Reference Correlation of the Thermal Conductivity of Cyclohexane from the Triple Point to 640 K and up to 175 MPa

Abstract

New, wide-range reference equations for the thermal conductivity of cyclohexane as a function of temperature and density are presented. The equations are based in part upon a body of experimental data that has been critically assessed for internal consistency and for agreement with theory whenever possible. We estimate the uncertainty (at the 95% confidence level) for the thermal conductivity of cyclohexane from the triple point (279.86 K) to 650 K at pressures up to 175 MPa to be 4% for the compressed liquid and supercritical phases. For the low–pressure gas phase (up to 0.1 MPa) over the temperature range 280 K to 680 K, the estimated uncertainty is 2.5%. Uncertainties in the critical region are much larger, since the thermal conductivity approaches infinity at the critical point and is very sensitive to small changes in density.

1. Introduction

In a series of recent papers, new reference correlations for the thermal conductivity of many fluids (normal and parahydrogen,¹ water,² sulfur hexafluoride,³ toluene,⁴ benzene,⁵ n-hexane,⁶ n-heptane,⁷ methanol,⁸ ethanol,⁹ ortho-xylene, meta-xylene, para-xylene and ethylbenzene,¹⁰ cyclopentane, iso-pentane and n-pentane,¹¹ carbon dioxide,¹² and ethene and propene¹³), covering a wide range of conditions of temperature and pressure, were reported. In this paper, the work is extended to the thermal conductivity of cyclohexane.

The goal of this work is to critically assess the available literature data, and provide wide-ranging correlations for the thermal conductivity of cyclohexane that are valid over gas, liquid, and supercritical states, and incorporate densities provided by the equation of state of Zhou et al..¹⁴

2. Methodology

The thermal conductivity λ is expressed as the sum of three independent contributions, as

$$\lambda (\rho ,T)={\lambda }_{\mathrm{o}}(T)+\mathrm{\Delta }\lambda (\rho ,T)+\mathrm{\Delta }{\lambda }_{\mathrm{c}}(\rho ,T),$$ (1)

where ρ is the density, T is the temperature, and the first term, λ_ο(T) = λ(0, T), is the contribution to the thermal conductivity in the dilute-gas limit, where only two-body molecular interactions occur. The final term, Δλ_c(ρ, T), the critical enhancement, arises from the long-range density fluctuations that occur in a fluid near its critical point, which contribute to divergence of the thermal conductivity at the critical point. Finally, the term Δλ(ρ, T), the residual property, represents the contribution of all other effects to the thermal conductivity of the fluid at elevated densities.

The identification of these three separate contributions to the thermal conductivity and to transport properties in general is useful because it is possible, to some extent, to treat both λ_ο(T) and Δλ_c(ρ, T) theoretically. In addition, it is possible to derive information about λ_ο(T) from experiment. In contrast, there is almost no theoretical guidance concerning the residual contribution, Δλ(ρ, T); its evaluation is based entirely on experimentally obtained data.

The analysis described above should be applied to the best available experimental data for the thermal conductivity. Thus, a prerequisite to the analysis is a critical assessment of the experimental data. For this purpose, two categories of experimental data are defined: primary data employed in the development of the correlation, and secondary data used simply for comparison purposes. According to the recommendation adopted by the Subcommittee on Transport Properties (now known as The International Association for Transport Properties) of the International Union of Pure and Applied Chemistry, the primary data are identified by a well-established set of criteria.¹⁵ These criteria have been successfully employed to establish standard reference values for the viscosity and thermal conductivity of fluids over wide ranges of conditions, with uncertainties in the range of 1%. However, in many cases, such a narrow definition unacceptably limits the range of the data representation. Consequently, within the primary data set, it is also necessary to include results that extend over a wide range of conditions, albeit with a poorer accuracy, provided they are consistent with other more accurate data or with theory. In all cases, the accuracy claimed for the final recommended data must reflect the estimated uncertainty in the primary information.

