Thermal Conductivity,Thermal Diffusivity,and Heat Capacity of Gaseous Argon and Nitrogen

Low-pressure thermal conductivity and thermal diffusivity measurements are reported for argon and nitrogen in the temperature range from 295 to 350 K at pressures from 0.34 to 6.9 MPa using an absolute transient hot-wire instrument. Thermal conductivity measurements were also made with the same instrument in its steady-state mode of operation. The measurements are estimated to have an uncertainty of 1% for the transient thermal conductivity, 3% for the steady-state thermal conductivity, and 4% for thermal diffusivity. The values of isobaric specific heat, derived from the measured thermal conductivity and thermal diffusivity, are considered accurate to 5% although this is dependent upon the uncertainty of the equation of state utilized.Paper presented at the Sixteenth European Conference on Thermophysical Properties, September 1–4, 2002, London, United Kingdom     

Measurement of the Thermal Conductivity of Stainless Steel AISI 304L Up to 550 K

New measurements of the thermal conductivity of stainless steel AISI 304L over the temperature range 300 to 550 K are reported. To perform the measurements, the transient hot-wire technique was employed, with a new wire sensor. The sensor makes use of a soft silicone paste material and of two thin polyimide films, between the hot wires of the apparatus and the stainless steel specimen. The transient temperature rise of the wire sensor is measured in response to an electrical heating step over a period of 40 s to 2 s, allowing an absolute determination of the thermal conductivity of the solid, as well as of the polyimide film and the silicone paste. The method is based on a full theoretical model with equations solved by a two-dimensional finite-element method applied to the exact geometry. At the 95% confidence level, the standard deviation of the thermal conductivity measurements is 0.6%, while the standard uncertainty of the technique is less than 1.5%.     

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 surface of argon: A fresh analysis

This paper presents a fresh analysis of the thermal conductivity surface of argon at temperatures between 100 and 325 K with pressures up to 70 MPa. The new analysis is justified for several reasons. First, we discovered an error in the compression-work correction, which is applied when calculating thermal conductivity and thermal diffusivity obtained with the transient hot-wire technique. The effect of the error is limited to low densities, i.e., for argon below 5 mol·L^–1. The error in question centers on the volume of fluid exposed to compression work. Once corrected, the low-density data agree very well with the available theory for both dilute-gas thermal conductivity and the first density coefficient of thermal conductivity. Further, the corrected low-density data, if used in conjunction with our previously reported data for the liquid and supercritical dense-gas phases, allow us to represent the thermal conductivity in the critical region with a recently developed mode-coupling theory. Thus the new surface incorporates theoretically based expressions for the dilute-gas thermal conductivity, the first density coefficient, and the critical enhancement. The new surface exhibits a significant reduction in overall error compared to our previous surface which was entirely empirical. The uncertainty in the new thermal conductivity surface is ±2.2% at the 95% confidence level.     

Thermal Conductivity of Saturated Liquid Toluene by Use of Anodized Tantalum Hot Wires at High Temperatures

Absolute measurements of the thermal conductivity of a distilled and dried sample of toluene near saturation are reported. The transient hot-wire technique with an anodized tantalum hot wire was used. The thermal conductivities were measured at temperatures from 300 K to 550 K at different applied power levels to assess the uncertainty with which it is possible to measure liquid thermal conductivity over wide temperature ranges with an anodized tantalum wire. The wire resistance versus temperature was monitored throughout the measurements to study the stability of the wire calibration. The relative expanded uncertainty of the resulting data at the level of 2 standard deviations (coverage factor k = 2) is 0.5 % up to 480 K and 1.5 % between 480 K and 550 K, and is limited by drift in the wire calibration at temperatures above 450 K. Significant thermal-radiation effects are observed at the highest temperatures. The radiation-corrected results agree well with data from transient hot-wire measurements with bare platinum hot wires as well as with data derived from thermal diffusivities obtained using light-scattering techniques.     

The Thermal Conductivity, Thermal Diffusivity and Isobaric Heat Capacity of Toluene and Argon

This paper presents absolute measurements for the thermal conductivity and thermal diffusivity of toluene obtained with a transient hot-wire instrument employing coated wires over the density interval of 735 to 870 kgm^–3. A new expression for the influence of the wire coating is presented, and an examination of the importance of a nonuniform wire radius is verified with measurements on argon from 296 to 323 K at pressures to 61 MPa. Four isotherms were measured in toluene between 296 and 423 K at pressures to 35 MPa. The measurements have an uncertainty of less than ±0.5% for thermal conductivity and ±2% for thermal diffusivity. Isobaric heat capacity results, derived from the measured values of thermal conductivity and thermal diffusivity, using a density determined from an equation of state, have an uncertainty of ±3% after taking into account the uncertainty of the applied equation of state. The measurements demonstrate that isobaric specific heat determinations can be obtained successfully with the transient hot wire technique over a wide range of fluid states provided density values are available.     

