Vapor-phase Thermal Conductivity of Binary Mixtures of Cyclopentane and R134a with R365mfc I. M. MARRUCHO AND N. S. OLIVEIRA CICECO, Departamento de Quı ´mica Universidade de Aveiro P-3810-193 Aveiro, Portugal R. DOHRN* Bayer Technology Services Center for Fluid Properties and Thermodynamics Building B310, D-51368 Leverkusen, Germany ABSTRACT: The thermal conductivity of mixtures of R365mfc (1,1,1,3,3- pentafluorobutane), with R134a (1,1,1,2-tetrafluoroethane) and cyclopentane were measured using a transient hot-wire method, in the pressure range between 0.1013 and 0.7 MPa and temperatures between 311 and 413 K. The composition of the measured mixtures was 93.0% R365mfc þ 7.0% R134a (kg/ kg), 27.0% R365mfc þ 73.0% R134a (kg/kg) and 62.8% R365mfc þ 37.2% Cyclopentane (kg/kg). The Wassiljewa mixing rules modified by Mason and Saxena and the Extended Corresponding States Theory were used to correlate and to predict the experimental results obtained, with an average absolute deviation of 1.8 and 10%, respectively. KEY WORDS: blowing agents, fluoroalkanes, mixture, R365mfc, thermal conductivity, transient hot-wire method. *Author to whom correspondence should be addressed. E-mail: [email protected]JOURNAL OF CELLULAR PLASTICS Volume 39 — March 2003 133 0021-955X/03/03 0133–21 $10.00/0 DOI: 10.1177/002195503033636 ß 2003 Sage Publications
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Vapor-phaseThermal ConductivityofBinary ...path.web.ua.pt/file/JCP 2003 39 133.pdfTable 1. Vapor-phase thermal conductivity of mixture A, 93.0% of R365mfcþ7.0% of R134a (kg/kg), from
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Vapor-phase ThermalConductivity of Binary
Mixtures of Cyclopentaneand R134a with R365mfc
I. M. MARRUCHO AND N. S. OLIVEIRA
CICECO, Departamento de Quımica
Universidade de Aveiro
P-3810-193 Aveiro, Portugal
R. DOHRN*Bayer Technology Services
Center for Fluid Properties and Thermodynamics
Building B310, D-51368 Leverkusen, Germany
ABSTRACT: The thermal conductivity of mixtures of R365mfc (1,1,1,3,3-pentafluorobutane), with R134a (1,1,1,2-tetrafluoroethane) and cyclopentanewere measured using a transient hot-wire method, in the pressure rangebetween 0.1013 and 0.7MPa and temperatures between 311 and 413K. Thecomposition of the measured mixtures was 93.0% R365mfcþ 7.0% R134a (kg/kg), 27.0% R365mfcþ 73.0% R134a (kg/kg) and 62.8% R365mfcþ 37.2%Cyclopentane (kg/kg). The Wassiljewa mixing rules modified by Mason andSaxena and the Extended Corresponding States Theory were used to correlateand to predict the experimental results obtained, with an average absolutedeviation of 1.8 and 10%, respectively.
Rigid polyurethane foams (PUR) belong to the most effectiveinsulation materials commercially available. Therefore, PUR foams
are widely used for technical insulation purposes, e.g. in the applianceindustry or for technical refrigeration processes. The heat transferthrough the foam, that is important for the properties as an insulatingmaterial, is around 65% due to the blowing agents trapped inside of thecellular-foam formed by the polymer. Also, the pressure generated bythe gaseous blowing agent and CO2 in the closed cells of the foam has astrong influence on the stability of the foam.Until recently, CFC-11 was the most widely used blowing agent to
fill the closed cells in a polyurethane foam. Since 1987, with theestablishment of the Montreal Protocol, and its reinforcement in 1992in Copenhagen, a lot of research has been produced in order to findadequate substitutes for chlorofluorocarbons (CFC) in general, CFC-11in particular. The vapor-phase thermal conductivity of severalpotential blowing agents, pure fluids as well as mixtures, has beenmeasured. The vapor-phase thermal conductivity of pure fluids such ascyclopentane, and hydrofluorocarbons (HFC) derived from methane,ethane, propane and butane [1,2], and cyclopentane mixtures withlower boiling hydrocarbons have been recently measured [3,4]. In aprevious paper [5], the vapor-phase thermal conductivity of R365mfcwas measured at pressures up to 0.5MPa and in the temperaturerange from 336.85 to 378.40K. In the same line of research, this workaddresses the measurement and correlation of the vapor-phase thermalconductivity of mixtures of R365mfc and R134a and R365mfc andcyclopentane in the pressure range 0.1013–0.8MPa and in thetemperature range of 311.25–413.28K. The experimental methodused was the transient hot-wire method, which is the IUPAC referencemethod [6].The modified Wassiljewa mixing rules [13] modified by Mason and
Saxena [14,15] were used to calculate the thermal conductivity of themixtures investigated. The Extended Corresponding States Theory(ECST) [7] was used for predicting the experimental results.
