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CORRELATIONS
A Correlation for the Prediction of Thermal Conductivity of Liquids
Dana M. Klaas and Dabir S. Viswanath*
Department of Chemical Engineering, University of MissourisColumbia, Columbia, Missouri 65211
Correlation and prediction of transport properties are important in the design of heat- and mass-
transfer equipment. Prediction of the thermal conductivity of liquids based only on theoretical
grounds does not give good results because the theories describing the liquid state are far from
satisfactory. In this paper, a semitheoretical method for the prediction of thermal conductivity
is proposed and the results are compared with the recent methods by Arikol and Gurbuz and
with the methods recommended by Reid et al.
Introduction
Thermal conductivity is an important property in the
prediction of heat- and mass-transfer coefficients under
both laminar and turbulent regimes. A number of
correlations have been developed to predict thermal
conductivity (Reid et al., 1987). Among them are the
recent correlations due to Baroncini et al. (1979),
Nagvekar (1984), and Arikol and Gurbuz (1992). Reid
et al. in the current edition of their book, The Properties
of Gases and Liquids, have included the Baroncini
method and have compared this method with the
methods of Sato and Reidel and of Missenard and
Riedel. However, many of these methods are restricted
to homologous series and require more than two or three
parameters. In addition, these parameters have not
been correlated with the readily available physical
properties. Not only does the correlation presented in
this paper have a theoretical basis but also the two
parameters are correlated with readily available physi-
cal properties.
Theory
Horrocks and McLaughlin (1960, 1963) considered the
energy transport occurring in a liquid as due to convec-
tive and vibrational contributions. The convective
transport occurs due to molecules “hopping” from oc-
cupied sites to holes in the liquid quasi-lattice. This
transfer is conditioned by both whether a molecule has
sufficient energy to move and whether there is a hole
close enough to accommodate it. Horrocks and McLaugh-
lin show that the convective contribution is negligible
and accounts for less than 5% of the thermal conductiv-
ity values for liquids. The vibrational effect is a function
of the distance between the nearest neighbors and the
difference in energy between layers of the quasi-lattice
due to a temperature gradient. Vibrating molecules
transfer energy whenever they collide. The higher the
temperature, the more the molecules will vibrate, send-
ing the energy and heat down the gradient. The
relation given by Horrocks and McLaughlin is
where p is the probability of energy transfer on collision,
v is the vibrational frequency, m is the number of
molecules per unit area, l is the distance between
adjacent planes, and Cv is the specific heat.
The 2 accounts for the fact that a molecule crosses a
plane perpendicular to its direction of motion twice in
every complete vibration. A limitation of the Horrocks
and McLaughlin theory is that the authors assumed p
to be unity as it is an extremely difficult task to evaluate
the probability of energy transfer on collision.
Equation 1, in turn, leads to the temperature depen-
dence of thermal conductivity as
where R, the coefficient of thermal expansion, controls
the temperature dependence. The Gruneisen constant,
(δ ln v/δ ln V)p, is independent of temperature.
Using the equation of state for a liquid in the form
PVl ) ZlRT and taking the changes with respect to
temperature gives
where P is the pressure, Vl is the liquid volume, Zl is
the liquid compressibility factor, T is the temperature,
and R is the gas constant.
The partial derivative of Z with respect to tempera-
ture is very small for a liquid. Viswanath and Rao
(1970) showed that combining eqs 2 and 3 yields
* Corresponding author. Telephone: (573) 884-0707. Fax:
(573) 884-4940. E-mail: viswanat@risc1.ecn.missouri.edu.
λ ) 2pvmlCv (1)
1
λ(dλ
dT)p
) -R〈1
3
- (δ ln(v)
d ln(V))p
〉 (2)
dVl
dT
)
R
P(Zl + T
dZl
dT) (3)
(λ
λ0
)) A(T
T0
)-b
(4)
2064 Ind. Eng. Chem. Res. 1998, 37, 2064-2068
S0888-5885(97)00683-0 CCC: $15.00 © 1998 American Chemical Society
Published on Web 04/01/1998
where λ0 is the value of thermal conductivity at T0 and
A and b are constants for a given substance.
The present method of estimating thermal conductiv-
ity is based on eq 4. The values of A and b were
determined using statistical software package Systat
and graphical analysis on Excel.
New Correlation of λ0. Physical and chemical
properties of a substance depend on the structure of the
molecules and attractive and repulsive force fields.
These factors along with the polar and nonpolar char-
acteristics of the molecules play an important role in
the behavior of the substances. In developing a cor-
relation for A and b in eq 4, these factors were
considered. Molar polarization was chosen as the
parameter to characterize the behavior of molecules.
