A Transient Heating Technique for Measuring the Thermal Diffusivity of Metals

A transient heating technique, improving the constant-rate-heating technique for the measurements of thermal diffusivities of metals, is proposed. For a physical model of a specimen to be measured, the transient heat-conduction equation was solved with some boundary conditions, and the solution obtained was used as the principle of the present transient heating technique for determining the thermal diffusivity of the specimen. Additionally, a thermal analysis was made to satisfy a boundary condition involved in the principle, that is, the condition of radiative thermal insulation at the two end surfaces of the specimen. To verify the validity of the present technique, the thermal diffusivity of iron, whose thermophysical properties are well-known, was measured with the same apparatus as used in our previous work, and the experimental results are discussed. Moreover, thermal diffusivities of thermocouple materials, namely, constantan, chromel, and alumel, were measured by the technique in the temperature range of 360 to 680 K.     

Measurements of Thermal Diffusivity for Thin Slabs by a Converging Thermal Wave Technique

The measurement of thermal diffusivity for thin slabs by a converging thermal wave technique has been studied. Temperature variation at the center of the heat source ring that is produced by a pulsed high-power laser is detected by an infrared detector. A computer program based on the finite difference method is developed to analyze the thermal diffusivity of the slabs. Materials of both high thermal diffusivity (CVD diamond wafer) and low thermal diffusivity (stainless-steel foil) have been used for the measurements. The measurements have been performed by varying the size and the thickness of specimen. The converging thermal wave technique has proved to be a good method to measure the thermal diffusivity of a CVD diamond without breaking the wafer into small specimens. The technique can be applied for a small slab if the diameter of the slab is two times larger than that of the heat source ring. The sensitivity of thickness in measuring the thermal diffusivity is low for ordinary CVD diamond. The use of the converging thermal wave technique for nonhomogeneous, nonuniform, and anisotropic materials has been accomplished by applying the finite difference method.     

Thermal Diffusivity Measurements of Liquid Silicate Melts

The effect of structure on the thermal diffusivities/conductivities for liquid silicates have been summarized based on recent experimental work carried out by the Royal Institute of Technology, Stockholm and the Tokyo Institute of Technology using the laser-flash and the hot-wire methods, respectively. In the former case, the effective thermal diffusivity was measured by a three-layer method. The relationship proposed by Mills that the thermal conductivity of silicates increases with a decrease in the ratio of NBO/T (number of non-bridging oxygens per tetrahedrally coordinated atom) has been well supported by the effective thermal diffusivity data for the liquid CaO-Al₂O₃-SiO₂ slags. However, it has been shown that for the slags having a higher CaO/Al₂O₃ ratio, the effective thermal diffusivity is roughly constant independent of the ratios of NBO/T. It has been concluded that when the silicate network is largely broken down, the phonon mean free path is not affected by the structure. It has been found by the hot-wire method that the magnitudes of thermal resistivity are in the hierarchy Li₂O-SiO₂2O-SiO₂2O-SiO₂ despite their similar values of NBO/T. It has been concluded that the ionicity of non-bridging oxygen ions is also a factor controlling the thermal conductivity of silicates as well as the number of broken bridges in the silicate network. The effective thermal diffusivity was measured for the CaO-Al₂O₃-SiO₂-FeO system to elucidate the radiation contribution to the effective thermal diffusivity. It has been found that the effective thermal diffusivity increases with an increase in FeO content. It can be considered that the strong absorption and emission within the liquid slag films caused by the Fe²⁺ ions enhances the photon heat transfer.     