3. The Correlation

Table 1 summarizes, to the best of our knowledge, the experimental measurements^16–38 of the thermal conductivity of cyclohexane reported in the literature. From the 23 sets shown in the table, 9 were considered as primary data.

TABLE 1.

Thermal-conductivity measurements of cyclohexane

1st author	Year Publ.	Technique employeda	Purity (%)	Uncertainty (%)	No. of data	Temperature range (K)	Pressure range (MPa)
Primary Data
Watanabe16	2004	THW	99.8	0.4	12	281–319	0.1
Tanaka17	1988	THW	99.5	1	45	284–374	0.1–175
Li18	1984	THW	99.5	0.3	48	309–361	5–145
Kashiwagi19	1982	THW	99.0	2	4	303–333	0.1
Grigoriev20	1981	CC	na	1.5	70	298–455	0.1–146
Naziev21	1974	CC	na	1.6	141	293–633	0.1–50
Vines22	1954	HW	na	1	7	373–435	0.1
Vines23	1953	HW	na	0.3	17	348–383	0.0–0.1
Lambert24	1950	HW	na	1	17	339–358	0.0–0.04
Secondary Data
Voss25	1989	THW	na	2	24	326–450	0.4–10
Rowley26	1988	THW	na	1.0	1	313	0.1
Shakhverdiev27	1980	CC	na	na	40	293–493	0.1–40
Nefedov28	1979	HF	na	1.5	50	290–618	2–30
Andersson29	1978	THW	99.5	3	15	305–339	0.1–75
Mogilevskii30	1970	THW	99.9	na	4	282–298	0.1
Filippov31	1968	CC	na	1.9	4	283–313	0.1
Barnette32	1967	PP	na	1.5	1	298	0.1
Mukhamedzyanov33	1964	HW	na	na	9	303–349	0.1
Horrocks34	1963	THW	na	na	5	295–345	0.1
Briggs35	1957	CC	na	3	5	293–333	0.1
Sakiadis36	1957	PP	99	1	8	309–348	0.1
Riedel37	1948	CC	na	1.0	1	293	0.1
Moser38	1913	HW	na	na	1	375	0.1

^aCC, coaxial cylinder; HF, hot filament; HW, hot wire; na, not available; PP, parallel plate; THW, transient hot wire.

The measurements of Li et al.,¹⁸ extending to high pressures, were obtained in an absolute transient hot-wire instrument with an uncertainty of 0.3%. Measurements performed by this group (of W.A. Wakeham of Imperial College London) have already been successfully employed in many thermal conductivity reference correlations,^{2, 4–6, 10–13} and are part of the primary dataset. The transient hot-wire technique was also employed by Watanabe and Kato,¹⁶ Tanaka et al.,¹⁷ and Kashiwagi et al.¹⁹ with corresponding uncertainties of 0.5, 1, and 2% respectively. Measurements from these three groups have already been successfully employed in previous correlations as primary data (Watanabe and Kato,¹⁶ in Refs. ^{4, 6, 7, 10, 11}, Tanaka et al.¹⁷ in Refs. ^{6, 7} and Kashiwagi et al.¹⁹ in Refs. ^{4–7, 10}).

Naziev et al.²¹ and Grigoriev and Ishkanov²⁰ employed concentric-cylinder instruments to measure the thermal conductivity with 1.6 and 1.5% uncertainty, respectively. The measurements of Naziev et al.²¹ have successfully been employed in previous reference correlations,^{6, 7, 9–11, 13} and therefore here are also considered as primary data. The measurements of Grigoriev and Ishkanov²⁰ were included in the primary data set as they extend to higher pressures (50 MPa) and higher temperatures (633 K).

Finally, the low-pressure vapor phase measurements of Vines,²³ Vines and Bennett²² and Lambert et al.²⁴ performed in hot-wire instruments with 0.3, 1, and 1% uncertainty, respectively, were also included in the primary data set. Measurements from both groups have previously successfully been employed in other thermal-conductivity reference correlations (Vines²³ and Vines and Bennett²² in Refs. ^{2, 8, 11} and Lambert et al.²⁴ in Refs. ^{6–8, 11, 13}). The remaining sets were considered as secondary data.

