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 Authors : MensahBrown, H., Sinayobye, E., Affo W, Yaya, A
 Paper ID : IJERTV2IS3618
 Volume & Issue : Volume 02, Issue 03 (March 2013)
 Published (First Online): 26032013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Thermal Conductivity of Liquid Toluene at Two Isotherms – 308.15 K and 320.15 K, and Pressures up to 300 MPa
1*MensahBrown, H., 1Sinayobye, E., 2Affo W, 3Yaya, A
1Department of Food Process Engineering, University of Ghana, Legon, Ghana
2Department of Chemistry, University of Ghana, Legon, Ghana
3Department of Materials Science and Engineering, University of Ghana, Legon, Ghana
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Abstract
The paper contains the results of measurements of the thermal conductivity of toluene in the liquid phase at two isotherms 308.15 K and 320.15 K and at pressures up to 300 MPa. The measurements were carried out with a transient hotwire instrument and have an accuracy of Â± 0.3%. The pressure dependency of the thermal conductivity of toluene has been investigated and a correlation has been developed. Also the representation of the thermal conductivity of pure liquids based on the hardsphere theory of transport in liquids has been explored for toluene and the density dependency of the thermal conductivity has been given. It is shown that all of the experimental data may be represented to within Â± 2% by a predictive procedure based on the hardsphere theory of liquids.
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Keywords: Thermal conductivity, toluene, rigid hardsphere, transient hotwire instrument.
Introduction
Despite the fact that there has been a number of significant advances in the measurement and prediction of the thermal conductivity of liquids and liquid mixtures [13], the search for standard reference fluids for thermophysical properties (including thermal conductivity, and viscosity) still continues. Most of these advances have been limited to hydrocarbons and their mixtures [4, 6, 7]. Toluene is one hydrocarbon that has been recommended as a standard reference liquid for thermal conductivity by the Commission on Physicochemical Measurements and Standards of the Physical Chemistry Division of the International Union of Pure and Applied Chemistry (IUPAC) [5]. Most of the accurate experimental thermal conductivity data have been obtained with the transient hotwire apparatus (THW) [1, 712]. The purpose of the present study is to use the THW method to obtain accurate experimental data for the thermal conductivity of toluene which can serve to firstly test accurate operation of the transient hotwire apparatus used and secondly to test the applicability of the hardsphere theory to thermal conductivity as a transport property [6, 1823].
experiment, and C=1.781 a numerical constant. A precision of 0.5 mK is secured in the temperature rise measurements and the configuration of the instrument is such that convective and radiative heat transfer are completely eliminated so that it is possible to secure an accuracy of 0.3% in the thermal conductivity data.
Toluene supplied by Fluka Chemicals Ltd with a purity in excess of 99.8% was degassed several times under vacuum. The thermal conductivity cells were filled by firstly evacuating them and subsequently introducing the liquid sample under pressure by the method described earlier [1]. The working equations for the analysis of the experimental data have been given elsewhere [3] and they are employed unchanged in this work.
The density and isobaric heat capacity values of pure toluene were required in order to make a number of small corrections during the analysis of the experimental data. For pure toluene, the density was obtained by employing the Taittype equation proposed by Kashiwagi et al. [13]
+ 1
Experiments
= 1 +
(2)
The measurements were carried out in a transient hotwire instrument for the measurement of the thermal conductivity of electrically insulating liquids described in detail elsewhere [8, 11, 12]. For the present work the cells of the instrument were equipped with platinum wires of 7 Âµm nominal diameter (purity 99.9%) supplied by Sigmund Cohn Corporation in a fashion described earlier [1]. An automatic Wheatstone bridge described elsewhere is employed to obtain the time evolution of temperature of the platinum wires during the application of a constant heat flux q Wm1 to the transient hotwire instrument. [11].
The essence of the method involves the determination of the time evolution of the temperature rise, Tid, of a thin (7 Âµm) platinum wire immersed in the fluid over a period of one second following initiation of a constant heat flux, q, in the wire at time t = 0. The thermal conductivity, , of the fluid is derived from the basic working equation (1) of the transient hot wire apparatus [811].
where Po=0.1 MPa, C=9.143×102. D and o are represented as functions of temperature by:
= 440.47 1.6047 + 1.5391032 (3)
and
= 1103.06 0.68074 4.2291042 (4)
where D is in MPa, o is in kgm3 and T in K. and the uncertainty in the density is estimated to be Â± 0.1%. The heat capacity of the liquid required to apply small corrections in the analysis of the experimental data which, in the present case, contributes no more than Â±1% to the measured temperature rise was obtained from the compilation of Vargaftik [14]. . As a result, even quite large errors in the heat capacity have a negligible effect upon the reported thermal conductivity.