EXPERIMENTAL
The experimental thermal conductivity measurements were carriedout in an apparatus based on the transient hot-wire method [6].Research on the use of a bare platinum wire or an anodized tantalumwire to measure the thermal conductivity of vapor polar compounds was
been done by other authors [8] and indicates that the results obtainedwith both methods were in good agreement.An overview of the development and technical details of the
measurements of the thermal conductivity of gases has been givenelsewhere [9,10]. The measuring cell (stainless steel, 1.4571) with alength of 267mm and diameter of 48mm consists of two parallelchambers with bare platinum wires of different lengths (ratio of lengths� 0.28) and 10 mm in diameter. The second wire was used to compensatethe end effects. The cavity around the hot wires is made of stainless steeland has a diameter of 16mm. The instrument is capable of operationfrom 298 to 523K at pressures up to 2MPa. The temperature wascontrolled with an air thermostat within �0.1K. The temperaturewas measured using calibrated PT 100 resistance thermometers withan uncertainty within �0.1K, which might lead to an error of�0.01mWm�1K�1 or 0.06% for the thermal conductivity of R365mfc.More information on the apparatus has been given elsewhere [2]. Thepressure sensors used in the measurements of the thermal conductivitywere transducers from Keller, which were calibrated using a pressurebalance (DESGRANGES ET HUOT; Druckblock 410, Type 26000 M,Terminal 20000). The uncertainty of the pressure measurement iswithin �0.1 kPa.The basic theory behind the transient hot-wire method is given by
Healy et al. [11]. The essential feature of the transient hot-wire methodis the precise determination of the transient temperature with a thinmetallic wire. This is determined from measurements of the resistanceof the wire over a period of a few seconds followed by the initiation of theheating cycle, with a �T¼ (2.000� 0.025)K. This resistance (tempera-ture) is recorded with a digital voltmeter during the transient run. Forcylindrical wires, with radius r0, the ideal temperature rise �T on thesurface of the wire can be calculated using Equation (1).
�Tid ¼q
4�� Tref , �refð Þln
4at
r20Cð1Þ
where �(Tref,�ref) is the thermal conductivity at the temperature anddensity reference conditions, a is thermal diffusivity, a¼ �/(�CP), q is theheat flow through the wire, t is the time, and C¼ exp(�)¼ 1.7811. . . isthe exponential of Euler’s constant �.In this work, several corrections to the ideal transient hot-wire
method were made. These corrections can be divided in two mainsources: corrections due to the wire and due to the existence of an outer
isothermal boundary layer. In the first correction, the finite radius of thewire (5 mm) is accounted for, which produces a short-time temperaturelag relative to the ideal model. The second correction accounts for thepenetration of the fluid temperature gradient to the outer cell wall,which leads to the transition from transient conduction into an infinitemedium to steady-state conduction in a concentric cylindrical region. Atlower pressures the linear region in the temperature rise versus thelogarithm of elapsed time is reduced. This is due to the high thermaldiffusivity of the gas, which is inversely proportional to the gas density.In this work, the lowest pressures of the measurements were selected
to give a sufficiently large linear portion to obtain reliable results for theslope of the temperature rise versus logarithm of time. For eachtemperature, between 40 and 80 individual data points were taken atdifferent pressures.Before starting the thermal conductivity measurements with the
R365mfc mixtures, the accuracy of the apparatus was checked bymeasuring the thermal conductivity of carbon dioxide at two tempera-tures. The values obtained are in excellent agreement (relativedifference of �0.03%) with the IUPAC recommended reference values[12]. The uncertainty at the level of 95% confidence of the experimentaldata, including the extrapolation of the data to atmospheric pressure, isestimated to be within �3%.