Thermal Conductivity of Polymethyl Methacrylate (PMMA) and Borosilicate Crown Glass BK7

The thermal conductivity of polymethyl methacrylate (PMMA) and borosilicate crown glass BK7 has been studied. The transient hot-wire technique has been employed, and measurements cover a temperature range from room temperature up to 350 K for PMMA and up to 500 K for BK7. The technique is applied here in a novel way that minimizes all remaining thermal-contact resistances. This allows the apparatus to operate in an absolute way and with very low uncertainty. The method makes use of a soft silicone paste material between the hot wires and the solid under test. Measurements of the transient temperature rise of the wires in response to an electrical heating step over a period of 20 μs up to 5 s allow an absolute determination of the thermal conductivity of the solid, as well as of the silicone paste. The method is based on a full theoretical model with equations solved by a two-dimensional finite-element method applied to the exact geometry. At the 95% confidence level, the standard deviations of the thermal conductivity measurements are 0.09% for PMMA and 0.16% for BK7, whereas the standard uncertainty of the technique is less than 1.5%.     

The Thermal Conductivity, Thermal Diffusivity, and Heat Capacity of Gaseous Argon

This paper presents new absolute measurements for the thermal conductivity and thermal diffusivity of gaseous argon obtained with a transient hot-wire instrument. Six isotherms were measured in the supercritical dense gas at temperatures between 296 and 423 K and pressures up to 61 MPa. A new analysis for the influence of temperature-dependent properties and residual bridge unbalance is used to obtain the thermal conductivity with an uncertainty of less than 1% and the thermal diffusivity with an uncertainty of less than 4%. Isobaric heat capacity results were derived from measured values of thermal conductivity and thermal diffusivity using a density calculated from an equation of state. The heat capacities presented here have a nominal uncertainty of 4% and demonstrate that this property can be obtained successfully with the transient hot wire technique over a wide range of fluid states. The technique will be useful when applied to fluids which lack specific heat data.     

Thermal Conductivity of 1,1-Difluoroethane (HFC-152a)

Thermal conductivity measurements were performed on 1,1-difluoroethane (HFC-152a) using the polarized transient hot-wire technique in the temperature range of 214 to 294 K and at pressures up to 19 MPa. This technique was used previously for measurements on other halocarbons along the saturation line and in the compressed liquid phase. No dependence of the polarization voltage was found for the thermal conductivity values, demonstrating that the technique was used with success. Also, no influence of heat transfer by radiation or convection was detected, in all the range of densities studied. The samples were supplied with stated purities greater than 99.9%. The reproducibility of the experiments was found to be 0.03%, while the total uncertainty is estimated to be 0.5%. The experimental data were compared with data from other sources. Values for the thermal conductivity along the saturation line for several temperatures were achieved by extrapolating the high-pressure data to the saturation density for each isotherm. The data obtained were also correlated using a modification of the van der Waals model (smooth hard spheres) with an uncertainty of 1.1%, at a 95% confidence level.     

An Improved Application of the Transient Hot-Wire Technique for the Absolute Accurate Measurement of the Thermal Conductivity of Pyroceram 9606 up to 420 K

This article describes the final refinements of a novel application of the transient hot-wire technique developed for the absolute, accurate measurements of the thermal conductivity of solids. Although the technique was originally developed five years ago, these new refinements allow a full understanding of the method and hence the performance of measurements with an absolute uncertainty of less than 1 %. New measurements of Pyroceram 9606 up to 420 K are reported. The maximum deviation of the present measurements is 0.54 %, while their standard deviation at the 95 % confidence level is 0.25 %. Since May 2007, Pyroceram 9606 is a European Commission certified thermal-conductivity reference material, designated as BCR-724, with an uncertainty of ±6.5 % at the 95 % confidence level.     

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.     

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.     

Thermal conductivity andPVT measurements of pentafluoroethane (refrigerant HFC-125)

By means of the transient and steady-state coaxial cylinder methods, the thermal conductivity of pentafluoroethane was investigated at temperatures from 187 to 419 K and pressures from atmospheric to 6.0 MPa. The estimated uncertainty of the measured results is ±(2–3)%. The operation of the experimental apparatus was validated by measuring the thermal conductivity of R22 and R12. Determinations of the vapor pressure andPVT properties were carried out by a constant-volume apparatus for the temperature range 263 to 443 K, pressures up to 6 MPa, and densities from 36 to 516 kg m^–3. The uncertainties in temperature, pressure, and density are less than ±10 mK, ±0.08%, and ±0.1%, respectively.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Quasi-Steady State Method: Uncertainty Assessment