Results
Pressure Dependence of the Thermal Conductivity
Owing to the modifications to the transient hot
Tid
=
4
ln 4
2
2
(1)
wire apparatus employed for the present measurements, it was appropriate to verify the correct
in which k=/Cp is the thermal diffusivity of the fluid, Cp is the heat capacity of the liquid, is density of the liquid, is the radius of the heated wire, t is the time elapsed from the beginning of the
operation of the instrument in accordance with the theory. Table I lists the present results for the thermal conductivity of pure toluene along two isotherms
308.15 K and 320.15 K. In each case, the experimental results have been corrected to nominal
temperatures by application of small linear temperature corrections that never exceeded Â±0.2%.
AAD , X
1 N X i X i, fit
It is estimated that the thermal conductivity listed has an accuracy of Â±0.5% and a slightly better precision
N i1
X i , (7)
of Â±0.3%.
For the purpose of comparison, the experimental data were represented by correlating equations of the form
where Xi is an experimental datum, Xi,fit is calculated from the correlation applied at the same state point, and N is the total number of points. The maximum absolute relative deviation (MAD,X) and the relative bias (Bias X) were calculated using eq. (8) and (9) respectively:
(x,T , P) (x,T ) b P*i
(5)
X i X i, fit
X
X
1 i i
Max
where
i0
MAD, X
i , (8)
P* (P P) / P
(6)
N ( X X )
1 i i, fit
and P=150 MPa is a scaling parameter and is
Bias, X
N i1 Xi
, (9)
approximately the average pressure along an isotherm. The values of the coefficients bi were determined by a nonlinear optimization technique described elsewhere [15, 16] thatminimized the average relative deviation defined for the thermal conductivity (property X) by eq. (7):
The values of the coefficients bi, the scaling parameter and the statistical parameters of the thermal conductivity for toluene are included in Table II. Figure 1 contains a comparison of the present experimental results and those Nieto de Castro et al. [17] for toluene with those of the correlating equation. The deviation plot has a maximum deviation of Â±0.3% which is consistent
Table I. Thermal Conductivity of Toluene
Thermal conductivity
Temperature, T 
Pressure, P 
Density, r 
(Tnom, r) 
(Tnom, P) 
(K) 
(MPa) 
(kg/m3) 
(mW.m1.K1) 
(mW.m1.K1) 
307.13 
0.1 
Tnom = 308.15 K 854.17 
130.5 
130.1 
307.19 
14.8 
865.6 
134.6 
134.3 
307.24 
43.1 
884.7 
142.3 
142.0 
307.27 
43.3 
884.8 
142.4 
142.2 
307.04 
76.7 
903.7 
150.3 
150.1 
307.07 
100.4 
915.3 
156.1 
156.0 
307.55 
102.0 
915.7 
156.8 
156.7 
307.35 
150.4 
936.2 
166.4 
166.3 
307.63 
207.4 
956.2 
175.2 
175.2 
308.69 
211.4 
956.9 
176.2 
176.3 
307.72 
239.1 
966.1 
180.0 
180.0 
307.50 
239.3 
966.3 
179.7 
179.6 
307.51 
274.0 
976.3 
183.5 
183.5 
307.84 
275.2 
977.0 
185.5 
185.4 
307.59 
305.5 
984.8 
190.3 
190.3 
320.24 
0.1 
Tnom = 320.15 K 841.7 
126.3 
126.2 
320.46 
25.1 
861.9 
133.7 
133.8 
320.46 
65.4 
887.9 
145.5 
145.6 
320.43 
65.1 
887.7 
145.6 
145.7 
320.71 
108.0 
909.7 
155.3 
155.5 
320.78 
108.1 
909.7 
155.2 
155.4 
320.85 
135.1 
921.6 
160.9 
161.1 
320.85 
135.1 
921.6 
161.0 
161.2 
321.02 
171.7 
936.0 
168.2 
168.5 
321.10 
220.2 
952.8 
176.9 
177.2 
320.86 
254.4 
963.5 
182.2 
182.4 
320.06 
286.1 
973.1 
186.5 
186.5 
320.96 
286.1 
972.6 
186.5 
186.7 
320.06 
305.5 
978.4 
189.2 
189.2 
320.07 
305.5 
978.4 
189.5 
Table II. Coefficients for the representation of the Thermal Conductivity of Toluene as a function of pressure according to Eq. (5)
T (K) 
' (mW.m1.K1 
P' (MPa) 
102b1 
102b2 
102b3 
102b4 
308.15 
166.323 
150 
1.6237 
6.4183 
1.484 
2.4849 
320.15 
164.280 
150 
1.7934 
3.4680 
1.0615 
0.7428 
Statistical Parameters: 
102AAD 
102MAD 
102Bias 

This work 
0.0 
0.3 
0.0 

Nieto de Castro, et al. [17] 
0.3 
2.4 
0.3 
with the estimated precision of the experimental results. However, the experimental data of Nieto de Castro et al [17] gave a maximum deviation of 2.4% from those of the present correlation equation. Figure
2 shows the thermal conductivity of toluene as afunction of pressure at two isotherms 308.15 K and 320.15 K.
