Radiative heat exchange method for thermal conductivity measurement applying a perpendicular heat flow to a thin-plate sample: Principle and apparatus

To measure thermal conductivity of materials of low conductivity (0.1 to 1 W·m^–1·K^–1), a method using a specimen of small size (2×25×25 mm) has been developed. This method applies a well-defined, steady, and uniform heat flux perpendicular to the surface of a small plate sample of polymers or ceramics jointly by means of radiative heat exchange as well as by an areal heater on the sample surface and allows a reasonably rapid (5-min) measurement of thermal conductivity. This method of measuring conductivity is an absolute and direct measurement method which does not need any standard reference materials or information about heat capacity. The principle of the method has been demonstrated by constructing a measurement apparatus and measuring thermal conductivity of a few materials. The thermal conductivities of silicone rubber and Pyrex (Corning 7740) glass measured by the present method between 30 and 90°C are compared with recommended values.     

Thermal conductivity,heat capacity,and thermal diffusivity of selected commercial AlN substrates

The thermal transport properties of four commercially available AlN substrates have been investigated using a combination of steady-state and transient techniques. Measurements of thermal conductivity using a guarded longitudinal heat flow apparatus are in good agreement with published room temperature data (in the range 130–170 W · m^–1 · K^–1). Laser flash diffusivity measurements combined with heat capacity data yielded anomalously low results. This was determined to be an experimental effect for which a method of correction is presented. Low-temperature measurements of thermal conductivity and heat capacity are used to probe the mechanisms that limit the thermal conductivity in AlN.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Thermal conductivity of pure monoisotopic silicon

The thermal conductivity of pure monoisotopic silicon is estimated by two methods, which give similar results. One estimate, based on the observed thermal conductivity of monoisotopic germanium, yields a maximum of 66 W · cm^–1 · K^–1 at 22 K. The other estimate, based on measurements of natural silicon and on the theoretical isotope scattering rate, yields 75 W · cm^–1 · K^–1 at 22 K, an increase of only 45% over the natural crystal. These values are for crystals of approximately 0.5 cm diameter; smaller crystals yield lower values of the maximum conductivity and smaller isotope effects. Silicon cooled to liquid hydrogen temperature seems promising for high-irradiance laser mirrors. The small gain obtained by using monoisotopic silicon would be substantially greater in cases when the generated phonon distribution is athermal and weighted to higher frequencies. The effective heat transport could then be increased by as much as a factor 60 through the use of monoisotopic silicon.     

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.     

Measurement of the heat of fusion of titanium and a titanium alloy (90Ti-6Al-4V) by a microsecond-resolution transient technique

A microsecond-resolution pulse heating technique was used for the measurement of the heat of fusion of titanium and a titanium alloy (90Ti-6Al-4V). The method is based on rapid (50- to 100-s) resistive self-heating of the specimen by a high-current pulse from a capacitor discharge system and measuring, as functions of time, current through the specimen, voltage across the specimen, and radiance of the specimen. Melting of the specimen is manifested by a plateau in the measured radiance. The time integral of the net power absorbed by the specimen during melting yields the heat of fusion. The values obtained for heat of fusion were 272 J · g^–1 (13.0 kJ · mol^–1) for titanium and 286 J · g^–1 for the alloy 90Ti-6Al-4V, with an estimated maximum uncertainty of ±6% in each value.Paper presented at the Second Workshop on Subsecond Thermophysics, September 20–21, 1990, Torino, Italy.     

Thermal Conductivity of Opacified Powder Filler Materials for Vacuum Insulations1

The thermal conductivity of powder fillings for load-bearing vacuum insulations is investigated. Different opacifiers have been tested in mixtures with perlite powder, precipitated silica, and fumed silica. Using temperature-dependent thermal conductivity measurements, the radiative thermal conductivity and the solid conductivity of the powder samples are separated. Additionally, the influence of the pressure load on the solid conductivity is studied. The thermal conductivities of silica powders with added opacifier powders (carbon black, magnetite, silicon carbide, titanium dioxide) can be as low as 0.003 W·m^–1·K^–1 if the powder boards are pressed with moderate loads. The use of microporous silica powders as filler materials allows internal gas pressures even beyond 10 hPa with only a moderate increase of the overall conductivity.     