Molar polarization is defined as (Viswanath and Prasad,
1974, 1981)
where Pmc is molar polarization, Rm is molar refraction
) (M/F)[(n2 - 1)/(n2 + 2)], µ is dipole moment in Debye
units, N is Avogadro’s number (6.023 × 1023 molecules/
mol), k is the Boltzmann constant, Tc is critical tem-
perature in K, n is the refractive index, M is molecular
weight in g/mol, and F is the density in g/cm3. The
advantages to using molar polarization are as follows:
(a) It has a sound theoretical basis as it is derived
from the Clausius-Mossotti (Debye, 1929) equation.
(b) It takes into consideration the structure of the
molecules in the molar refraction term.
(c) It accounts for the polar nature of the molecules
in the dipole moment, µ, term.
(d) It is temperature dependent.
(e) It contains parameters which can be determined
easily.
(f) It does not contain parameters such as critical
properties which are not easily determinable. Further,
if a compound decomposes on heating, it will be difficult
to determine the critical properties. No such thing is
encountered in this parameter.
(g) Dipole moments are available for more compounds
compared to other properties such as the critical proper-
ties.
(h) The value of molar polarization does not depend
on the technique used to evaluate it. For example,
different values of acentric factors are used by different
authors based on the vapor pressure-temperature data
used and the method of evaluating the slope at Tr )
0.7.
Present Correlation. Experimental thermal con-
ductivity values for a variety of substances at different
temperatures were gathered mainly from two sources,
Jamieson and Tudhope (1963) and Vargaftik (1975).
Jamieson and Tudhope compiled thermal conductivity
data from a number of sources and then analyzed and
ranked the data based on accuracy. Wherever possible,
the most accurate data as determined by Jamieson and
Tudhope were used in this work; however, the scatter
of the values is apparent as shown in Figure 1 for
n-decane. The scatter in the “best” experimental data
is close to (5-10%. The data tabulated by Vargaftik,
on the other hand, appear to be smoothed-out, as is also
shown in Figure 1. Vargaftik’s alkane data were used
to develop the new correlation. The data were plotted
using the lowest temperature and the corresponding
Table 1. Summary of Results with Parameters A and B Obtained from Figure 2
alkanes alkenes alcohols aromatic halogen misc. glycols nitrogen total
no. of substances 21 3 13 8 10 13 3 2 73
no. of data points 284 20 93 53 51 66 34 10 611
no. of occurrences
error range (%) alkanes alkenes alcohols aromatic halogen misc. glycols nitrogen total
<1 73 10 15 9 13 8 2 1 131
1-3 147 7 37 26 25 23 9 5 279
3-5 38 2 22 6 6 18 4 3 99
5-10 25 1 15 7 6 12 10 1 77
10-20 1 0 4 5 1 4 8 0 23
20-40 0 0 0 0 0 0 1 0 1
>40 0 0 0 0 0 1 0 0 1
Pmc ) Rm + 4πNµ2
/9kTc (5)
Figure 1. Temperature vs thermal conductivity for a typical
substance (n-decane).
Figure 2. Correlation for A and b vs Pmc.
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 2065
thermal conductivity data as T0 and λ0, respectively, and
the values for A and b were evaluated for individual
substances. These A and b values for different sub-
stances were then plotted against molar polarization,
as shown in Figure 2. The trendline equations derived
from this plot were then used to calculate thermal
conductivity of the substances at various temperatures
using eq 4. As can be seen, the correlation of A and b
with molar polarization is weak, but the correlation was
developed using only alkane data. It is likely that the
Table 2. Comparison of the New Method with the Arikol and Gurbuz Methoda
new method Arikol and Gurbuz
substance T range (K) AAD (%) MAD (%) AAD (%) MAD (%)
methane 99.2-112.2 2.7 7.2 6.4 11.8
propane 213.2-223.2 0.2 0.3 4.6 5.5
n-pentane 273.2-303.2 1.7 9.5 2.7 11.4
isopentane 273.2-293.2 0.3 0.5 3.2 4.5
n-hexane 273.2-333.2 2.8 9.3 4.9 8.4
n-heptane 273.2-353.2 1.7 7.4 6.2 14.1
n-octane 233.2-393.2 2.1 4.9 5.6 8.0
isooctane 290.0-370.0 2.7 6.5 8.1 9.6
n-nonane 233.2-413.2 3.0 8.8 3.6 8.8
n-decane 253.2-433.2 2.0 6.2 4.0 8.0
n-undecane 253.2-453.2 2.3 6.1 3.8 7.7
n-dodecane 273.2-473.2 3.2 9.5 8.7 10.7
n-tridecane 273.2-501.2 2.3 5.7 4.3 5.6
n-tetradecane 293.2-513.2 2.0 7.9 11.4 12.7
n-pentadecane 293.2-533.2 2.1 11.6 6.4 7.6
n-hexadecane 303.2-553.2 2.3 8.5 4.7 5.9
n-heptadecane 303.2-573.2 2.3 8.4 4.6 5.9
n-octadecane 305.2-573.2 2.5 9.1 8.9 11.2
n-nonadecane 313.2-593.2 2.0 7.7 5.9 7.1
n-eicosane 313.2-613.2 1.6 3.6 13.2 13.8
a AAD ) average absolute deviation (%). MAD ) maximum absolute deviation (%).