Figures 1 and 2 show the range of the primary measurements outlined in Table 1, and the saturation curve may be seen in Fig. 2. Temperatures for all data were converted to the ITS–90 temperature scale.³⁹ The development of the correlation requires accurate values for the density; Zhou et al.¹⁴ have reviewed the thermodynamic properties of cyclohexane and developed an accurate, wide–ranging equation of state. For the density, the estimated uncertainty of the new equation of state is less than 0.1% (liquid and vapor) up to 500 K, and 0.2% above 500 K, with higher uncertainties within the critical region. Between 283 and 473 K with pressures lower than 30 MPa, the uncertainty is as low as 0.03% in density in the liquid phase. We also adopt their values for the critical temperature, T_c, the critical density, ρ_c, and the triple–point temperature as 553.6 K, 271.33 kg m⁻³, and 279.86 K, respectively. Finally, the isobaric ideal–gas heat capacity was also obtained from the same source.

FIGURE 1.

Temperature–pressure range of the primary experimental thermal conductivity data for cyclohexane.

FIGURE 2.

Temperature–density range of the primary experimental thermal conductivity data for cyclohexane. (– –) saturation curve.

3.1. The dilute-gas limit

In order to be able to extrapolate the temperature range of the measurements, a theoretically-based scheme was preferred in order to correlate the dilute-gas limit thermal conductivity, λ_ο(T), over a wide temperature range. The traditional kinetic approach for thermal conductivity results in an expression involving three generalized cross sections.^{40, 41} However, it is possible to derive an equivalent kinetic theory expression for thermal conductivity by making use of the approach of Thijsse et al.⁴² and Millat et al.,⁴³ where one considers expansion in terms of total energy, rather than separating translational from internal energy as is done traditionally. In this case, the dilute-gas limit thermal conductivity, λ_ο(T) (mW m⁻¹ K⁻¹), of a polyatomic gas can be shown to be inversely proportional to a single generalized cross section,^40–43 S(10E) (nm²), as

$${\lambda }_{\mathrm{o}}(T)=1000\frac{5k_{\mathrm{B}}^2(1+r^2)T}{2m{\langle \nu \rangle }_{\mathrm{o}}S(10E)}{f}_{\lambda },$$ (2)

where k_B is the Boltzmann constant (1.380 648 52×10⁻²³ J K⁻¹), T (K) is the absolute temperature, f_λ (−) is the dimensionless higher-order correction factor, m (kg) is the molecular mass of cyclohexane [(0.084 159 48 / 6.022 140 857×10²³) kg], and ${\langle \nu \rangle }_{\mathrm{o}}=4\sqrt{k_{\mathrm{B}}T/\pi m}(\mathrm{m}/\mathrm{s})$ is the average relative thermal speed. The quantity r² is defined by $r^2=2C_{\text{int}}^{\mathrm{o}}/5k_{\mathrm{B}}$, where $C_{\text{int}}^{\mathrm{o}}$ is the contribution of both the rotational, $C_{\text{rot}}^{\mathrm{o}}$, and the vibrational, $C_{\text{vib}}^{\mathrm{o}}$, degrees of freedom to the isochoric ideal-gas heat capacity $C_v^{\mathrm{o}}$.

The recent classical trajectory calculations^44–46 confirm that for most molecules studied, the higher-order thermal-conductivity correction factor is near unity. One can take advantage of this finding to define the effective generalized cross section S_λ (= S(10E)/f_λ) (nm²), and rewrite Eq. (2) for the dilute-gas limit thermal conductivity of cyclohexane, λ_ο(T) (mW m⁻¹ K⁻¹), as

$${\lambda }_{\mathrm{o}}(T)=0.0608085\frac{(C_p^{\mathrm{o}}/k_{\mathrm{B}})\sqrt{T}}{S_{\lambda }}.$$ (3)