Thermal-wave resonant-cavity measurements of the thermal diffusivity of air: A comparison between cavity-length and modulation-frequency scans

The application of a thermal-wave resonant cavity to thermal-diffusivity measurements of gases has been investigated. The cavity was constructed using a thin aluminum foil wall as the intensitv-modulated laser-beam oscillator source opposite a pyroclectric polyvilidene fluoride wall acting as a signal transducer. Theoretically, cavity-length and modulation-frequency scans both produce resonance-like extrema in lock-in in-phase and quadrature curses. These extrema can be used to measure the thermal diffusivity of the gas within the cavity. It was found experimentally that one can obtain. very accurate and reproducible measurements of the thermal diffusivity of the gas by using simple cavity-length scanning without any signal normalization procedure. rather than traditional modulation-frequency scanning; normalized by the frequency-dependent transfer function of the instrumentation. By scanning the cavity length, the thermal diffisivity of room air at 299 K was measured with three-significant figure precision as 0.216±11.001 cm²·s^–1, with a standard deviation 0.5%. Only two significant figure accuracy could be obtained by scanning the frequency: 0.22±0.03 cm²·s^–1, with a standard deviation of 14%. Cavity-length scanning consistently exhibited a much higher signal-to-noise ratio.     

Knudsen-effect errors with transient line-source measurement in fluids

This paper decribes the Knudsen-effect errors of the transient line-source method used for accurate measurements of the thermal conductivity and thermal diffusivity of fluids. The analysis demonstrates that the instrument can be used with a good accuracy (>0.5%) to lower densities than previously thought. The principal errors are illustrated by measurements on propane in the temperature range 250–300 K at densities less than 9 kg · m^–3.     

Thermal conductivity and thermal diffusivity of xylene isomers in the temperature range 308–360 K at pressures up to 0.38 GPa

New, absolute measurements of the thermal conductivity of the three xylene isomers within the temperature range 308–360 K for pressures up to 0.38 GPa are reported. In addition, for two of the isomers, m-xylene and p-xylene, it has been possible to measure the thermal diffusivity simultaneously within the same range of conditions. The accuracy of the thermal conductivity data reported is one of ±0.3%, whereas for the thermal diffusivity the estimated accuracy is ±6%. It is found that the density dependence of the thermal conductivity for all of the xylenes can be well represented by one equation based on a rigid-sphere model in the same way that has proved successful for normal alkanes. The thermal diffusivity data have been employed to derive heat capacities for the xylenes over a range of pressures.     

Thermophysical Parameters of Optical Glass BK 7 Measured by the Pulse Transient Method

This paper is focused on the pulse transient method. The theory of the method and the measuring regime (time window) are analyzed. The results of the analysis are verified on borosilicate crown glass BK7, which is a candidate for a standard for thermal conductivity. Thermal contact and surface effects affect the length of the time window in which the evaluation procedure is applied. The one-point evaluation technique is compared with the results of the fitting procedure that uses the time window found by difference analysis. The values of the thermal conductivity, thermal diffusivity, and specific heat were found to be 1.05 W· m^–1 · K^–1, 0.548 × 10^–6m ^{– 2} · s^–1, and 767 J· kg^–1 · K^–1, respectively, using the one-point evaluation technique.Paper presented at the Sixteenth European Conference on Thermophysical Properties, September 1–4, 2002, London, United Kingdom.     

The thermal conductivity of xylene isomers in the temperature range 290–360 K

New absolute measurements of the thermal conductivity of the three xylene isomers are reported. The measurements have been carried out in the temperature range 290–360 K, at atmospheric pressure, in a transient hot-wire instrument. The accuracy of the measurements is estimated to be ±0.5%. The measurements presented in this paper have been used in conjuction with our earlier reported measurements of liquid benzene and toluene, at atmospheric pressure, to develop a consistent theoretically based predictive scheme for the thermal conductivity of these five aromatic hydrocarbons. The proposed scheme, containing just one parameter characteristic of each fluid, permits the prediction of the thermal conductivity of the five aromatic hydrocarbons in the temperature range 290–360 K and at pressures up to 350 MPa, with an accuracy of ±2.5%.     