Table 3. Comparison between Calculated and Experimental Values of Liquid Thermal Conductivity (Taken from Reid
et al., Table 10-7)
percent errorb
compound T, K λL,a exptl Latini et al. Sato and Riedel Missenard and Riedel new method
propane 323 0.0783 -19 27 18 36.1
n-pentane 293 0.114 -5.7 20 17 1.3
303 0.111 -5.9 20 17 1.7
n-decane 314 0.127 -3.2 -2.0 9.5 0.2
349 0.119 -2.9 -1.8 9.8 -0.4
cyclohexane 293 0.124 -1.2 11 3.7 -2.1
methylcyclopentane 293 0.121 -3.2 13 3.8 0.3
311 0.115 -2.2 14 4.7 1.4
benzene 293 0.148 0 -3.4 -5.1 -7.0
323 0.137 1.9 -2.1 -4.0 -6.0
389 0.114 5.1 0 -1.8 -0.3
ethylbenzene 293 0.132 2.0 2.2 4.4 0.0
353 0.118 2.9 3.2 5.3 -1.2
ethanol 293 0.165 -3.3 15 24 2.7
313 0.152 0 19 28 6.7
347 0.135 3.5 22 32 12.2
n-octanol 293 0.166 -11 -19 5.6 -3.3
tert-butyl alcohol 311 0.116 4.5 26 77 10.3
m-cresol 293 0.150 10 -3.6 28 2.1
353 0.145 3.8 -8.6 21 -6.6
aniline 290 0.178 -15 10 -5.1
propionic acid 285 0.173 -8.9 -3.4 15 -4.4
methylene chloride 253 0.159 -17 -13 -6.3 2.0
293 0.148 -19 -15 -7.9 -0.6
carbon tetrachloride 253 0.110 -6.4 -0.8 15 0.2
293 0.103 -7.3 -1.6 14 -3.1
ethyl bromide 293 0.103 2.0 7.7 -6.9 0.5
chlorobenzene 233 0.141 -0.5 0.0 2.6 5.0
353 0.111 2.4 4.1 7.1 1.3
iodobenzene 253 0.106 -15 -0.4 5.1 7.5
353 0.0938 -17 -0.9 4.5 -2.5
ethyl acetate 293 0.147 2.9 -7.1 3.1 1.0
333 0.141 2.4 -12 -2.7 -3.2
butyl acetate 293 0.137 2.5 -4.9 9.2 1.4
acetone 273 0.171 -9.8 -2.2 3.7 2.8
313 0.151 -6.9 0.5 6.6 6.7
diethyl ether 293 0.129 3.9 4.5 22 5.6
acetaldehyde 293 0.190 -12 -11 -0.2
a All values of λL are in W/(m‚K). b Percent error ) [(calcd - exptl)/exptl] × 100.
2066 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998
values of A and b will differ slightly depending on the
homologous series used.
The present correlation gives good results for the
temperature range between the normal melting point
and the normal boiling point of a substance. Beyond
this region the pressure contribution would be greater
and would likely have to be factored into the correlation.
Results and Discussion
Table 1 contains a summary of the results. The
analysis shows that over 83% of the 611 data points
tested have a deviation less than 5%, with the average
deviation being approximately 2%. Since the correlation
was developed using only the alkane data, it gives
excellent results for broad types of C-H compounds
including alkanes, alkenes, aromatic hydrocarbons, and
cyclic hydrocarbons, whereas the predicted thermal
conductivities of C-OH compounds such as alcohols
show slightly higher errors. This could, in part, be due
to the occurrence of hydrogen bonding. The data set
also includes other hydrogen-bonding substances, highly
polar compounds, and halogen-substituted compounds
besides a variety of aromatics and alcohols.
The results from this new correlation were compared
to the values calculated using the Arikol and Gurbuz
method (1992). This method was chosen in part because
it is a recent correlation and in part because the authors
report fairly good results. As can be seen in Table 2, in
most cases the average and maximum deviations are
lower for the new correlation compared to the results
calculated using the Arikol and Gurbuz method. Over-
all, the two methods show similar results. However,
the correlation of Arikol and Gurbuz is based on
homologous series and, in addition, it has more adjust-
able parameters.