Measurements of Thermal Conductivity and Thermal Diffusivity of CVD Diamond

The thermal conductivity of natural, gem-quality diamond, which can be as high as 2500 Wm^–1 K^–1 at 25°C, is the highest of any known material. Synthetic diamond grown by chemical vapor deposition (CVD) of films up to 1 mm thick exhibits generally lower values of but under optimal growth conditions it can rival gem-quality diamond with values up to 2200 Wm^–1 K^–1. However, it is polycrystalline and exhibits a columnar microstructure. Measurements on free-standing CVD diamond, with a thickness in the range 25–400 m, reveal a strong gradient in thermal conductivity as a function of position z from the substrate surface as well as a pronounced anisotropy with respect to z. The temperature dependence of in the range 4 to 400 K has been analyzed to determine the types and numbers of phonon scattering centers as a function of z. The defect structure, and therefore the thermal conductivity, are both correlated with the microstructure. Because of the high conductivity of diamond, these samples are thermally thin. For example, laser flash data for a 25-m-thick diamond sample is expected to be virtually the same as laser flash data for a 1-m-thick fused silica sample. Several of the techniques described here for diamond are therefore applicable to much thinner samples of more ordinary material.     

Measurements of the Thermal Conductivity and Thermal Diffusivity of Polymer Melts with the Short-Hot-Wire Method

In this paper, the thermal conductivity and thermal diffusivity of four kinds of polymer melts were measured by using the transient short-hot-wire method. This method was developed from the hot-wire technique and is based on two-dimensional numerical solutions of unsteady heat conduction from a wire with the same length-to-diameter ratio and boundary conditions as those in the actual experiments. The present method is particularly suitable for measurements of molten polymers where natural convection effects can be ignored due to their high viscosities. The results have shown that the present method can be used to measure the thermal conductivity and thermal diffusivity of molten polymers within uncertainties of 3 and 6%, respectively. Further, the thermal conductivity and thermal diffusivity of solidified samples were also measured and discussed.     

Absolute Measurements of the Thermal Diffusivity of Aqueous Solutions of Sodium Chloride

The laser-induced thermal grating technique was used to determine the thermal diffusivity of aqueous solutions of sodium chloride. In comparison with conventional measurement methods, this noninvasive optical technique has the advantage that no sensors need to be inserted in the sample. Therefore, this technique is especially suitable for the measurement of electrically conducting and corrosive liquids. The aqueous solutions studied have weight fractions of 5, 10, 15, and 20% sodium chloride. Measurement results for the thermal diffusivity are presented for aqueous solutions of sodium chloride in the temperature range 293 to 373 K at atmospheric pressure.     

Thermal Diffusivity Measurements in Edible Oils using Transient Thermal Lens

Time resolved thermal lens (TL) spectrometry is applied to the study of the thermal diffusivity of edible oils such as olive, and refined and thermally treated avocado oils. A two laser mismatched-mode experimental configuration was used, with a He–Ne laser as a probe beam and an Ar⁺ laser as the excitation one. The characteristic time constant of the transient thermal lens was obtained by fitting the experimental data to the theoretical expression for a transient thermal lens. The results showed that virgin olive oil has a higher thermal diffusivity than for refined and thermally treated avocado oils. This measured thermal property may contribute to a better understanding of the quality of edible oils, which is very important in the food industry. The thermal diffusivity results for virgin olive oil, obtained from this technique, agree with those reported in the literature.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5-8, 2005, Bratislava, Slovak Republic.     

Simultaneous Measurements of the Thermal Conductivity and Thermal Diffusivity of Molten Salts with a Transient Short-Hot-Wire Method

A transient short-hot-wire technique has been successfully used to measure the thermal conductivity and thermal diffusivity of molten salts (NaNO₃, Li₂CO₃/K₂CO₃, and Li₂CO₃/Na₂CO₃) which are highly corrosive. This method was developed from the hot-wire technique and is based on two-dimensional numerical solutions of unsteady heat conduction from a short wire with the same length-to-diameter ratio and boundary conditions as those used in the actual experiments. In the present study, the wires are coated with a pure Al₂O₃ thin film by using a sputtering apparatus. The length and radius of the hot wire and the resistance ratio of the lead terminals and the entire probe are calibrated using water and toluene with known thermophysical properties. Using such a calibrated probe, the thermal conductivity and thermal diffusivity of molten nitrate are measured within errors of 3 and 20%, respectively. Also, the thermal conductivity of the molten carbonates can be measured within an error of 5%, although the thermal diffusivity can be measured within an error of 50%.     