THERMAL CONDUCTIVITY MODELING
Two methods were used to calculate the thermal conductivity of themixtures measured in this work: the Wassiljewa [13] mixing rulesmodified by Mason and Saxena [14,15] and the Extended CorrespondingStates Theory [7,16]. The gas mixture thermal conductivity, �m, usingthe Wassiljewa mixing rules can be calculated using Equation (2),
�m ¼Xni¼1
yi�iPnj¼1 yjAij
ð2Þ
where n is the number of components of the mixture, �i is the thermalconductivity of pure component i, yi and yj are mole fractions of i and j,respectively. The Wassiljewa function, Aij, can be calculated as proposedby Mason and Saxena in Equation (3),
where M is the molecular weight, " is an adjustable parameter nearunity and �tr is the monatomic value of the thermal conductivity. Theratio of translational thermal conductivities, �tri/�trj, was calculated asproposed by Roy and Thodos [15],
�tri�trj
¼�j exp 0:0464Trið Þ � exp �0:2412Trið Þ½
�i exp 0:0464Trj
� �� exp �0:2412Trj
� �� � ð4Þ
where Tr is the reduced temperature and � is given by Equation (5).
� ¼ 210TcM
3
P4c
1=6
ð5Þ
The thermal conductivity was also predicted using the ExtendedCorresponding States Theory according to the formalism of Ely andHanley [7], where the thermal conductivity is considered to be asummation of two terms: one arising from the transfer of energy duetranslational effects, �trans, and the other due to the internal degrees offreedom, �int. Thus,
� �,Tð Þ ¼ �trans �,Tð Þ þ �int Tð Þ ð6Þ
The contribution to �trans is expressed as a sum of a low-densitycontribution, �, and a density-dependent contribution, �þ,
�trans �,Tð Þ ¼ � Tð Þ þ �þ �,Tð Þ ð7Þ
The exact equations to calculate these contributions have been derivedbefore [7,16]. It was observed that the density-dependent translationalcontribution, �þ �,Tð Þ, is almost negligible for the thermal conductivity oflow pressure gases (below few tenths of a percent), and the shape factorscould be set to unity. The term �int Tð Þ has the dominating role in thethermal conductivity value of low-pressure gases. It is usually calculatedusing the modified Eucken correction for polyatomic gases [19]
�int ¼fint�
MCpid �
5R
2
ð8Þ
where �is the dilute-gas viscosity, which can be estimated from kinetictheory, Cpid the constant pressure ideal gas heat capacity, R the
universal gas constant and fint a proportionality factor. In this work,Cpid was calculated using Joback’s group-contribution method [15]. Inthe original Eucken correlation, fint is constant and equal to 1� 10�3
when R and Cpid are in Jmol�1 K�1, � is in mPa s, M is in gmol�1 and �is in Wm�1K�1. Huber et al. [16] used the value 1.32� 10�3. In thiswork, the thermal conductivity was calculated using the relationshipsuggested by Chapman and Cowling [20]
fint ¼M�D
�ð9Þ
where D is the self-diffusion coefficient calculated by the Lee and Thodoscorrelation [21].