Table 3 shows a comparison of the present method
with the correlations of Latini et al., Sato and Riedel,
and Missenard and Riedel. These methods were com-
pared by Reid et al. (1987), in their monograph The
Properties of Gases and Liquids, as acceptable correla-
tions to predict the thermal conductivity of liquids. The
results in Table 3 show that the new method gives
better results except for propane at 323 K. This
temperature is above the boiling point of propane, and
prediction methods should be restricted to temperatures
at or below the boiling point unless satisfactory pressure
corrections are developed particularly for low-boiling
substances. The present method has other advantages.
As pointed out by Reid et al., the predicted data for
certain compounds, such as cresols, depend on whether
they are treated as aromatics or alcohols. The present
correlation does not depend on this type of judgment
as the input data for a particular substance is unique
and the method, at present, does not depend on the
homologous series. Another advantage is that several
methods depend on parameters such as critical proper-
ties, boiling point, and acentric factor, and these proper-
ties do not show appreciable differences for isomers. On
the other hand, molar polarization changes appreciably
among isomers as both molecular structure and dipole
moment are involved in its evaluation. This allows for
better characterization of the substances involved in the
correlation and hence more accurate prediction of
thermal conductivity data. The present correlation has
not taken advantage of the temperature function in the
definition of molar polarization. This will be incorpo-
rated in future work, and the results will be published
at a later date. As molar polarization is characteristic
of the structure of the molecules, a study of different
transport properties of liquids and liquid mixtures using
this parameter would increase the understanding of the
equilibrium and nonequilibrium operative in liquids and
liquid mixtures.
Figure 2 shows that the value of b is fairly constant
at approximately 2/3 and that A increases slightly but
is approximately unity. These values for A and b were
used in the correlation with good results (see Table 4).
This means that the thermal conductivity of a substance
can be found at various temperatures just by knowing
the thermal conductivity at a reference temperature.
This makes predicting thermal conductivity especially
easy.
In conclusion, the proposed correlation for thermal
conductivity not only has a strong theoretical basis but
also predicts thermal conductivity values with better
accuracy. The method will be tested more exhaustively
and applied to liquid mixtures.
Literature Cited
Arikol, M.; Gurbuz, H. A New Method for Predicting Thermal
Conductivity of Pure Organic Liquids and Their Mixtures. Can.
J. Chem. Eng. 1992, 70, 1157.
Baroncini, C.; Di Filippo, P.; Latini, G.; Pacetti, M. Thermal
Conductivity of Liquids: Comparison of predicted values with
experimental results at different temperatures. High Temp.-
High Pressures 1979, 11, 581.
Debye, P. Polar Molecules; The Chemical Catalog Co., Inc.: New
York, 1929.
Horrocks, J. K.; McLaughlin, E. Thermal Conductivity of Simple
Molecules in the Condensed State. Trans. Faraday Soc. 1960,
56, 206.
Horrocks, J. K.; McLaughlin, E. Temperature Dependence of the
Thermal Conductivity of Liquids. Trans. Faraday Soc. 1963,
59, 1709.
Table 4. Summary of Results with Constants A ) 1.0 and b ) 2/3
alkanes alkenes alcohols aromatic halogen misc. glycols nitrogen total
no. of substances 21 3 13 8 10 13 3 2 73
no. of data points 284 20 93 53 51 66 34 10 611
no. of occurrences
error range (%) alkanes alkenes alcohols aromatic halogen misc. glycols nitrogen total
<1 73 11 22 18 18 24 6 3 175
1-3 75 7 20 11 16 18 4 1 152
3-5 86 1 20 11 8 10 4 1 141
5-10 49 1 29 8 9 10 8 5 119
10-20 1 0 2 5 0 2 8 0 18
20-40 0 0 0 0 0 1 4 0 5
>40 0 0 0 0 0 1 0 0 1
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 2067
Jamieson, D. T.; Tudhope, J. S. A Simple Device for Measuring
the Thermal Conductivity of Liquids with Moderate Accuracy;
NEL Report No. 81; National Engineering Laboratory: East
Kilbride, Glasgow, U.K., 1963.
Miller, J.; Joseph, W.; McGinley, J. J.; Yaws, C. L. Thermal
Conductivity of Liquids. Chem. Eng. 1976, 133.
Nagvekar, M. A Group Contribution Method for Liquid Thermal
Conductivity. M.S. Thesis, The Pennsylvania State University,
State College, PA, 1984.
Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of
Gases and Liquids, 4th ed.; McGraw-Hill Book Co.: New York,
1987.
Vargaftik, N. B. Tables on Thermophysical Properties of Gases and
Liquids; Hemisphere Publishing Co.: Washington, DC, 1975.
Viswanath, D. S.; Rao, M. B. Thermal conductivity of liquids and
its temperature dependence. J. Phys. D: Appl. Phys. 1970, 1444.
Viswanath, D. S.; Prasad, D. H. Generalized Thermodynamic
Properties of Real Fluids Using Molar Polarization at the
Critical Temperature as the Third Parameter; Department of
Chemical Engineering, Indian Institute of Science: Bangalore,
India, 1974.