Thermal conductivity measurements of pacific illite sediment

Results are reported for effective thermal conductivity measurements performed in situ and in core samples of illite marine sediment. The measurements were obtained during a recent oceanographic expedition to a study site in the north central region of the Pacific Ocean. This study was undertaken in support of the U.S. Subseabed Disposal Project, the purpose of which is to investigate the scientific feasibility of using the fine-grained sediments of the sea floor as a repository for high-level nuclear waste. In situ measurements were made and 1.5-m-long hydrostatic piston cores were taken, under remote control, from a platform that was lowered to the sea floor, 5844 m below sea level. The in situ measurement of thermal conductivity was made at a nominal depth of 80 cm below the sediment surface using a specially developed, line-source, needle probe. Thermal conductivity measurements in three piston cores and one box core (obtained several kilometers from the study site) were made on shipboard using a miniature needle probe. The in situ thermal conductivity was approximately 0.91 W · m^–1 · K^–1. Values determined from the cores were within the range 0.81 to 0.89 W · m^–1 · K^–1.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Thermal conductivity of hydrogen for temperatures between 78 and 310 K with pressures to 70 MPa

The paper presents new experimental measurements of the thermal conductivity of hydrogen. The ortho-para compositions covered are normal, near normal, para, and para-rich. The measurements were made with a transient hot wire apparatus. The temperatures covered the range from 78 to 310 K with pressures to 70 MPa and densities from 0 to a maximum of 40 mol · L^–1. For compositions normal and near normal, the isotherms cover the entire range of pressure, and the temperatures are 78, 100, 125, 150, 175, 200, 225, 250, 275, 294, 300, and 310K. The para measurements include eight isotherms at temperatures from 100 to 275 K with intervals of 25 K, pressures to 12 MPa, and densities from 0 to 12 mol · L^–1. Three additional isotherms at 150, 250, and 275 K cover para-rich compositions with para percentages varying from 85 to 72%. For these three isotherms the pressures reach 70 MPa and the density a maximum of 30 mol · L^–1. The data for all compositions are represented by a single thermal conductivity surface. The data are compared with the experimental measurements of others through the new correlation. The precision (2) of the hydrogen measurements is between 0.5 and 0.8% for wire temperature transients of 4 to 5 K, while the accuracy is estimated to be 1.5%.     

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.     

Measurement of the heat of fusion of molybdenum by a microsecond-resolution transient technique

A microsecond-resolution pulse-heating technique was used for the measurement of heat of fusion of molybdenum. The method is based on rapid resistive self-heating of the specimen by a high-current pulse from a capacitor discharge system and measuring current through the specimen, voltage across the specimen, and radiance temperature of the specimen as functions of time. Melting of the specimen is manifested by a plateau in the temperature versus time function. The time integral of the power absorbed by the specimen during melting yields the heat of fusion. Measurements gave a value of 36.4 kJ · mol^–1 for the heat of fusion of molybdenum with an estimated maximum uncertainty of±6%.Paper presented at the First Workshop on Subsecond Thermophysics, June 20–21, 1988, Gaithersburg, Maryland, U.S.A.Formerly National Bureau of Standards     

Thermal conductivity and heat capacity per unit volume of poly(methyl methacrylate) under high pressure

The thermal conductivity and heat capacity per unit volume of poly(methyl methacrylate) (25 and 350 kg · mol^– in molecular weight) have been measured in the temperature range 155–358 K at pressures up to 2 GPa using the transient hot-wire method. The bulk modulus has been measured up to 1.0 GPa at 294 K and yielded a constant valueg = 3.4 ± 0.3 for the Bridgman parameter. No dependence on molecular weight could be detected in the properties we measured.     

A microsecond-resolution transient technique for measuring the heat of fusion of metals: Niobium

A microsecond-resolution pulse-heating technique is described for the measurement of the heat of fusion of refractory metals. The method is based on rapid resistive self-heating of the specimen by a high-current pulse from a capacitor discharge system and measurement of the current through the specimen, the voltage across the specimen, and the radiance temperature of the specimen as a function of time. Melting of the specimen is manifested by a plateau in the temperature versus time function. The time integral of the power absorbed by the specimen during melting yields the heat of fusion. Measurements gave a value of 31.1 kj · mol^–1 for the heat of fusion of niobium, with an estimated maximum uncertainty of ±5%. Electrical resistivity of solid and liquid niobium at its melting temperature was also measured.     