The ideal-gas isobaric heat capacity, $C_p^{\mathrm{o}}(=C_{int}^{\mathrm{o}}+2.5k_{\mathrm{B}})$ in (J/K), can be obtained from Zhou et al.¹⁴ as

$$\frac{C_p^{\mathrm{o}}}{k_{\mathrm{B}}}=4+\sum _{k=1}^4{v}_k{\left(\frac{u_k}{T}\right)}^2\frac{exp(u_{k}T)}{{\left[exp(u_{k}T)-1\right]}^2},$$ (4)

where the values of the coefficients ν_k and u_k are: ν₁ = 0.83775, ν₂ = 16.036, ν₃ = 24.636, ν₄ = 7.1715, u₁ = 773 K, u₂ = 941, u₃ = 2185 K, u₄ = 4495 K.

It has been previously noted,⁴³ and recently confirmed⁴¹ for smaller molecules, that the cross section S(10E) exhibits a nearly linear dependence on the inverse temperature. Hence, in order to develop the correlation, we have fitted the effective cross section S_λ (nm²), obtained from the low-pressure (< 0.1 MPa) vapor measurements of Naziev et al.,²¹ Vines and Bennett,²² Vines,²³ and Lambert et al.,²⁴ by means of Eq. (3), to a polynomial in inverse temperature, resulting in the following expression,

$$S_{\lambda }=0.378+255.27/T.$$ (5)

Equations (3)–(5) form a consistent set of equations for the calculation of the dilute-gas limit thermal conductivity of cyclohexane.

The values of the dilute–gas limit thermal conductivity, λ₀(T) in mW m⁻¹ K⁻¹, obtained by the scheme of Eqs. (3)–(5), were fitted as a function of the reduced temperature T_r = T / T_c for ease of use to the following equation:

$${\lambda }_0(T)=\frac{6.52149-39.8399T_{\mathrm{r}}+65.3275T_{\mathrm{r}}^2-202.857T_{\mathrm{r}}^3+78.7909T_{\mathrm{r}}^4}{-2.3043+1.83274T_{\mathrm{r}}-2.66787T_{\mathrm{r}}^2+T_{\mathrm{r}}^3}.$$ (6)

Values calculated by Eq. (6) do not deviate from the values calculated by the scheme of Eqs. (3)–(5) by more than 0.04% over the temperature range from 280 K to 680 K. Equation (6) is hence employed in the calculations that will follow.

The experimental dilute-limit thermal-conductivity values as well as the values calculated by Eq. (6) are shown in Fig. 3, while Fig. 4 presents the percentage deviations of the dilute-gas experimental data from the values calculated by Eq. (6). The selected data are represented within ±2.5%, which is commensurate with the uncertainty of the data. No obvious systematic trends are observed.

FIGURE 3.

Dilute-gas limit thermal-conductivity of cyclohexane as a function of temperature. Naziev et al.²¹ (◇), Vines and Bennett²² (●), Vines²³ (○), Lambert et al.²⁴ (▲), and Eq. (6) (––).

FIGURE 4.

Percentage deviations of the dilute-gas limit thermal-conductivity measurements of cyclohexane from the scheme of Eqs. (3)–(5) as a function of temperature. Naziev et al.²¹ (◇), Vines and Bennett²² (●), Vines²³ (○), Lambert et al.²⁴ (▲), and Eq. (6) (––). Note that on the scale of this figure Eq. (6) is almost indistinguishable from the zero line representing the full correlation.

Therefore, based on the aforementioned discussion, Eqs. (3)–(5) or Eq. (6) represent the dilute-gas limit thermal conductivity to within 2.5% at the 95% confidence level.