The newly developed quasi-steady state (QSS) method to measure the thermal conductivity combines characteristic advantages of transient and steady-state techniques but avoids their major drawbacks. Based upon a transient hot strip setup, the QSS technique can be realized by adding only two temperature sensors at different radial distances from the strip. After a short settling time, the QSS output signal which is the measure for the thermal conductivity is constant in time as it is for steady-state instruments. Moreover, in contrast to transient techniques, the QSS signal is not altered by homogeneous boundary conditions. Thus, there is no need to locate a time window as has to be done with the transient hot wire or transient hot strip techniques. This paper describes the assessment of the QSS standard uncertainty of thermal conductivity according to the corresponding ISO Guide. As has already been done in previous papers on the uncertainty of the transient hot wire and transient hot strip techniques, first, the most significant sources of error are analyzed and numerically evaluated. Then the results are combined to yield an estimated overall uncertainty of 3.8%. Simultaneously, the present assessment is used as an aid in planning an experiment and in designing a QSS sensor to achieve minimal uncertainty. Such a sensor is used to verify the above mentioned standard uncertainty from a run on the candidate reference material polymethyl methacrylate.     

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.     

The thermal conductivity and heat capacity of gaseous argon

This paper presents new absolute measurements of the thermal conductivity and of the thermal diffusivity of gaseous argon obtained with a transient hot-wire instrument. We measured seven isotherms in the supercritical dense gas at temperatures between 157 and 324 K with pressures up to 70 MPa and densities up to 32 mol · L^–1 and five isotherms in the vapor at temperatures between 103 and 142 K with pressures up to the saturation vapor pressure. The instrument is capable of measuring the thermal conductivity with an accuracy better than 1% and thermal diffusivity with an accuracy better than 5%. Heat capacity results were determined from the simultaneously measured values of thermal conductivity and thermal diffusivity and from the density calculated from measured values of pressure and temperature from an equation of state. The heat capacities presented in this paper, with a nominal accuracy of 5%, prove that heat capacity data can be obtained successfully with the transient hot wire technique over a wide range of fluid states. The technique will be invaluable when applied to fluids which lack specific heat data or an adequate equation of state.     

New Measurements of the Thermal Conductivity of PMMA,BK7, and Pyrex 7740 up to 450K

New measurements of the thermal conductivity of polymethyl methacrylate (PMMA), BK7, and Pyrex 7740 are presented. The technique employed is a refined transient hot-wire technique, based on a full theoretical model with equations solved by finite elements for the exact geometry. At the 95 % confidence level, the standard deviations of the thermal conductivity measurements of PMMA, BK7, and Pyrex 7740 are 0.47 %, 1.0 %, and 0.8 %, respectively. The technique is absolute and is characterized by an uncertainty of <1 %.     

A New Instrument for the Measurement of the Thermal Conductivity of Fluids

The transient hot-wire technique is at present the best technique for obtaining standard reference data for the thermal conductivity of fluids. It is an absolute technique, with a working equation and a complete set of corrections reflecting departures from the ideal model, where the principal variables are measured with a high degree of accuracy. It is possible to evaluate the uncertainty of the experimental thermal conductivity data obtained using the best metrological recommendations. The liquids proposed by IUPAC (toluene, benzene, and water) as primary standards were measured with this technique with an uncertainty of 1% or better (95% confidence level). Pure gases and gaseous mixtures were also extensively studied. It is the purpose of this paper to report on a new instrument, developed in Lisbon, for the measurement of the thermal conductivity of gases and liquids, covering temperature and pressure ranges that contain the near-critical region. The performance of the instrument for pressures up to 15 MPa was tested with gaseous argon, and measurements on dry air (Synthetic gas mixture, with molar composition certified by Linde AG, Wiesbaden, Germany, Ar – 0.00920; O₂ – 0.20966; N₂ – 0.78114), from room temperature to 473 K and pressures up to 10 MPa are also reported. The estimated uncertainty is 1%.M. L. V. Ramires: DeceasedPaper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

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.     

Transient Hot Wire (THW) Method: Uncertainty Assessment

The standard method for measuring thermal transport properties of dielectric solids such as ceramics and refractories is the transient hot wire (THW) technique. In its simplest arrangement, a thin wire is embedded between two sample halves, where it acts simultaneously as a resistive heat source and a thermometer. From its temperature signal, the thermal conductivity and the thermal diffusivity of the dielectric can be derived. Up to now, there is no uncertainty assessment for this technique strictly following the ISO Guide to the Expression of Uncertainty in Measurement. Here we analyze the ISO standard uncertainty of the THW technique in the same way as in a previous paper on the uncertainty of the closely related transient hot strip (THS) technique. The two papers provide a comprehensive comparison of the most important advantages and disadvantages of these two transient techniques. The results obtained here for the uncertainty (5.8% for the thermal conductivity and 30% for the thermal diffusivity) are nearly the same as those for the THS method. Experiments on a Pyrex standard-reference sample confirm the results.