Thermal Conductivity during Phase Transitions

Thermal conductivity is a very basic property that determines how fast a material conducts heat, which plays an important and sometimes a dominant role in many fields. However, because materials with phase transitions have been widely used recently, understanding and measuring temperature‐dependent thermal conductivity during phase transitions are important and sometimes even questionable. Here, the thermal transport equation is corrected by including heat absorption due to phase transitions to reveal how a phase transition affects the measured thermal conductivity. In addition to the enhanced heat capacity that is well known, it is found that thermal diffusivity can be abnormally lowered from the true value, which is also dependent on the speed of phase transitions. The extraction of the true thermal conductivity requires removing the contributions from both altered heat capacity and thermal diffusivity during phase transitions, which is well demonstrated in four selected kinds of phase transition materials (Cu₂Se, Cu₂S, Ag₂S, and Ag₂Se) in experiment. This study also explains the lowered abnormal thermal diffusivity during phase transitions in other materials and thus provides a novel strategy to engineer thermal conductivity for various applications.     

Thermal conductivity and diffusivity measurements at cryogenic temperatures by double specimen technique

A double specimen technique is used in measuring the thermal conductivity and diffusivity of low thermal conductivity materials. In this technique good thermal contact is maintained between the heat source and sink and two geometrically similar specimens. A thin-copper heater plate is compressed between the two specimens and the temperature difference is measured between the heat source and the temperature controlled heat sink. Thermal conductivity is determined at steady state conditions by the differential method while the diffusivity is determined from transient measurements combined with an analytical solution to the one dimensional solution of the diffusion equation.     

Determination of Thermophysical Properties for Polymer Films using Conduction Analysis of Laser Heating

Determination of the thermophysical properties of thin film materials is important for modeling and optimizing laser microvia drilling of organic substrates in microelectronics applications. Techniques to measure the density, thermal conductivity, thermal diffusivity, thermal decomposition point, and specific ablation heat of thin polymer films are described. An experimental apparatus was set up for laser heating of the sample. To measure the thermal diffusivity, an analytic heat transfer model is developed. One-dimensional heat conduction is assumed due to the small thickness of the film compared to the radius of the laser beam. The value of thermal diffusivity is obtained by fitting the experimental data to the theory. The specific ablation heat is obtained by measuring the mass loss during laser ablation. The experimental apparatus and the property determination methodology can also be applied to thin samples of other materials.     

Calorimetric and transport properties of Zircalloy 2, Zircalloy 4, and Inconel 625

This paper presents the measurements and the results on thermal and electrical transport properties of three nuclear reactor cladding materials: Zircalloy 2, Zircalloy 4, and Inconel 625. Study of these materials constituted a part of the IAEA coordinated research program aimed at the generation and establishment of a reliable and complete database of the thermal properties of reactor materials. Measured properties include thermal diffusivity, specific heat, and electrical resistivity. Thermal diffusivity was measured by the laser pulse technique. Specific heat and electrical resistivity were measured using a millisecond-resolution direct electrical pulse heating technique. Thermal conductivity was computed from the experimentally determined thermal difusivity and specific heat functions and the room temperature density values. Measurements were performed in the 20 to 1500°C temperature range, depending on the material and property concerned.     

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.     

Thermophysical Properties of Plant Leaves and Their Influence on the Environment Temperature

It is known that the thermal properties of a material influence the temperature around it. Once heated, the rate at which a material transfers the absorbed heat into the surroundings is determined by the thermal effusivity (or thermal inertia) of the material, and it depends on the well-known thermal properties, thermal conductivity, and specific heat capacity. Since a direct measurement of these properties is rather difficult for thin biological specimens such as plant leaves, a photothermal technique is used to measure the thermal effusivity, thermal diffusivity, thermal conductivity, and specific heat capacity for a few representative species of plant leaves. Measurements have been carried out on fresh as well as dry leaves to estimate the differences in their properties. Thermal properties of plant leaves are compared with the corresponding properties of two materials abundant in the environment and discussed. The influence of thermal properties, particularly the thermal effusivity and specific heat capacity, of plant leaves on controlling the temperature of the environment around them is discussed.     

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.     

Transient Characteristics of Thermal Conduction in Dispersed Composites

The effective thermal conductivity of dispersed composites with a hot-melt-adhesive matrix, measured using the steady-state method, is compared with the apparent thermal conductivity calculated from the average heat capacity and from the thermal diffusivity measured by the laser-flash method. The transient effect has been observed obviously at higher volume percentages for various dispersed particle sizes and ratios of the thermal conductivity values of dispersed and continuous phases. All of the experimental results are compared with those calculated by existing models and by the finite element method (FEM). An attempt has been made to show how the criterion for the homogeneity of dispersed composites under transient conditions is affected by the percentages of dispersed phase, dispersed particle size, and ratio of the thermal conductivity values of dispersed and continuous phases.     

