The thermal conductivity surface for mixtures of methane and ethane

A correlation is presented for the extensive series of thermal conductivity measurements of binary methane-ethane mixtures. The composition dependences of the thermal conductivity in the dilute-gas region, dense-gas and liquid region, and critical region are discussed. The average absolute percentage deviation of the thermal conductivity surface as a function of temperature, density, and composition, from the experimental data, is 1.60%.     

Thermal Conductivity of Carbon Dioxide–Methane Mixtures at Temperatures Between 300 and 425 K and at Pressures up to 12 MPa

The thermal conductivities of carbon dioxide and three mixtures of carbon dioxide and methane at six nominal temperatures between 300 and 425 K have been measured as a function of pressure up to 12 MPa. The measurements were made with a transient hot-wire apparatus. The relative uncertainty of the reported thermal conductivities at a 95% confidence level is estimated to be ±1.2%. Results of the low-density analysis of the obtained data were used to test expressions for predicting the thermal conductivity of nonpolar mixtures in a dilute-gas limit developed by Schreiber, Vesovic, and Wakeham. The scheme was found to underestimate the experimental thermal conductivity with deviations not exceeding 5%. The dependence of the thermal conductivity on density was used to test the predictive scheme for the thermal conductivity of gas mixtures under pressure suggested by Mason et al. and improved by Vesovic and Wakeham. Comparisons reveal a pronounced critical enhancement on isotherms at 300 and 325 K for mixtures with methane mole fractions of 0.25 and 0.50. For other states, comparisons of the experimental and predicted excess thermal conductivity contributions showed a smaller increase of the experimental data with deviations approaching 3% within the examined range of densities.     

Thermal Conductivity of Nitrogen-Methane Mixtures at Temperatures Between 300 and 425 K and at Pressures Up to 16 MPa

The thermal conductivities of nitrogen and three mixtures of nitrogen and methane at six nominal temperatures between 300 and 425 K have been measured as a function of pressure up to 16 MPa. The relative uncertainty of the thermal conductivity measurements at a 95% confidence level is estimated to be less then 1%. The data obtained and the results of the low-density analysis were used to test two prediction methods for the thermal conductivity of gas mixtures under pressure and for the thermal conductivity of dilute polyatomic gas mixtures. Reasonable agreement was found with expressions for predicting thermal conductivity of nonpolar mixtures in a dilute-gas limit developed by Schreiber et al. The scheme underestimates the experimental thermal conductivity with deviations not exceeding 3%. The prediction scheme for the thermal conductivity of gas mixtures under pressure suggested by Mason et al. and improved by Vesovic and Wakeham underestimates the experimental thermal conductivities throughout, likely due to its use of the Hirchsfelder–Eucken equation at the low-density limit.     

Contributions of the Van der Waals Laboratory to the Knowledge of Transport Properties of Fluids

After the presentation of Enskog's theory of the transport phenomena at high densities in 1922, one of the aims of the Van der Waals Laboratory was to check this theory with accurate experimental results. As early as 1931, Michels and Gibson published data on the viscosity of nitrogen taken by means of the Van der Waals vertical-capillary viscometer. In 1952, Michels and Botzen presented thermal-conductivity measurements on nitrogen taken by means of the parallel-plate heat-conductivity apparatus. Finally, in 1968 Trappeniers and Oosting presented data on the self-diffusion coefficient of methane obtained with a nuclear magnetic resonance spin-echo spectrometer. In all of these cases agreement with either the Enskog theory or the modified Enskog theory was not obtained. In 1973 Trappeniers and J. Michels showed that the self-diffusion coefficient of krypton obtained with a tracer method deviates from Enskog theory due to the formation of clusters. Measurements of the thermal conductivity of argon in 1955 motivated a study of transport phenomena of fluids in the critical region. This resulted, in 1962, in the first proof of the existence of a rather strong divergence in the thermal conductivity of carbon dioxide, by Michels, Sengers, and Van der Gulik. In 1978 Offringa showed that the viscosity has only a small critical anomaly, while Oosting showed as early as 1968 that, for selfdiffusion, such an anomaly could not be detected. In 1991 Mostert, and in 1996 Sakonidou, showed that the anomaly in the thermal conductivity is finite in mixtures near the vapor–liquid critical line. In the 1970s a vibrating-wire viscometer suited for measuring the viscosity near the melting line of simple gases was developed to check predictions by computer simulations of the viscosity of hard spheres. From the comparisons, it could be concluded that in the density range from the critical density up to twice this density, a special version of the hard-sphere Enskog theory describes the measurements within the experimental accuracy. With this result it was possible to describe the viscosity in the low-density range, up to the critical density, by a model of a gradual transition from intercluster transport described by the Chapman–Enskog theory to intracluster transport described by the hard-sphere Enskog theory, a model inspired by J. Michels' conclusion that the formation of clusters influences the transport properties.     