Thermal properties of MoSi2 and SiC whisker-reinforced MoSi2

The heat capacity, thermal conductivity and coefficient of thermal expansion of MoSi₂ and 18 vol % SiC whisker-reinforced MoSi₂ were investigated as a function of temperature. The materials were prepared by hot isostatic pressing between 1650 and 1700 °C, the hold time at temperature being 4 h. The heat capacity of MoSi₂ showed an increase from about 0.44 Wsg^–11K^–1 at room temperature to 0.53 at 700 °C. Whisker reinforcement increased heat capacity by about 10%. Thermal conductivity exhibited a decreasing trend from 0.63 Wcm^–1 K^–1 at room temperature to 0.28 Wem^–1 K^–1 at 1400°C. Whiskers reduced conductivity by about 10%. The thermal expansion coefficient increased from 7.42 °C^–1 between room temperature and 200 °C to 9.13 °C^–1 between room temperature and 1200 °C. There was a 10% decrease resulting from the whiskers. The measured data are compared with literature values. The trends in the data and their potential implications for high-temperature aerospace applications of MoSi₂ are discussed.     

The thermal conductivity of propane

This paper presents thermal conductivity measurements of propane over the temperature range of 192–320 K, at pressures to 70 MPa, and densities to 15 mol · L^–1, using a transient line-source instrument. The precision and reproducibility of the instrument are within ±0.5%. The measurements are estimated to be accurate to ±1.5%. A correlation of the present data, together with other available data in the range 110–580 K up to 70 MPa, including the anomalous critical region, is presented. This correlation of the over 800 data points is estimated to be accurate within ±7.5%.Nomenclature a _n, b_ij, b_n, c_n Parameters of regression model - C Euler's constant (=1.781) - P Pressure, MPa (kPa) - P _cr Critical pressure, MPa - Q ₁ Heat flux per unit length, W · m^–1 - t time, s - T Temperature, K - T _cr Critical temperature, K - T ₀ Equilibrium temperature, K - T _re Reference temperature, K - T _r Reduced temperature = T/T _cr - T _TP Triple-point temperature, K Greek symbols Thermal diffusivity, m² · s^–1 - T _i Temperature corrections, K - T Temperature difference, K - T _w Temperature rise of wire between time t ₁ and time t ₂, K - T ^* Reduced temperature difference (T–T _cr)/T_cr - _corr Thermal conductivity value from correlation, W · m^–1 · K^–1 - _cr Thermal conductivity anomaly, W · m^–1 · K^–1 - _e Excess thermal conductivity, W · m^–1 · K^–1 - ^* Reduced density difference - Thermal conductivity, W^–1 · m^–1 · K^–1, mW · m^–1 · K^–1 - _bg Background thermal conductivity, W · m^–1 · K^–1 - ₀ Zero-density thermal conductivity, W · m^–1 · K^–1 - Density, mol · L^–1 - _cr Critical density, mol · L^–1 - _re Reference density, mol · L^–1 - _r Reduced density Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Comparison of thermal conductivity data for partially stabilized zirconia with values derived from thermal diffusivity results

The thermal conductivity of partially stabilized zirconia was measured over the temperature range 320–1273 K using the radial heat flow method. The data have an absolute uncertainty of about ±2% and repeat measurements showed no evidence of changes in the thermal conductivity at high temperatures. This also was true for the thermal diffusivity data, which were obtained in vacuum over the temperature range 300–1473 K. Both sets of thermal conductivity data pass through minima at high temperatures. Quantitative differences were observed in the temperatures and thermal conductivities of the two minima. The results were analyzed by assuming parallel conduction by phonons and photons, and the phonon component was identified by fitting lower-temperature data. Extrapolating this curve allowed identification of the photon contribution to the thermal conductivity at high temperatures. The photon contribution approached a T ³ function and was larger in the thermal conductivity specimens. The difference in the photon contributions correlates with changes in the optical properties of the samples produced during the high temperature measurments.