Thermophysical Properties of Automotive Metallic Brake Disk Materials

The temperature distribution, the thermal deformation, and the thermal stress of automotive brake disks have quite close relations with car safety; therefore, much research in this field has been performed. However, successful and satisfactory results have not been obtained because the temperature-dependent thermophysical properties of brake disk materials are not sufficiently known. In this study, the thermophysical properties (thermal diffusivity, the specific heat, and the coefficient of thermal expansion) of three kinds of iron alloy series brake disk materials, FC250, FC170, and FCD50, and two kinds of aluminum alloy series brake disk materials, Al MMC and A356, were measured in the temperature range from room temperature to 500 °C, and the thermal conductivity was calculated using the measured thermal diffusivity, specific heat capacity, and density. As expected, the results show that the two series have significant differences in respect of the thermophysical properties, and to reduce the thermal deformation of the brake disk, the aluminum alloys with a high thermal conductivity and the iron alloys with low thermal expansion are recommended.     

Intercomparison of Thermophysical Property Measurements on an Austenitic Stainless Steel

The results of an inter laboratory comparison of thermal conductivity, thermal diffusivity, specific heat capacity, and thermal expansion measurements on austenitic stainless steel in the temperature range between 20 and 1000°C are presented here. Mean values are presented for the physical properties studied. Reliable relative expanded uncertainties can be stated for the properties determined, which were achieved by applying good measurement practice, i.e., 3% for thermal expansion, 5% for specific heat capacity and thermal diffusivity, and 6% for thermal conductivity. The mean values derived from this intercomparison agree well with the results of a previous intercomparison in 1990. An erratum to this article is availabale at .     

Some Thermal Properties of a Copper–Tin Alloy

The thermal properties (heat capacity, thermal diffusivity, and electrical resistivity) of a Cu + 10 wt% Sn alloy in both solid and liquid phases have been reported. Using these values it was confirmed that the Lorenz relation is suitable for obtaining thermal conductivity from electrical resistivity in the liquid phase of this alloy. Also, the temperature differential (d/dT) obtained from such an approach was in excellent agreement with the thermal conductivity values calculated from thermal diffusivity.     

Measurement and evaluation of the thermal diffusivity of two-layered materials

Transient methods, such as those with pulse- or step-wise heating, have often been used to measure thermal diffusivity of various materials including layered composite materials. The aim of the present study is to investigate effects of various parameters on the measurement of thermal diffusivity when the transient methods are applied. Mainly a two-layered material in the pulsewise heating method is considered because of its simplicity and usefulness in identifying and determining the effects of the parameters. First, it has been shown that there exists a special condition for determining the thermal diffusivity of a component in the two-layered material whose other relevant thermophysical properties are known. Second, it has been shown that the thickness of the laserbeam absorption layer, which inevitably makes sample material into the twolayered material, may cause a relatively large error when the thermal diffusivity of the base material is high. Finally, it has been derived a definite relation between the apparent thermal diffusivity obtained from the temperature response and the mean thermal diffusivity, which has a physical meaning related to the thermal resistance.     

A multi-scale model for coupled heat conduction and deformations of viscoelastic functionally graded materials

An integrated micromechanical-structural framework is presented to analyze coupled heat conduction and deformations of functionally graded materials (FGM) having temperature and stress dependent viscoelastic constituents. A through-thickness continuous variation of the thermal and mechanical properties of the FGM is approximated as an assembly of homogeneous layers. Average thermo-mechanical properties in each homogeneous medium are computed using a simplified micromechanical model for particle reinforced composites. This micromechanical model consists of two isotropic constituents. The mechanical properties of each constituent are time–stress–temperature dependent. The thermal properties (coefficient of thermal expansion and thermal conductivity) of each constituent are allowed to vary with temperature. Sequentially coupled heat transfer and displacement analyses are performed, which allow analyzing stress/strain behaviors of FGM having time and temperature dependent material properties. The thermo-mechanical responses of the homogenized FGM obtained from micromechanical model are compared with experimental data and the results obtained from finite element (FE) analysis of FGMs having microstructural details. The present micromechanical-modeling approach is computationally efficient and shows good agreement with experiments in predicting time-dependent responses of FGMs. Our analysis forecasts a better design for creep resistant materials using particulate FGM composites.     

An Experimental Study on Thermal and Electrical Properties of Packed Carbon Nanofibers

In the present study, the thermal and electrical properties of packed carbon nanofibers (P-CNFs) have been investigated. A short-hot-wire (SHW) technique was applied to determine simultaneously the thermal conductivity and thermal diffusivity of P-CNFs. In SHW measurements, a platinum wire coated with an alumina layer served as both the heating source and the thermometric sensor. A curve fitting method by matching the experimental data and numerical simulated values was proposed for determining the thermal conductivity and thermal diffusivity of P-CNFs with different packed densities. The electrical conductivities were measured by a four-terminal method where a special vessel with electrodes with circular plates was used. The results indicated that the electrical conductivity increases linearly with an increase in packed density. The thermal conductivity and thermal diffusivity also increase with an increase in packed density. The relation between the thermal conductivity and the electrical conductivity has been shown to be approximately linear. The SHW technique combined with the curve fitting method would be applicable to many kinds of materials.Paper presented at the Seventh Asian Thermophysical Properties Conference, August 23–28, 2004, Hefei and Huangshan, Anhui, P. R. China.     