RESULTS
For three different mixtures, Mixture A, 93.0% R365mfcþ 7.0%R134a (kg/kg), Mixture B, 27.0% R365mfcþ 73.0% R134a (kg/kg) andMixture C, 62.8% R365mfcþ 37.2% Cyclopentane (kg/kg), the vapor-phase thermal conductivity was measured for different pressures atconstant temperature. The experimental results are listed in Tables 1–3.In Figures 1–3, the pressure dependence of the thermal conductivity foreach mixture in the working temperature range is presented. The usualbehavior of gas thermal conductivity with pressure [15] is sometimesnot observed. Instead, the thermal conductivity decreases with risingpressure. A possible explanation for this fact is a formation of an electriclayer on the surface of the naked platinum wire due to the polarcharacteristics of the working fluids. These kind of fluids can solvatecations in the measuring cell, and with an increase of pressure, moremolecules are engaged in the solvation process, meaning that lessmolecules are available for the energy transfer, and consequently thegas thermal conductivity decreases. The phenomenon increases with theincreasing temperature. For example, in Figure 2, Mixture B, 27.0% ofR365mfc with 73.0% of R134a (kg/kg), shows the increase of this effectwith temperature.The pressure dependence of the experimental results can be
represented by a linear function
� ¼ a 1ð ÞPþ a 0ð Þ ð6Þ
where P is the pressure in MPa and � is in mWm�1K�1, as presented inthe Tables 4–6, where a(1) and a(0) are the coefficients of the linear
Table 1. Vapor-phase thermal conductivity of mixture A, 93.0% of R365mfcþ 7.0% of R134a (kg/kg), from 327.54 to 388.65 K;data points at 0.1013 MPa are extrapolated values.
T¼ 327.54 K T¼339.08 K T¼ 354.59 K T¼369.28 K T¼ 388.65 K
equation. The values for atmospheric pressure were attained by anextrapolation of the experimental data at higher pressures. In the sametables, the temperature dependence of the thermal conductivity isrepresented by a linear function
� ¼ b 1ð ÞT þ b 0ð Þ ð7Þ
where T is the temperature in K, b(1) and b(0) are the coefficients. Ifexperimental data are available for four or more temperatures betweenthe melting temperature and 90% of the critical temperature, theDymond equation [11] can be used.
� ¼ A 1þ B 1� Trð Þ1=3
þC 1� Trð Þ2=3
þD 1� Trð Þ� �
ð8Þ
where Tr is the reduced temperature and A, B, C and D are adjustablecoefficients. As expected, the Dymond equation represents the experi-mental results better than the linear equation.Figures 4 and 5 show the experimental thermal conductivity at
0.1013MPa and the results of the thermal conductivity predicted withECST. The ECST was described in detail in an earlier paper [5]. InFigure 6, the thermal conductivity at 0.1013MPa of Mixtures A–C iscompared with the thermal conductivity of some pure blowing agents,
Table 3. Vapor-phase thermal conductivity of Mixture C, 62.8% of R365mfcþ 37.2% of cyclopentane (kg/kg), from 354.78 to415.67 K; data points at 0.1013 MPa are extrapolated values.
T¼ 354.78 K T¼370.53 K T¼384.37 K T¼ 397.27 K T¼ 415.67 K
similar thermal conductivity of the pure components in the investigatedtemperature range, in both systems the thermal conductivity goesthrough an extremum with rising content of R365mfc. While in thesystem R365mfcþ cyclopentane (Figure 8), the thermal conductivitygoes through a maximum with increasing content of R365mfc in themixture; it goes through a minimum in the system R365mfcþR134a
17
19
21
23
25
27
29
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Pressure/MPa
The
rmal
Con
duct
ivity
/mW
m-1
K-1
352.74 K368.40 K382.17 K394.99 K413.29 K
Figure 3. Pressure dependence of the thermal conductivity of 62.8% of R365mfc with
37.2% of cyclopentane (kg/kg) at temperatures between 352.74 and 413.29K.
Table 4. Pressure and temperature dependence of the gasthermal conductivity of mixture A, 93.0% of R365 mfc with 7.0%
(Figure 7). This latter behavior is similar to the behavior of the binarysystems argonþn-pentane and argonþ diethylether [22].The modified Wassiljewa mixing rules by Mason and Saxena and
ECST were applied to correlate and to predict the experimental resultsof these mixtures. In Table 7, the adjustable parameter, ", for themodified Wassiljewa mixing rules is presented. As can be seen fromFigures 7 and 8, the predictive ECST model shows a larger deviationfrom the experimental data, which is partly due to the fact that ECSTdoes not precisely predict the pure-component thermal conductivity. Forthe systems investigated, the thermal conductivity predicted with ECST
Table 6. Pressure and temperature dependence of thegas thermal conductivity of mixture C, 62.8% of R365mfc
does not go through a maximum or minimum with changing composi-tion of the mixture. Further work is needed in this field.