Thermal Diffusivity Measurements of Thermographite

This paper presents results of measurements of a graphite proposed to serve as a thermophysical property reference or standard reference material. The reported measurements contribute to a program launched in 1999 by Anter Corp. with the objective to provide a replacement for the NIST thermal property reference material RM AXM-5Q graphite whose supplies were being exhausted. Measurements of the thermal diffusivity performed on five specimens taken from different positions within a large graphite block between room temperature and 1300 K were in good mutual agreement. Measurements of NIST reference AXM-5Q graphite sample supplied to minimize effects of different contributors to a common base were also in good agreement, both with the NBS reference function established by Hust in 1984 and contributions to the NBS project from the Vinca Institute of Nuclear Sciences carried out in 1979. The influence of different data reduction techniques on the measured thermal diffusivity values is illustrated and discussed.     

Experimental Study on the Effective Thermal Conductivity and Thermal Diffusivity of Nanofluids

This paper reports measurements of the effective thermal conductivity and thermal diffusivity of various nanofluids using the transient short-hot-wire technique. To remove the influences of the static charge and electrical conductance of the nanoparticles on measurement accuracy, the short-hot-wire probes are carefully coated with a pure Al₂O₃ thin film. Using distilled water and toluene as standard liquids of known thermal conductivity and thermal diffusivity, the length and radius of the hot wire and the thickness of the Al₂O₃ film are calibrated before and after application of the coating. The electrical leakage of the short-hot-wire probes is frequently checked, and only those probes that are coated well are used for measurements. In the present study, the effective thermal conductivities and thermal diffusivities of Al₂O₃/water, ZrO₂/water, TiO₂/water, and CuO/water nanofluids are measured and the effects of the volume fractions and thermal conductivities of nanoparticles and temperature are clarified. The average diameters of Al₂O₃, ZrO₂, TiO₂, and CuO particles are 20, 20, 40, and 33 nm, respectively. The uncertainty of the present measurements is estimated to be within 1% for the thermal conductivity and 5% for the thermal diffusivity. The measured results demonstrate that the effective thermal conductivities of the nanofluids show no anomalous enhancement and can be predicted accurately by the model equation of Hamilton and Crosser, when the spherical nanoparticles are dispersed into fluids.     

Multidimensional Flash Diffusivity Measurements of Orthotropic Materials

A generalization of the radial flash technique is presented whereby the thermal diffusivity of an orthotropic solid is measured in directions parallel and perpendicular to the flash source. The theoretical formulation is based on a Green's function approach which assumes a general orthotropic solid with three mutually orthogonal thermal diffusivities (or conductivities). Using this approach, a solution to this problem is presented which can be used to develop solutions for arbitrary pulse waveforms and incident geometries. Analytical and numerical results are presented for two-dimensional and three-dimensional cases of finite and semiinfinite solids. Characteristic equations which describe the ratio of the temperatures at two points along a principal axis are given. The equations show excellent agreement with numerical predictions as well as experimental results. A parameter estimation approach is given which improves on the accuracy of the radial flash technique in the determination of thermal diffusivity from experimental data.     

New Apparatus for Thermal Diffusivity and Specific Heat Measurements at Very High Temperature

The thermal characterization of a material under its conditions of use (temperature, pressure, etc.) is an essential step to check its adequacy with regard to a specific application and to predict its behavior. For needs of material characterization, Commissariat à l’Energie Atomique (CEA) has developed with Laboratoire National de Métrologie et d’Essais (LNE) a new apparatus to study thermophysical properties of solid materials in the range from 300 to 3300 K. This setup allows measurements of either the thermal diffusivity by the laser flash method or the specific heat by drop calorimetry. First, thermal diffusivity measurements have been performed on Armco iron and POCO AXM-5Q1 graphite. The measured values are in agreement with results obtained by other laboratories with a relative deviation of less than 6%.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