Viswanath, D. S.; Prasad, D. H. A New Three Parameter Law of
Corresponding States. Presented at the AIChE National Meet-
ing, Houston, TX, 1981.
Received for review September 22, 1997
Revised manuscript received January 29, 1998
Accepted February 17, 1998
IE9706830
2068 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998

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A correlation for the prediction of thermal conductivity of liquids

  • 1. CORRELATIONS A Correlation for the Prediction of Thermal Conductivity of Liquids Dana M. Klaas and Dabir S. Viswanath* Department of Chemical Engineering, University of MissourisColumbia, Columbia, Missouri 65211 Correlation and prediction of transport properties are important in the design of heat- and mass- transfer equipment. Prediction of the thermal conductivity of liquids based only on theoretical grounds does not give good results because the theories describing the liquid state are far from satisfactory. In this paper, a semitheoretical method for the prediction of thermal conductivity is proposed and the results are compared with the recent methods by Arikol and Gurbuz and with the methods recommended by Reid et al. Introduction Thermal conductivity is an important property in the prediction of heat- and mass-transfer coefficients under both laminar and turbulent regimes. A number of correlations have been developed to predict thermal conductivity (Reid et al., 1987). Among them are the recent correlations due to Baroncini et al. (1979), Nagvekar (1984), and Arikol and Gurbuz (1992). Reid et al. in the current edition of their book, The Properties of Gases and Liquids, have included the Baroncini method and have compared this method with the methods of Sato and Reidel and of Missenard and Riedel. However, many of these methods are restricted to homologous series and require more than two or three parameters. In addition, these parameters have not been correlated with the readily available physical properties. Not only does the correlation presented in this paper have a theoretical basis but also the two parameters are correlated with readily available physi- cal properties. Theory Horrocks and McLaughlin (1960, 1963) considered the energy transport occurring in a liquid as due to convec- tive and vibrational contributions. The convective transport occurs due to molecules “hopping” from oc- cupied sites to holes in the liquid quasi-lattice. This transfer is conditioned by both whether a molecule has sufficient energy to move and whether there is a hole close enough to accommodate it. Horrocks and McLaugh- lin show that the convective contribution is negligible and accounts for less than 5% of the thermal conductiv- ity values for liquids. The vibrational effect is a function of the distance between the nearest neighbors and the difference in energy between layers of the quasi-lattice due to a temperature gradient. Vibrating molecules transfer energy whenever they collide. The higher the temperature, the more the molecules will vibrate, send- ing the energy and heat down the gradient. The relation given by Horrocks and McLaughlin is where p is the probability of energy transfer on collision, v is the vibrational frequency, m is the number of molecules per unit area, l is the distance between adjacent planes, and Cv is the specific heat. The 2 accounts for the fact that a molecule crosses a plane perpendicular to its direction of motion twice in every complete vibration. A limitation of the Horrocks and McLaughlin theory is that the authors assumed p to be unity as it is an extremely difficult task to evaluate the probability of energy transfer on collision. Equation 1, in turn, leads to the temperature depen- dence of thermal conductivity as where R, the coefficient of thermal expansion, controls the temperature dependence. The Gruneisen constant, (δ ln v/δ ln V)p, is independent of temperature. Using the equation of state for a liquid in the form PVl ) ZlRT and taking the changes with respect to temperature gives where P is the pressure, Vl is the liquid volume, Zl is the liquid compressibility factor, T is the temperature, and R is the gas constant. The partial derivative of Z with respect to tempera- ture is very small for a liquid. Viswanath and Rao (1970) showed that combining eqs 2 and 3 yields * Corresponding author. Telephone: (573) 884-0707. Fax: (573) 884-4940. E-mail: viswanat@risc1.ecn.missouri.edu. λ ) 2pvmlCv (1) 1 λ(dλ dT)p ) -R〈1 3 - (δ ln(v) d ln(V))p 〉 (2) dVl dT ) R P(Zl + T dZl dT) (3) (λ λ0 )) A(T T0 )-b (4) 2064 Ind. Eng. Chem. Res. 1998, 37, 2064-2068 S0888-5885(97)00683-0 CCC: $15.00 © 1998 American Chemical Society Published on Web 04/01/1998