CONCLUSIONS
For mixtures of different composition of cyclopentane and R134awith R365mfc, the vapor-phase thermal conductivity was measuredusing the transient hot-wire method. Especially at higher temperatures,an unusual behavior of the vapor-phase thermal conductivity wasobserved that needs further investigation. Due to the similar thermal
13
15
17
19
21
23
310 320 330 340 350 360 370 380 390 400
Temperature / K
The
rmal
Con
duct
ivit
y /m
Wm
-1K
-1 Mixture AMixture BECST Mixture AECST Mixture B
Figure 4. Experimental thermal conductivity at 0.1013MPa compared with the ECST
results for mixture A, 93.0% of R365mfcþ7.0% of R134a (kg/kg) and for mixture B, 27.0%
of R365mfcþ73.0% of R134a (kg/kg).
15
17
19
21
23
25
27
350 360 370 380 390 400 410 420
Temperature / K
The
rmal
Con
duct
ivit
y /m
Wm-1
K-1
Mixture C
ECST Mixture C
Figure 5. Experimental thermal conductivity at 0.1013MPa compared with the ECSTresults for Mixture C, 62.8% of R365mfcþ 37.2% of cyclopentane (kg/kg).
conductivity of the pure components in the investigated temperaturerange, in both systems the thermal conductivity goes through anextremum with rising content of R365mfc.The experimental data could be well correlated by using the modified
Wassiljewa mixing rules by Mason and Saxena. Predictions using ECST
10
12
14
16
18
20
22
24
26
0 0,2 0,4 0,6 0,8 1mole fraction of R365mfc
The
rmal
Con
duct
ivity
/mW
m-1
K-1
T=318.15 K T=353.15 K T=393.15 KMW 318.15 K MW 353.15 K MW 393.15 KECST 318.15 K ECST 353.15 K ECST 393.15 K
Figure 7. Comparison of the experimental thermal conductivity for the mixture ofR365mfc with R134a at 0.1013MPa with the modified Wassiljewa mixing rules and ECST.
0
5
10
15
20
25
280 300 320 340 360 380 400 420
Temperature / K
The
rmal
Con
duct
ivit
y /m
Wm-1
K-1
carbon dioxide HCFC141bMixture A cyclopentaneMixture B CFC11Mixture C
Figure 6. Experimental thermal conductivity of mixtures A–C and of pure blowing agents
carbon dioxide, cyclopentane, HCFC141b, and CFC11 as a function of temperature at0.1013MPa.
lead to thermal conductivities that are in general lower than theexperimental data. For the systems investigated, the thermal conduc-tivities predicted with ECST do not go through a maximum or aminimum with changing composition of the mixture. Further researchwork is needed in this field.
NOMENCLATURE
Greek Symbols
�¼ thermal conductivity� ¼Euler’s constant�¼ density
7
9
11
13
15
17
19
21
23
25
27
0 0,2 0,4 0,6 0,8 1mole fraction of R365mfc
The
rmal
Con
duct
ivity
/mW
m-1
K-1
T=323 K T=363 K T=403 KMW 323 K MW 363 K MW 403 KECST 323 K ECST 363 K ECST 403 K
Figure 8. Comparison of the experimental thermal conductivity for the mixture of
R365mfc with cyclopentane at 0.1013MPa with the modified Wassiljewa mixing rules andECST.
Table 7. The adjustable parameters, ", of the Equation (4).
a¼ thermal diffusivityb¼ cell radiusC¼heat capacityC¼ constant, C¼ exp(�)P¼ total pressureq¼heat flow through the wirer¼ radius of the wireT¼ temperaturet¼ time
�T¼ temperature rise of the wire
Subscripts
0¼ designates the surface of the wireC¼ critical conditionsid¼ idealP¼ at constant pressurer¼ reduced value
ref¼ at reference conditions
ACKNOWLEDGMENTS
N. S. Oliveira thanks to Fundacao para a Ciencia e a Tecnologia thePhD scholarship (SFRH/BD/6690/2001).
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