Determining Thermal Conductivity and Thermal Diffusivity of Low-Density Gases Using the Transient Short-Hot-Wire Method

The transient short-hot-wire method for measuring thermal conductivity and thermal diffusivity makes use of only one thermal-conductivity cell, and end effects are taken into account by numerical simulation. A search algorithm based on the Gauss–Newton nonlinear least-squares method is proposed to make the method applicable to high-diffusivity (i.e., low-density) gases. The procedure is tested using computer-generated data for hydrogen at atmospheric pressure and published experimental data for low-density argon gas. Convergence is excellent even for cases where the temperature rise versus the logarithm of time is far from linear. The determined values for thermal conductivity from experimental data are in good agreement with published values for argon, while the thermal diffusivity is about 10 % lower than the reference data. For the computer-generated data, the search algorithm can return both thermal conductivity and thermal diffusivity to within 0.02 % of the exact values. A one-dimensional version of the method may be used for analysis of low-density gas data produced by conventional transient hot-wire instruments.     

Prediction of the viscosity for molecular fluids from the dilute-gas properties via the inversion procedure for spherically symmetric pair potentials

A prediction scheme is presented for the viscosity and translation part of the thermal conductivity (frozen thermal conductivity) of molecular fluids via the application of the original inversion algorithm for spherically symmetric pair potentials. The latter allows us to invert the centrally symmetrical effective interaction potential for two types of dilute-gas properties- - the pressure second virial coefficient and the low-density gas viscosity. Such a potential is then used for the computation of fluid transport properties, Several weakly anisotropic molecular systems were considered (N₂O_COCO₂CH₄), Analysis of the results obtained reveals that the class of spherically symmetric potentials may still be used for the prediction of fluid transport coefficients from the dilute-gas equilibrium and kinetic characteristics.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

A High-Temperature Transient Hot-Wire Thermal Conductivity Apparatus for Fluids

A new apparatus for measuring both the thermal conductivity and thermal diffusivity of fluids at temperatures from 220 to 775 K at pressures to 70 MPa is described. The instrument is based on the step-power-forced transient hot-wire technique. Two hot wires are arranged in different arms of a Wheatstone bridge such that the response of the shorter compensating wire is subtracted from the response of the primary wire. Both hot wires are 12.7 µm diameter platinum wire and are simultaneously used as electrical heat sources and as resistance thermometers. A microcomputer controls bridge nulling, applies the power pulse, monitors the bridge response, and stores the results. Performance of the instrument was verified with measurements on liquid toluene as well as argon and nitrogen gas. In particular, new data for the thermal conductivity of liquid toluene near the saturation line, between 298 and 550 K, are presented. These new data can be used to illustrate the importance of radiative heat transfer in transient hot-wire measurements. Thermal conductivity data for liquid toluene, which are corrected for radiation, are reported. The precision of the thermal conductivity data is ± 0.3% and the accuracy is about ±1%. The accuracy of the thermal diffusivity data is about ± 5%. From the measured thermal conductivity and thermal diffusivity, we can calculate the specific heat, C_p, of the fluid, provided that the density is measured, or available through an equation of state.     

The thermal conductivity of liquid argon for temperatures between 110 and 140 K with pressures to 70 MPa

The paper presents new experimental measurements of the thermal conductivity of liquid argon for four temperatures between 110 and 140 K with pressures to 70 MPa and densities between 23 and 36 mol · L ^–1. The measurements were made with a transient hot-wire apparatus. A curve fit of each isotherm allows comparison of the present results to those of others and to correlations. The results are sufficiently detailed to illustrate several features of the liquid thermal conductivity surface, for example, the dependence of its curvature on density and temperature. If these details are taken into account, the comparisons show the accuracy of the present results to be 1 %. The present results, along with several other sets of data, are recommended for selection as standard thermal conductivity data along the saturated liquid line of argon, extending the standards into the cryogenic temperature range. The results cover a fairly wide range of densities, and we find that a hard-sphere model cannot represent the data within the estimated experimental accuracy.     

Thermal conductivity of multicomponent polyatomic dilute gas mixtures

A new expression for the thermal conductivity of anN-component polyatomic gas mixture in the dilute-gas limit has been derived, based on the Thijsse approximation. The results are presented in terms of experimentally accessible quantities to allow for easier calculation of the thermal conductivity and easier interpretation of the experimentally available data. The resulting expression are much simpler than other formulae hitherto available. An additional new expression for the thermal conductivity of anN-component polyatomic gas mixture has been derived by replacing the effective cross-section by their spherical limits. These results are cast in a form which is analogous with, and no more complicated than, the corresponding expressions for purely monatomic mixtures. Paper dedicated to Professor Edward A. Mason.     