  • 2. where λ0 is the value of thermal conductivity at T0 and A and b are constants for a given substance. The present method of estimating thermal conductiv- ity is based on eq 4. The values of A and b were determined using statistical software package Systat and graphical analysis on Excel. New Correlation of λ0. Physical and chemical properties of a substance depend on the structure of the molecules and attractive and repulsive force fields. These factors along with the polar and nonpolar char- acteristics of the molecules play an important role in the behavior of the substances. In developing a cor- relation for A and b in eq 4, these factors were considered. Molar polarization was chosen as the parameter to characterize the behavior of molecules. Molar polarization is defined as (Viswanath and Prasad, 1974, 1981) where Pmc is molar polarization, Rm is molar refraction ) (M/F)[(n2 - 1)/(n2 + 2)], µ is dipole moment in Debye units, N is Avogadro’s number (6.023 × 1023 molecules/ mol), k is the Boltzmann constant, Tc is critical tem- perature in K, n is the refractive index, M is molecular weight in g/mol, and F is the density in g/cm3. The advantages to using molar polarization are as follows: (a) It has a sound theoretical basis as it is derived from the Clausius-Mossotti (Debye, 1929) equation. (b) It takes into consideration the structure of the molecules in the molar refraction term. (c) It accounts for the polar nature of the molecules in the dipole moment, µ, term. (d) It is temperature dependent. (e) It contains parameters which can be determined easily. (f) It does not contain parameters such as critical properties which are not easily determinable. Further, if a compound decomposes on heating, it will be difficult to determine the critical properties. No such thing is encountered in this parameter. (g) Dipole moments are available for more compounds compared to other properties such as the critical proper- ties. (h) The value of molar polarization does not depend on the technique used to evaluate it. For example, different values of acentric factors are used by different authors based on the vapor pressure-temperature data used and the method of evaluating the slope at Tr ) 0.7. Present Correlation. Experimental thermal con- ductivity values for a variety of substances at different temperatures were gathered mainly from two sources, Jamieson and Tudhope (1963) and Vargaftik (1975). Jamieson and Tudhope compiled thermal conductivity data from a number of sources and then analyzed and ranked the data based on accuracy. Wherever possible, the most accurate data as determined by Jamieson and Tudhope were used in this work; however, the scatter of the values is apparent as shown in Figure 1 for n-decane. The scatter in the “best” experimental data is close to (5-10%. The data tabulated by Vargaftik, on the other hand, appear to be smoothed-out, as is also shown in Figure 1. Vargaftik’s alkane data were used to develop the new correlation. The data were plotted using the lowest temperature and the corresponding Table 1. Summary of Results with Parameters A and B Obtained from Figure 2 alkanes alkenes alcohols aromatic halogen misc. glycols nitrogen total no. of substances 21 3 13 8 10 13 3 2 73 no. of data points 284 20 93 53 51 66 34 10 611 no. of occurrences error range (%) alkanes alkenes alcohols aromatic halogen misc. glycols nitrogen total <1 73 10 15 9 13 8 2 1 131 1-3 147 7 37 26 25 23 9 5 279 3-5 38 2 22 6 6 18 4 3 99 5-10 25 1 15 7 6 12 10 1 77 10-20 1 0 4 5 1 4 8 0 23 20-40 0 0 0 0 0 0 1 0 1 >40 0 0 0 0 0 1 0 0 1 Pmc ) Rm + 4πNµ2 /9kTc (5) Figure 1. Temperature vs thermal conductivity for a typical substance (n-decane). Figure 2. Correlation for A and b vs Pmc. Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 2065
  • 3. thermal conductivity data as T0 and λ0, respectively, and the values for A and b were evaluated for individual substances. These A and b values for different sub- stances were then plotted against molar polarization, as shown in Figure 2. The trendline equations derived from this plot were then used to calculate thermal conductivity of the substances at various temperatures using eq 4. As can be seen, the correlation of A and b with molar polarization is weak, but the correlation was developed using only alkane data. It is likely that the Table 2. Comparison of the New Method with the Arikol and Gurbuz Methoda new method Arikol and Gurbuz substance T range (K) AAD (%) MAD (%) AAD (%) MAD (%) methane 99.2-112.2 2.7 7.2 6.4 11.8 propane 213.2-223.2 0.2 0.3 4.6 5.5 n-pentane 273.2-303.2 1.7 9.5 2.7 11.4 isopentane 273.2-293.2 0.3 0.5 3.2 4.5 n-hexane 273.2-333.2 2.8 9.3 4.9 8.4 n-heptane 273.2-353.2 1.7 7.4 