Simultaneous measurements of thermal conductivity and diffusivity of Se80Te20-xInx (x = 2, 4, 6 and 10) chalcogenide glasses at room temperature

Measurements of thermal conductivity and thermal diffusivity of twin pellets of Se₈₀Te_20-xIn_x (x = 2, 4, 6 and 10) glasses, prepared under a load of 5 tons were carried out at room temperature using transient plane source (TPS) technique. The measured values of both thermal conductivity and diffusivity were used to determine the specific heat per unit volume of the said materials in the composition range of investigation. Results indicated that both the values of thermal conductivity and thermal diffusivity increased with the addition of indium at the cost of tellurium whereas the specific heat remained almost constant. This compositional dependence behaviour of the thermal conductivity and diffusivity has been explained in terms of the iono-covalent type of bond which In makes with Se as it is incorporated in the Se-Te glass.     

Measurement of thermophysical properties of metals and ceramics by the laser-flash method

Several recent advances made in the author's laboratory in the experimental apparatus and measuring procedures for precise measurements of thermophysical properties by the laser-flash method are reviewed. Heat-capacity measurement has been done on metals and ceramics within an accuracy of ±0.5% in the range from 80 to 800 K, and within ±2% from 800 to 1100 K. Thermal diffusivity has been also measured from 80 to 1300 K with reasonable corrections for heat leak and finite pulse width. As an example of the experimental results by the method, the data of heat capacity, thermal diffusivity, and thermal conductivity of vanadium-oxygen alloys containing 1.07 and 3.46 at.% of oxygen from 80 to 800 K are presented and compared with those of pure vanadium metal.Presented at the Japan-United States Joint Seminar on Thermophysical Properties, October 24–26, 1983, Tokyo, Japan.     

Effect of radiation heat transfer on thermal diffusivity measurements

Experimental data on thermal conductivity and thermal diffusivity of a semitransparent material generally include an error due to the radiation heat transfer. This error varies in accordance with the experimental conditions such as the temperature level of the sample and the measuring method. In this paper, research on the influence of radiation heat transfer on thermal diffusivity are reviewed, and as an example, the method to correct the radiation component in the apparent thermal diffusivity measured by the stepwise heating technique is presented. The transient heat transfer by simultaneous thermal conduction and radiation in a semitransparent material is analyzed when the front surface is subjected to stepwise heating. The apparent thermal diffusivity, which includes the radiation component, is calculated for various parameters.Paper presented at the Second U.S.-Japan Joint Seminar on Thermophysical Properties, June 23, 1988, Gaithersburg, Maryland, U.S.A.     

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 thermal properties of liquids with an AC heated-wire technique

An apparatus for the simultaneous absolute measurement of the thermal activity, thermal diffusivity, thermal conductivity, and heat capacity of nonconducting liquids with the AC heated-wire (strip) technique is described. The main advantage of this technique is that the temperature oscillations field can be confined around the sensor in a liquid layer thin enough to suppress the hydrodynamic currents. This leads to the elimination of the convective heat transport. Carrying measurements at different frequencies, the inertia of the sensor can be considered, and the radiative heat transport can be estimated for liquids with known optical properties. The apparatus was constructed and tested using six different liquids in a limited temperature range. The thermal properties of these liquids at 20°C are reported. The thermal conductivity data of toluene and n-heptane (recommended as proposed thermal conductivity standards) are given in the temperature range 10–40°C. Good agreement was found with data reported by other investigators at 20°C, but there is still a considerable discrepancy in the temperature coefficient of thermal conductivity.     

Thermophysical Properties of Ceramic Substrates with Modified Surfaces

Laser induced changes of thermophysical properties using a laser supported modification process have been studied. Metal–ceramic composites have been produced by a laser dispersing process. Two types of substrates have been included, namely, pure Al₂O₃ and Al₂O₃ reinforced with 10 mass% ZrO₂. As a modifying material during the laser process, hard metal powders like TiN and WC have been applied in order to produce a metal–ceramic composite with a metal concentration between 30 and 50%. Standard measurement techniques such as the laser-flash method and differential scanning calorimetry (DSC) have been used to measure the thermal diffusivity and the heat capacity of the ceramics before and after the laser processing. These properties have been evaluated within a temperature range from room temperature to 1400°C. The experimental results show that the effective thermal conductivity will be enhanced within the laser modified region. The increase of this heat transport property due to particle dispersion into the ceramic matrix depends on the thermal conductivity of the second-phase material. Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.