3.2. The residual thermal conductivity

The thermal conductivities of pure fluids exhibit an enhancement over a large range of densities and temperatures around the critical point and become infinite at the critical point. This behavior can be described by models that produce a smooth crossover from the singular behavior of the thermal conductivity asymptotically close to the critical point to the residual values far away from the critical point.^47–49 The density-dependent terms for thermal conductivity can be grouped according to Eq. (1) as [Δλ(ρ, T) + Δλ_c(ρ, T)]. To assess the critical enhancement theoretically, we need to evaluate, in addition to the dilute-gas thermal conductivity, the residual thermal-conductivity contribution. The procedure adopted during this analysis used ODRPACK (Ref. ⁵⁰) to fit all the primary data simultaneously to the residual thermal conductivity and the critical enhancement, while maintaining the values of the dilute-gas thermal-conductivity data already obtained. The density values employed were obtained by the equation of state of Zhou et al.¹⁴ The primary data were weighted in inverse proportion to the square of their uncertainty.

The residual thermal conductivity was represented with a polynomial in temperature and density:

$$\mathrm{\Delta }\lambda (\rho ,T)=\sum _{i=1}^5\left(B_{1,i}+B_{2,i}(T/T_{\mathrm{c}})\right){\left(\rho /{\rho }_{\mathrm{c}}\right)}^i.$$ (7)

Coefficients B_1,i and B_2,i are shown in Table 2.

TABLE 2.

Coefficients of Eq. (5) for the residual thermal conductivity of cyclohexane.

i	B1,i (mW m−1 K−1)	B2,i (mW m−1 K−1)
1	1.897 32×101	2.149 42×100
2	−6.278 89×101	3.154 82×101
3	1.007 48× 102	−6.290 82×101
4	−4.779 88×101	3.220 47×101
5	7.322 62×100	−4.878 01×100

3.3. The critical enhancement

The theoretically based crossover model proposed by Olchowy and Sengers^47–49 is complex and requires solution of a quartic system of equations in terms of complex variables. A simplified crossover model has also been proposed by Olchowy and Sengers.⁵¹ The critical enhancement of the thermal conductivity from this simplified model is given by

$$\mathrm{\Delta }{\lambda }_{\mathrm{c}}=\frac{\rho C_p{R}_{\mathrm{D}}{k}_{\mathrm{B}}T}{6\pi \overline{\eta }\xi }\left(\overline{\mathit{\Omega }}-{\overline{\mathit{\Omega }}}_0\right),$$ (8)

with

$$\overline{\mathit{\Omega }}=\frac{2}{\pi }\left[\left(\frac{C_p-C_v}{C_p}\right)arctan\left({\overline{q}}_{\mathrm{D}}\xi \right)+\frac{C_v}{C_p}{\overline{q}}_{\mathrm{D}}\xi \right]$$ (9)

and

$${\overline{\mathrm{\Omega }}}_0=\frac{2}{\pi }\left[1-exp\left(-\frac{1}{{({\overline{q}}_{\mathrm{D}}\xi )}^{-1}+{({\overline{q}}_{\mathrm{D}}\xi {\rho }_{\mathrm{c}}/\rho )}^2/3}\right)\right].$$ (10)

In Eqs. (8)–(10), k_B is Boltzmann’s constant, η̄ (Pa s) is the viscosity, and C_p and C_v (J kg⁻¹ K⁻¹) are the isobaric and isochoric specific heat obtained from the equation of state. The correlation length ξ (m) is given by

$$\xi ={\xi }_0{\left(\frac{p_{\mathrm{c}}\rho }{\mathrm{\Gamma }{\rho }_{\mathrm{c}}^2}\right)}^{\nu /\gamma }{\left[{\frac{\partial \rho (T,\rho )}{\partial p}|}_T-{\left(\frac{T_{\text{ref}}}{T}\right)\frac{\partial \rho (T_{\text{ref}},\rho )}{\partial p}|}_T\right]}^{\nu /\gamma }.$$ (11)