6.2 14.1 n-octane 233.2-393.2 2.1 4.9 5.6 8.0 isooctane 290.0-370.0 2.7 6.5 8.1 9.6 n-nonane 233.2-413.2 3.0 8.8 3.6 8.8 n-decane 253.2-433.2 2.0 6.2 4.0 8.0 n-undecane 253.2-453.2 2.3 6.1 3.8 7.7 n-dodecane 273.2-473.2 3.2 9.5 8.7 10.7 n-tridecane 273.2-501.2 2.3 5.7 4.3 5.6 n-tetradecane 293.2-513.2 2.0 7.9 11.4 12.7 n-pentadecane 293.2-533.2 2.1 11.6 6.4 7.6 n-hexadecane 303.2-553.2 2.3 8.5 4.7 5.9 n-heptadecane 303.2-573.2 2.3 8.4 4.6 5.9 n-octadecane 305.2-573.2 2.5 9.1 8.9 11.2 n-nonadecane 313.2-593.2 2.0 7.7 5.9 7.1 n-eicosane 313.2-613.2 1.6 3.6 13.2 13.8 a AAD ) average absolute deviation (%). MAD ) maximum absolute deviation (%). Table 3. Comparison between Calculated and Experimental Values of Liquid Thermal Conductivity (Taken from Reid et al., Table 10-7) percent errorb compound T, K λL,a exptl Latini et al. Sato and Riedel Missenard and Riedel new method propane 323 0.0783 -19 27 18 36.1 n-pentane 293 0.114 -5.7 20 17 1.3 303 0.111 -5.9 20 17 1.7 n-decane 314 0.127 -3.2 -2.0 9.5 0.2 349 0.119 -2.9 -1.8 9.8 -0.4 cyclohexane 293 0.124 -1.2 11 3.7 -2.1 methylcyclopentane 293 0.121 -3.2 13 3.8 0.3 311 0.115 -2.2 14 4.7 1.4 benzene 293 0.148 0 -3.4 -5.1 -7.0 323 0.137 1.9 -2.1 -4.0 -6.0 389 0.114 5.1 0 -1.8 -0.3 ethylbenzene 293 0.132 2.0 2.2 4.4 0.0 353 0.118 2.9 3.2 5.3 -1.2 ethanol 293 0.165 -3.3 15 24 2.7 313 0.152 0 19 28 6.7 347 0.135 3.5 22 32 12.2 n-octanol 293 0.166 -11 -19 5.6 -3.3 tert-butyl alcohol 311 0.116 4.5 26 77 10.3 m-cresol 293 0.150 10 -3.6 28 2.1 353 0.145 3.8 -8.6 21 -6.6 aniline 290 0.178 -15 10 -5.1 propionic acid 285 0.173 -8.9 -3.4 15 -4.4 methylene chloride 253 0.159 -17 -13 -6.3 2.0 293 0.148 -19 -15 -7.9 -0.6 carbon tetrachloride 253 0.110 -6.4 -0.8 15 0.2 293 0.103 -7.3 -1.6 14 -3.1 ethyl bromide 293 0.103 2.0 7.7 -6.9 0.5 chlorobenzene 233 0.141 -0.5 0.0 2.6 5.0 353 0.111 2.4 4.1 7.1 1.3 iodobenzene 253 0.106 -15 -0.4 5.1 7.5 353 0.0938 -17 -0.9 4.5 -2.5 ethyl acetate 293 0.147 2.9 -7.1 3.1 1.0 333 0.141 2.4 -12 -2.7 -3.2 butyl acetate 293 0.137 2.5 -4.9 9.2 1.4 acetone 273 0.171 -9.8 -2.2 3.7 2.8 313 0.151 -6.9 0.5 6.6 6.7 diethyl ether 293 0.129 3.9 4.5 22 5.6 acetaldehyde 293 0.190 -12 -11 -0.2 a All values of λL are in W/(m‚K). b Percent error ) [(calcd - exptl)/exptl] × 100. 2066 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998
  • 4. values of A and b will differ slightly depending on the homologous series used. The present correlation gives good results for the temperature range between the normal melting point and the normal boiling point of a substance. Beyond this region the pressure contribution would be greater and would likely have to be factored into the correlation. Results and Discussion Table 1 contains a summary of the results. The analysis shows that over 83% of the 611 data points tested have a deviation less than 5%, with the average deviation being approximately 2%. Since the correlation was developed using only the alkane data, it gives excellent results for broad types of C-H compounds including alkanes, alkenes, aromatic hydrocarbons, and cyclic hydrocarbons, whereas the predicted thermal conductivities of C-OH compounds such as alcohols show slightly higher errors. This could, in part, be due to the occurrence of hydrogen bonding. The data set also includes other hydrogen-bonding substances, highly polar compounds, and halogen-substituted compounds besides a variety of aromatics and alcohols. The results from this new correlation were compared to the values calculated using the Arikol and Gurbuz method (1992). This method was chosen in part because it is a recent correlation and in part because the authors report fairly good results. As can be seen in Table 2, in most cases the average and maximum deviations are lower for the new correlation compared to the results calculated using the Arikol and Gurbuz method. Over- all, the two methods show similar results. However, the correlation of Arikol and Gurbuz is based on homologous series and, in addition, it has more adjust- able parameters. Table 3 shows a comparison of the present method with the correlations of Latini et al., Sato and Riedel, and Missenard and Riedel. These methods were com- pared by Reid et al. (1987), in their monograph The Properties of Gases and Liquids, as acceptable correla- tions to predict the thermal conductivity of liquids. The results in Table 3 show that the new method gives better results except for propane at 323 K. This temperature is above the boiling point of propane, and prediction methods should be restricted to temperatures at or below the boiling point unless satisfactory pressure corrections are developed particularly for low-boiling substances. The present method has