3%
2%
Deviation, /
Deviation, /
1%
0%
1%
2%
3%
0 100 200 300
p/MPa
Figure 1. Deviations of experimental thermal conductivity data of toluene from the correlation of Eq. (5). This work: 308.15 K, 320.15 K; Nieto de Castro, et al. [17]: 308.15 K, 320.15 K.
corresponding relation between experimental transport coefficients (subscript exp) of rough non spherical was assumed by Assael, et al. [1923] and for thermal conductivity we have:
= (10)
where R is the roughness factor and accounts for the effects of nonspherical molecular shape. Assael, Dymond and their collaborators in a series of papers [1923] have investigated the manner in which the model of a hardsphere fluid can be used as a basis of procedure to represent the experimental data for the transport properties of polyatomic liquids and their mixtures.
The systems they considered in their investigations included normal alkanes and their mixtures as well as pure aromatic hydrocarbons, organic and inorganic molecules. The success of the proposed scheme of Assael et al. [1923] is noteworthy and it is worthwhile to examine the extent to which the present experimental data for toluene, as a standard reference liquid for thermal conductivity can be represented by the established scheme. For the purpose of establishing the extent to
which the present system conforms to the scheme of Assael et al. [1923], we employ a reduced thermal conductivity, *, which is given in terms of experimental quantities as,
M 1 2 V 2 3
exp
exp
200 * 1.936 107 exp
(11)
RT R
/(mW/(m.K))
/(mW/(m.K))
180
160
here exp is the measured thermal conductivity of the fluid with a molar mass M, a molar volume, V at a temperature T. As a result of the modifications of the rough hardsphere theory of dense fluids, the thermal
conductivity may be represented as:
V
V
140 * R * V
o
(12)
120
0 100 200 300
p/MPa
Figure 2. Thermal conductivity of toluene as a function of pressure. 308.15 K, 320.15 K
Density Dependence of Thermal Conductivity
Chandler [18] in his work demonstrated the transport coefficients of rouh hard sphere molecules can be directly related to the smooth hardsphere (subscript shs) transport coefficients. Thus a
[1620], wherein R is a roughness factor for the thermal conductivity which is temperature and density independent, while *(V/Vo) is a function only of the ratio of the molar volume, V, to the characteristic molar volume Vo, which, for a particular fluid, depends only on temperature. Values of R and Vo(T) for the system determined using areference function *(V/Vo) and a wellestablished
curve fitting procedure described elsewhere [8,15].
Prediction Scheme
In order to examine the ability of the general scheme of Dymond, Assael and their collaborators
[1923] to predict the present experimental data, wehave employed representation of * given by
4
their proposed universal as a reference function. It is
i
Conclusions
New accurate experimental data for the thermal conductivity of toluene have been obtained over a
log* R a 1
(13)
wide range of pressures up to 300 MPa and at two
exp
where,
Vr V
i0
V
V
u o
i Vr
(14)
isotherms (308.15 K and 320.15 K) using the transient hotwire method. The pressure dependence of the thermal conductivity of toluene has successfully been represented by a correlation with an estimated accuracy of less than Â±1%. The predictive procedure developed based on the rigid
and the superscript u indicates the use of the
universal function of Eq. (13) in the definition of Vo. The coefficients ai are given in the work of Assael et al. [1923]. For pure toluene studied here the values of R and Vo have been determined by means of the superimposition of the experimental values of * for the pure liquid at each temperature upon the universal function given by Eq. (13).
Figure 3 shows a plot of the deviations of the experimental data from those predicted by the predictive scheme developed by Assael et al [23]. The results have a maximum deviation of Â±2% which is consistent with the claims of Assael et al. [1923] that their procedure has an accuracy of Â±6% for the estimation of the thermal conductivity of pure liquids and their mixtures. Thus, their procedure can be employed to predict the thermal conductivity of toluene over a relatively wide range of thermodynamic states with the same level of confidence. Furthermore the density dependency of the reduced thermal conductivity of the toluene can be represented by a single function *(V/Vo).
3%
2%
Deviation, /
Deviation, /
1%
0%
1%
2%
3%
2.20 2.40 2.60 2.80 3.00
Reduced Volume, V/Vo
Figure 3. Deviations of experimental thermal conductivity data of toluene from their representation by means of the predictive scheme of Assael et al. [23], Eq. (13). 308.15 K, 320.15 K.
sphere theory, is able to generate values with an uncertainty of Â±2% which are less than Â±6% claimed for the procedure by Assael et al. [1923].
At a higher level of precision, however, the present experimental data confirm the universality of the density dependence of the reduced thermal conductivity of liquids. It is important to note that one of the major attributes of the hardsphere theory, which isolates the temperature dependence of the thermal conductivity within a hardcore volume, is still valid.
Acknowledgements
The authors are extremely grateful for the contributions of Mr. M. Dix of Department of Chemical Engineering & Chemical Technology, Imperial College, London; particularly for the maintenance of our experimental installation. The input and guidance of Prof. Sir W.A. Wakeham of Imperial College, London, is highly acknowledged.
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