As already mentioned, the coefficients B_1,i and B_2,i in Eq. (7) were fitted with ODRPACK (Ref. ⁵⁰) to the primary data for the thermal conductivity of cyclohexane. This crossover model requires the universal amplitude, R_D = 1.02 (−), and the universal critical exponents, ν = 0.63 and γ =1.239, and the system–dependent amplitudes Γ and ξ₀. For this work, we adopted the values Γ = 0.058 (−), ξ₀ = 0.230×10⁻⁹ m, using the universal representation of the critical enhancement of the thermal conductivity by Perkins et al.⁵² In the particular case of cyclohexane, as there were very few measurements in the critical region, it was preferred to adopt for the effective cutoff wavelength ${\overline{q}}_{\mathrm{D}}^{-1}(\mathrm{m})$, the value of 6.68×10⁻¹⁰ m, proposed by the aforementioned scheme of Perkins et al.⁵²

The viscosity required for Eq. (8) was calculated with the correlation of Tariq et al.⁵³ The reference temperature T_ref, far above the critical temperature where the critical enhancement is negligible, was calculated by T_ref = (³/₂) T_c,⁵⁴ which for cyclohexane is 830.4 K.

Table 3 summarizes comparisons of the primary data with the correlation. We note that measurements of Naziev et al.²¹ over 650 kg/m³ were excluded, as they started to deviate from all the other measurements, and measurements of lower uncertainty exist in that region. We have defined the percentage deviation as PCTDEV = 100*(λ_exp–λ_fit)/λ_fit, where λ_exp is the experimental value of the thermal conductivity and λ_fit is the value calculated from the correlation. Thus, the average absolute percentage deviation (AAD) is found with the expression AAD = (Σ|PCTDEV|)/n, where the summation is over all n points, and the bias percent is found with the expression BIAS = (ΣPCTDEV)/n. We estimate the uncertainty (at the 95% confidence level) for the thermal conductivity in the liquid and supercritical phases from the triple point (279.86 K) to 680 K and up to 175 MPa, to be 4%. Uncertainties in the critical region are much larger, since the thermal conductivity approaches infinity at the critical point and is very sensitive to small changes in density.

TABLE 3.

Evaluation of the cyclohexane thermal-conductivity correlation for the primary data.

1st Author	Year Publ.	AAD (%)	BIAS (%)
Watanabe16	2004	0.21	−0.19
Tanaka17	1988	1.81	−1.39
Li18	1984	0.37	0.19
Kashiwagi19	1982	3.33	3.33
Grigoriev20	1981	1.43	−1.42
Naziev21	1974	2.06	0.45
Vines22	1954	2.02	−2.02
Vines23	1953	0.49	0.12
Lambert24	1950	1.70	1.70
Entire data set		1.41	−0.28

Figure 5 shows the percentage deviations of all primary thermal–conductivity data from the values calculated by Eqs. (1), (6)–(11), as a function of density. Figures 6 and 7 show the same deviations but as a function of temperature and pressure, respectively.

FIGURE 5.

Percentage deviations of primary experimental data of cyclohexane from the values calculated by the present model, Eqs. (1), (6)–(11), as a function of density. Watanabe and Kato¹⁶ (●), Tanaka et al.¹⁷ (■), Li et al.¹⁸ (□;), Kashiwagi et al.¹⁹ (◆), Grigoriev and Ishkanov²⁰ (◇), Naziev et al.²¹ (△), Vines and Bennett²² (⨉), Vines²³ ( ), Lambert et al.²⁴ (+).

FIGURE 6.

Percentage deviations of primary experimental data of cyclohexane from the values calculated by the present model, Eqs. (1), (6)–(11), as a function of temperature. Watanabe and Kato¹⁶ (●), Tanaka et al.¹⁷ (■), Li et al.¹⁸ (□), Kashiwagi et al.¹⁹ (◆), Grigoriev and Ishkanov²⁰ (◇), Naziev et al.²¹ (△), Vines and Bennett²² (⨉), Vines²³ ( ), Lambert et al.²⁴ (+).

FIGURE 7.

Percentage deviations of primary experimental data of cyclohexane from the values calculated by the present model, Eqs. (1), (6)–(11), as a function of pressure. Watanabe and Kato¹⁶ (●), Tanaka et al.¹⁷ (■), Li et al.¹⁸ (□), Kashiwagi et al.¹⁹ (◆), Grigoriev and Ishkanov²⁰ (◇), Naziev et al.²¹ (△), Vines and Bennett²² (⨉), Vines²³ ( ), Lambert et al.²⁴ (+).

