasuredwithastandardthermometer.
3.3ElectricalsystemAblockdiagramoftheelectricalsystemisshowninfigure5.Inthisdiagram,RIandRsrepresenttheresistanceoflongandshortwire,respectively.Thetemperatureriseofthewire,theendeffectsarecompensatedusinglongandshortwire,isconvertedintovoltagechangewithabridgecircuit.Thevoltagechangeismeasuredbyanintegratingdigitalvoltmeter(Yokogawatype2501),whichisexternallytriggeredbyapulsegeneratorwitharepetitionrateofsixpersecond.These
1437
-
YNagasakaandANagashima
0X
012345TimeIs)Figure6Magnitudeofl/tterminequation(13).
Firstly, the deviation from the linear relationship of A TI In t, owing to the heat capacity of the wire and the insulation layer, is calculated from equation (13). An example of this calculation, in the case of measuring the aqueous NaClsolutionat45"C,isshowninfigure6.ThepropertiesofeachlayerusedinthecalculationareAI
=71.5(Wm1Kl),
KI=2.5x105(m2s1)(estimatederrorf5%)(Touloukianeta11970),hz=0.141,~2=8.32xlo*,(estimatederrorf10%)(BrandrupandImmergut1967),=0.619,
K3=1.57xlo'(estimatederrorf1%)(densityfromRoweandChou1970andspecificheatfromWashburn1928).As
showninfigure6,thel/ttermofequation(13)decreaseswithtimeandafterFigure4Thehotwirecellassembly,1,terminal2,Cupacking3,teflonpacking4,pressurevessel5,insulated
acertainperiodoftime,thevariationofthistermbecomessmallenoughsothatthethermalconductivity
A3
canbePtwire6,susrod7,
ABS
disc8,grandretainingring9,insulatedCurod.
Ideterminedbyequation(15).Thisconclusionisvalidforthemeasurementofliquidsinwhichthermalconductivitiesandthermaldiffusivitiesdonotdifferdrasticallycomparedwith
Digitalvoltmeter
b
Ithesampleliquidinthepresentmeasurement.
It is very difficult to measure the magnitudes of the thermal contact resistance between the metallic wire and insulation layer in situ. However, according to the correlation of Veziroglu (1967) h is roughly estimated to be in the order of 106 (m2 K W1) thus the relative magnitudes of the term involving h compared with (B In t+ C) can be calculatedtoabout10%.ThiscausesonlynegligibleeffecttohT1htrelation.
r
PulsegeneratorInordertodemonstratethattheinstrumentoperatesinaccordancewiththemathematicaldescriptionofit,figure7,
represents deviations of the measured AT1 from the fitted straight line for a typical run. As shown in this figure devia tions 15 s. never The average exceed deviations 0.15 % during from the linearity available is about time 0.05 duration
-
%.Theaccuracyofthethermalconductivityvalueinthepresentmeasurementisestimatedasfollows.ThetemperatureComputer
Figure5Blockdiagramofelectricalsystem.
Imeasuredvoltagechangesarerecordedanddeducedtother
010malconductivityvaluesusingadesktopcomputer(HP85).R2isa10standardresistorandthecurrentthroughthewireismeasuredbythevoltageacrossit.RDisusedforstabilisingthecurrentthroughthewirebeforeinitiatingthemeasurement.
4EstimationofaccuracyInthefollowing,theapplicabilityoftheinstrumenttoelectricallyconductingliquids,anaqueousNaClsolutioninthepresentwork,isanalysedusingtheresultsin82andtheoverallaccuracyisestimated.
I&p
01
c00
0
,IO
Q,02
II
I
I
0051015InfFigure7DeviationsofmeasuredATIfromfittedstraightline.
1438
-
Thermalconductiaityofconductingliquids
Table1
ThermalconductivityofanaqueousNaClsolution(3.027molality).
Referencetemperatureqh("C)(Wm1)(Wm1K1)
0.960.89060,550815.340.89590.576430.890.92040.600045.820.94050.6218
coefficient of the wire resistance was determined by the calibration carried out in the temperature range 0 to 45C during the course of the measurement and its accuracy was 0.17%. The uncertainty of dATl/d In t was 0.16% which is estimated by the deviations from linearity and a number of available ATl(ti) plots. The heat generation per unit length ofwireqisaccurateto0.1%.Includingalltheothersmallestimatedfactors,thetobeoverallI0.5accuracy%.
ofthepresentmeasurementis
5SampleofmeasurementInthepresentwork,theapparatusdescribedherehasbeenemployedtomeasurethethermalconductivityofanaqueousNaClsolutionwithaconcentrationof15.03wt%(3.027molality)asasampleofelectricallyconductingliquidsinatemperaturerange0to45Catatmosphericpressure.TheaqueoussolutionusedforthesemeasurementsweremadebyweightwithreagentgradeNaClstatedpurityof99.9%(withoutfurtherpurification)andionexchanged,twicedistilledwater.Table1containsthemeanvaluesofthethermalconductivityobtainedinthesemeasurements.Themeasurementswereperformedunderthesameconditionssixtotentimesandthereproducibilitywas+0.1%to+0.2%,astandarddeviationwhichisconsistentwiththeestimatedaccuracy.Thetemperatureriseofthesurfaceoftheinsulationlayerduringthemeasurementwaslessthan1Kandaperiodofabout30minwasallowedbetweenruns,
1020304050
TemperatureI
OCI
Figure8ThermalconductivityofanaqueousNaClsolution(3.027molality).D,Riedel(1950),Riedel(1951)0,presentwork.
In figure 8, the present experimental data are compared with those of earlier works. As far as this concentration of an aqueous NaCl solution, only the works of Riedel (1950, 1951) who measured the thermal conductivities of many kinds of aqueous salt solutions, are available. The figure shows that agreement with the present data and those of Riedelarewithintheaccuracyclaimed.
This method has the possibility of being applied to measure ments for electrically conducting liquids at high temperaturesusingaceramiccoatedwire.
AcknowledgmentsWewouldliketothankDrKTanishitaofTokyoWomen'sMedicalCollegeforhisvaluableadviceinhandlingofthiswireandMrTItoandMrHOkada,studentsofKeioUniversityatthattime,fortheirassistanceincarryingouttheseexperiments.
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OJ
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E:Sci.Instrum.9107380DietzFJ,deGrootJJandFranckEU1980Highpressurethermalconductivitymeasurementsofwaterwith
AC
and
DC
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YNagasakaandANagashima
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