Thermal Conductivity Modeling of Pure Refrigerants in a Three-Parameter Corresponding States Format

The potential of the corresponding states (CS) principle for modeling a pure fluid thermal conductivity surface is studied here. While for thermodynamic properties and for viscosity, successful results have been previously obtained by directly applying an improved three-parameter CS method, significant difficulties were encountered while trying to extend this method to thermal conductivity and, in particular, it fails if applied without separately dealing with the dilute-gas term, and the residual and critical enhancement contributions. These last two parts are also combined in the excess term. It is shown that the dilute-gas term cannot be expressed in such a format, and it has necessarily to be individually modeled for each target fluid. On the contrary, the excess contribution can be described through a specific conductivity scaling factor that can be individually determined from a single saturated liquid conductivity experimental value. The model for the excess part is set up in a three-parameter CS format on two reference fluids, in the present case, methane and R134a, for which dedicated thermal conductivity equations are available, and it has a predictive character. The models for the dilute-gas and for the excess contributions are then combined to give the final TC model. The model has been successfully validated for two homologous families of refrigerant fluids obtaining an AAD of 3.67% for 3332 points for haloalkanes and an AAD of 2.87% for 354 points for alkanes.Paper presented at the Sixteenth European Conference on Thermophysical Properties, September 1–4, 2002, London, United Kingdom.     

Thermal conductivity and viscosity of 2,2-dichloro-1,1,1-trifluoroethane (HCFC-123)

The thermal conductivity and the viscosity data of CFC alternative refrigerant HCFC-123 (2,2-dichloro-1,1,1-trifluoroethane: CHCI₂-CF₃) were critically evaluated and correlated on the basis of a comprehensive literature survey. Using the residual transport-property concept, we have developed the three-dimensional surfaces of the thermal conductivity-temperature-density and the viscosity-temperature-density. A dilute-gas function and an excess function of simple form were established for each property. The critical enhancement contribution was taken no account because reliable crossover equations of state and the thermal conductivity data are still missing in the critical region. The correlation for the thermal conductivity is valid at temperatures from 253 to 373 K, pressures up to 30 MPa, and densities up to 1633 kg m^–3. The correlation for the viscosity is valid at temperatures from 253 to 423 K, pressures up to 20 MPa. and densities up to 1608 kg·m^–3. The uncertainties of the present correlations are estimated to be 50% for both properties, since the experimental data are still scarce and somewhat contradictory in the vapor phase at present.     

Thermal conductivity of carbon tetrachloride in the temperature range 310 to 364 K at pressures up to 0.22 GPa

The paper reports new measurements of the thermal conductivity of carbon tetrachloride in the temperature range 310 to 364 K at pressures up to 0.22 GPa. The experimental data have an estimated uncertainty to ±0.3%. The hard-sphere theory of transport in dense fluids is employed to formulate a correlation scheme for the thermal conductivity as a function of density. A single equation represents the dependence of the thermal conductivity on density for all isotherms, the isotherms being distinguished by a characteristic value of the molar volume. It is shown that earlier measurements of the viscosity and self-diffusion coefficient of carbon tetrachloride may be represented in a similar fashion using consistent values of the characteristic volume.     

An extended corresponding states model for the thermal conductivity of refrigerants and refrigerant mixturesModèle d'états correspondants étendus pour la conductivité thermique de frigorigènes et de mélanges de frigorigènes

The extended corresponding states (ECS) model of Huber et al. (Huber, M.L., Friend, D.G., Ely, J.F. Prediction of the thermal conductivity of refrigerants and refrigerant mixtures. Fluid Phase Equilibria 1992;80:249–61) for calculating the thermal conductivity of a pure fluid or fluid mixture is modified by the introduction of a thermal conductivity shape factor which is determined from experimental data. An additional empirical correction to the traditional Eucken correlation for the dilute-gas conductivity was necessary, especially for highly polar fluids. For pure fluids, these additional factors result in significantly improved agreement between the ECS predictions and experimental data. A further modification for mixtures eliminates discontinuities at the pure component limits. The method has been applied to 11 halocarbon refrigerants, propane, ammonia, and carbon dioxide as well as mixtures of these fluids. The average absolute deviations between the calculated and experimental values ranged from 1.08 to 5.57% for the 14 pure fluids studied. Deviations for the 12 mixtures studied ranged from 2.98 to 9.40%. Deviations increase near the critical point, especially for mixtures.     