Table 4 shows the average absolute percentage deviation (AAD) and the bias for the secondary data. Finally, Figs. 8 and 9 show plots of the thermal conductivity of cyclohexane as a function of the temperature for different pressures, and as a function of the density for different temperatures.

TABLE 4.

Evaluation of the cyclohexane thermal–conductivity correlation for the secondary data.

1st Author	Year Publ.	AAD (%)	BIAS (%)
Voss25	1989	7.19	−7.19
Rowley26	1988	0.36	0.36
Shakhverdiev27	1980	6.00	6.00
Nefedov28	1979	11.37	−11.35
Andersson29	1978	2.99	−2.82
Mogilevskii30	1970	1.69	1.69
Filippov31	1968	4.37	4.37
Barnette32	1967	2.83	2.83
Mukhamedzyanov33	1964	3.45	3.45
Horrocks34	1963	1.16	1.16
Briggs35	1957	6.52	6.52
Sakiadis36	1957	2.35	2.35
Riedel37	1948	4.04	4.04
Moser38	1913	8.66	−8.66

FIGURE 8.

Thermal conductivity of cyclohexane as a function of temperature for different pressures.

FIGURE 9.

Thermal conductivity of cyclohexane as a function of density for different temperatures.

3.1.4. Recommended Values

In Table 5, recommended values for the thermal conductivity of cyclohexane are shown. For checking computer implementations of the correlation, a point is provided for testing code with critical enhancement at 554.0 K and 350.0 kg m⁻³ (4.1718 MPa), where the thermal conductivity is 79.66 mW m⁻¹ K⁻¹; the dilute–gas thermal conductivity, λ_ο(554 K) = 43.09 mW m⁻¹ K⁻¹, the residual term Δλ(350 kg m⁻³, 554 K) = 22.03 mW m⁻¹ K⁻¹, and the critical enhancement term, Δλ_c(350.0 kg m⁻³, 554 K) = 14.54 mW m⁻¹ K⁻¹. The viscosity used in the calculation of the enhancement for this state point is 44.42 μPa s, obtained from the correlation of Tariq et al.⁵³

TABLE 5.

Recommended values of cyclohexane thermal conductivity (mW m⁻¹ K⁻¹)

Pressure (MPa)	Temperature (K)
	300	400	500	600	700
0	11.0	21.7	35.0	50.2	66.4
0.1	117.6	21.9	35.2	50.4	66.5
50		116.0	110.0	108.8	110.6
100		130.2	124.4	124.9	128.1
150		143.2	136.6	137.3	141.2

4. Conclusion

New, wide-ranging reference equations for the thermal conductivity of cyclohexane were presented. The equations are based in part upon a body of experimental data that has been critically assessed for internal consistency and for agreement with theory whenever possible. In the case of the dilute–gas thermal conductivity, a theoretically based correlation was adopted in order to guide extrapolation behavior. In the critical region, the enhancement of the thermal conductivity is well represented by a theoretically based model.⁵² The remaining contribution to the thermal conductivity was obtained by fitting critically-assessed data to an empirical equation that is a function of temperature and density.

We estimate the uncertainty (at the 95% confidence level) for the thermal conductivity from the triple point (279.86 K) to 650 K at pressures up to 175 MPa to be 4% for the compressed liquid and supercritical phases. For the low–pressure gas phase (up to 0.1 MPa) over the temperature range 280 K to 680 K, the estimated uncertainty is 2.5%. The equation of state of Zhou et al.¹⁴ is valid from the triple point (279.86 K) to 700 K at pressures up to 250 MPa. The correlation behaves in a physically reasonable manner and we feel it can be used over this entire range, although the uncertainty will be larger where there were no experimental data. Uncertainties in the critical region are much larger, since the thermal conductivity approaches infinity at the critical point and is very sensitive to small changes in density.