other advantages. As pointed out by Reid et al., the predicted data for certain compounds, such as cresols, depend on whether they are treated as aromatics or alcohols. The present correlation does not depend on this type of judgment as the input data for a particular substance is unique and the method, at present, does not depend on the homologous series. Another advantage is that several methods depend on parameters such as critical proper- ties, boiling point, and acentric factor, and these proper- ties do not show appreciable differences for isomers. On the other hand, molar polarization changes appreciably among isomers as both molecular structure and dipole moment are involved in its evaluation. This allows for better characterization of the substances involved in the correlation and hence more accurate prediction of thermal conductivity data. The present correlation has not taken advantage of the temperature function in the definition of molar polarization. This will be incorpo- rated in future work, and the results will be published at a later date. As molar polarization is characteristic of the structure of the molecules, a study of different transport properties of liquids and liquid mixtures using this parameter would increase the understanding of the equilibrium and nonequilibrium operative in liquids and liquid mixtures. Figure 2 shows that the value of b is fairly constant at approximately 2/3 and that A increases slightly but is approximately unity. These values for A and b were used in the correlation with good results (see Table 4). This means that the thermal conductivity of a substance can be found at various temperatures just by knowing the thermal conductivity at a reference temperature. This makes predicting thermal conductivity especially easy. In conclusion, the proposed correlation for thermal conductivity not only has a strong theoretical basis but also predicts thermal conductivity values with better accuracy. The method will be tested more exhaustively and applied to liquid mixtures. Literature Cited Arikol, M.; Gurbuz, H. A New Method for Predicting Thermal Conductivity of Pure Organic Liquids and Their Mixtures. Can. J. Chem. Eng. 1992, 70, 1157. Baroncini, C.; Di Filippo, P.; Latini, G.; Pacetti, M. Thermal Conductivity of Liquids: Comparison of predicted values with experimental results at different temperatures. High Temp.- High Pressures 1979, 11, 581. Debye, P. Polar Molecules; The Chemical Catalog Co., Inc.: New York, 1929. Horrocks, J. K.; McLaughlin, E. Thermal Conductivity of Simple Molecules in the Condensed State. Trans. Faraday Soc. 1960, 56, 206. Horrocks, J. K.; McLaughlin, E. Temperature Dependence of the Thermal Conductivity of Liquids. Trans. Faraday Soc. 1963, 59, 1709. Table 4. Summary of Results with Constants A ) 1.0 and b ) 2/3 alkanes alkenes alcohols aromatic halogen misc. glycols nitrogen total no. of substances 21 3 13 8 10 13 3 2 73 no. of data points 284 20 93 53 51 66 34 10 611 no. of occurrences error range (%) alkanes alkenes alcohols aromatic halogen misc. glycols nitrogen total <1 73 11 22 18 18 24 6 3 175 1-3 75 7 20 11 16 18 4 1 152 3-5 86 1 20 11 8 10 4 1 141 5-10 49 1 29 8 9 10 8 5 119 10-20 1 0 2 5 0 2 8 0 18 20-40 0 0 0 0 0 1 4 0 5 >40 0 0 0 0 0 1 0 0 1 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 2067
  • 5. Jamieson, D. T.; Tudhope, J. S. A Simple Device for Measuring the Thermal Conductivity of Liquids with Moderate Accuracy; NEL Report No. 81; National Engineering Laboratory: East Kilbride, Glasgow, U.K., 1963. Miller, J.; Joseph, W.; McGinley, J. J.; Yaws, C. L. Thermal Conductivity of Liquids. Chem. Eng. 1976, 133. Nagvekar, M. A Group Contribution Method for Liquid Thermal Conductivity. M.S. Thesis, The Pennsylvania State University, State College, PA, 1984. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill Book Co.: New York, 1987. Vargaftik, N. B. Tables on Thermophysical Properties of Gases and Liquids; Hemisphere Publishing Co.: Washington, DC, 1975. Viswanath, D. S.; Rao, M. B. Thermal conductivity of liquids and its temperature dependence. J. Phys. D: Appl. Phys. 1970, 1444. Viswanath, D. S.; Prasad, D. H. Generalized Thermodynamic Properties of Real Fluids Using Molar Polarization at the Critical Temperature as the Third Parameter; Department of Chemical Engineering, Indian Institute of Science: Bangalore, India, 1974. Viswanath, D. S.; Prasad, D. H. A New Three Parameter Law of Corresponding States. Presented at the AIChE National Meet- ing, Houston, TX, 1981. Received for review September 22, 1997 Revised manuscript received January 29, 1998 Accepted February 17, 1998 IE9706830 2068 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998