A New Model for the Thermal Conductivity of Molten Salts

A new model based on rough hard-sphere theory is proposed for the thermal conductivity of molten salts. The model incorporates a smooth hard-sphere contribution using the properties of argon, as well as characteristic parameters based on the melting point of the molten salt. It is demonstrated that it is possible to correlate the thermal conductivity of monovalent and multivalent molten salts within experimental error using this approach. Furthermore, in salts with a common anion, the single adjustable parameter in the model exhibits regular behavior with the molecular weight of the salt. It is also shown that the thermal conductivity of several molten-salt mixtures can be predicted without any mixture parameters.     

Thermal Conductivity of Pure Noble Gases at Low Density from Ab Initio Prandtl Number

The experimental data reported in the literature after 2000 have been investigated for the viscosity and thermal conductivity of helium-4, neon, and argon at low density. The well-established values of thermal conductivity by transient hot-wire measurements are not reliable enough for noble gases in the low-pressure gas region. These facts motivate us to determine the thermal conductivity from accurate viscosity data and the ab initio Prandtl number, with an uncertainty of 0.25 % for temperatures ranging between 200 K and 700 K. The theoretical accuracy is superior to the accuracy of the best measurements. The calculated results are accurate enough to be applied as standard values for the thermal conductivity of helium-4, neon, and argon over the considered temperature range.     

Thermal conductivity of carbon tetrafluoride with argon and helium

The paper presents new measurements of the thermal conductivity of the binary mixtures of carbon tetrafluoride with helium and argon. Measurements were performed in a transient, hot-wire instrument at a nominal temperature of 27.5°C and over a range of densities (pressure up to 12 MPa). The accuracy is estimated to be 0.4%, deteriorating to 0.7% around the critical density. The paper provides polynomial fits which represent the data with a standard deviation of 0.4%. An analysis in terms of the Monchick-Pereira-Mason theory, with the translational contributions computed on the basis of earlier measurements of the viscosity of these mixtures, leads to a reasonable representation of the composition dependence of the zero-density thermal conductivity; the collision numbers _ij are treated here as adjustable parameters to obtain an optimum fit for each mixture.     

Prediction of the Thermal Conductivity of Gas Mixtures at Low Pressures

Three methods, namely, Mason–Saxena–Wassiljewa (MSW), Hirschfelder–Eucken (HE), and Schreiber–Vesovic–Wakeham (SVW), for predicting the thermal conductivity of nonpolar, multicomponent, molecular mixtures in the dilute-gas limit were tested against the available experimental data. Overall, the accuracy of the MSW method is judged to be of the order of ±6 to 8% while that of HE and SVW is ±2 to 3%. For the latter two methods this is a remarkably good agreement, considering the approximations made in deriving the prediction scheme from the kinetic theory results. The agreement achieved indicates that the HE and SVW methods can form the basis of accurate engineering estimation techniques for the thermal conductivity of gaseous mixtures at low pressures.     

Prediction of transport properties of dense gases and liquids by the Peng-Robinson (PR) equation of state

An attempt is made in this work to combine the Enskog theory of transport properties with the simple cubic Peng-Robinson (PR) equation of state. The PR equation of state provides the density dependence of the equilibrium radial distribution function. A slight empirical modification of the Enskog equation is proposed to improve the accuracy of correlation of thermal conductivity and viscosity coefficient for dense gases and liquids. Extensive comparisons with experimental data of pure fluids are made for a wide range of fluid states with temperatures from 90 to 500 K and pressures from 1 to 740 atm. The total average absolute deviations are 2.67% and 2.02% for viscosity and thermal conductivity predictions, respectively. The proposed procedure for predicting viscosity and thermal conductivity is simple and straightforward. It requires only critical parameters and acentric factors for the fluids.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Thermal conductivity and mechanical properties of expanded graphite

The thermophysical and mechanical properties of compacted expanded graphite (EG) were studied. The experimental results were interpreted with application of similarity theory. The compacted EG critical density corresponding to the observed jump in the thermal conductivity coefficient and elasticity modulus was shown to depend on the expandable graphite preparation method, EG bulk density, and dispersion degree and amounted to 0.01 and 0.005 g/cm³ for the studied EGs.     

Vapor-Phase Thermal Conductivity Measurements of Refrigerants

The paper reports further developments of the transient hot-wire technique. The particular development of interest is the extension of the technique to study polar, or electrically-conducting gases with a relatively low thermal conductivity but a high thermal diffusivity, circumstances which occur at low density and therefore low pressure, for gases of high molecular weight. The theory of the transient hot-wire instrument is examined again in order to guide a revised design of the thermal conductivity cell with this particular application in mind. Test measurements have then been conducted on helium, argon, and propane at low and moderate pressures to confirm that the instrument operates in accordance with the theory of it. The satisfactory completion of these tests demonstrates that the new equipment overcomes many of the defects observed in earlier variants of the instrument for application to the study of refrigerant gases.