A Method for Thermal Diffusivity Determination of Thermal Insulators

A so-called “three-point” (3P) method has been developed for thermal diffusivity measurements of thermal insulating materials. One side of a cylindrical specimen, sandwiched between two thin metal plates, is subjected to intense light from an incandescent lamp to generate a thermal perturbance. The temperature response is measured in three locations along the test specimen. Thermocouples are located at the front and rear faces of the specimen, and the third is placed inside the specimen at a known location. The two outside temperatures are used as boundary conditions, and the unknown thermal diffusivity is calculated from the third temperature versus time curve. The method combines the advantages of rapid transient non-contact heating methods with the well-defined boundary conditions of steady-state methods. The results of the 3P method are compared with those from steady-state methods for a micro-porous insulation material and for a honeycomb structure.     

Thermal Diffusivity Measurements in Fluids Containing Metallic Nanoparticles using Transient Thermal Lens

Thermal diffusivity measurements are carried out in nanofluids, solutions containing gold nanoparticles (~ 10–40 nm size), using the mode-mismatched dual-beam thermal lens technique. An Ar+ laser is used as the heating source, and an intensity stabilized He–Ne laser serves as the probe beam. This technique provides a reliable photothermal alternative for measuring thermal diffusivities of nanofluids and semitransparent samples. The characteristic time constant of the transient thermal lens was obtained by fitting the experimental data to the theoretical expression for the transient thermal lens. From this characteristic time, the fluid thermal diffusivity, which increases when the particle sizes increase was obtained. The size of the nanoparticles was obtained from transmission electron microscopy (TEM) analysis.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

Novel Transmission Open Photoacoustic Cell Configuration for Thermal Diffusivity Measurements in Liquids

In this paper the photoacoustic technique in the thermal-wave transmission configuration is applied to thermal diffusivity measurements in liquids. The one-dimensional heat diffusion problem involving three layers, and assuming surface absorption only, is solved for this goal. Linear relations among the photoacoustic amplitude (on a semi-log scale) and phase, as functions of the liquid sample thickness, are shown in each case. An analytical procedure involving linear fits to the experimental data is developed to produce two independent values for thermal diffusivity. The thermal diffusivity of three homogeneous liquids (distilled water, ethylene-glycol, and olive oil) was measured, and excellent agreement was obtained between results from both the amplitude and phase, as well as with thermal-diffusivity values reported in the literature.     

Uncertainty of Thermal Diffusivity Measurements by Laser Flash Method

The laser-pulse method is a well-established nonsteady-state measurement technique for measuring the thermal diffusivity, a, of solid homogeneous isotropic opaque materials. BNM-LNE has developed its own bench based on the principle of this method in which the thermal diffusivity is identified according to the “partial time moments method.” Uncertainties of thermal diffusivity by means of this method have been calculated according to the ISO/BIPM “Guide to the Expression of Uncertainty in Measurement.” Results are presented for several cases (Armco iron, Pyroceram 9606) in the temperature range from 20 to 800°C. The relative expanded (k = 2) uncertainty of the thermal diffusivity determination is estimated to be from ±3 to ±5%, depending on the material and the temperature. Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22–27, 2003, Boulder, Colorado, U.S.A.     

New Transient Hot-Bridge Sensor to Measure Thermal Conductivity, Thermal Diffusivity, and Volumetric Specific Heat

A high sensitivity thermoelectric sensor to measure all relevant thermal transport properties has been developed. This so-called transient hot bridge (THB) decidedly improves the state of the art for transient measurements of the thermal conductivity, thermal diffusivity, and volumetric specific heat. The new sensor is realized as a printed circuit foil of nickel between two polyimide sheets. Its layout consists of four identical strips arranged in parallel and connected for an equal-ratio Wheatstone bridge. At uniform temperature, the bridge is inherently balanced, i.e., no nulling is required prior to a run. An electric current makes the unequally spaced strips establish an inhomogeneous temperature profile that turns the bridge into an unbalanced condition. From then on, the THB produces an offset-free output signal of high sensitivity as a measure of the properties mentioned of the surrounding specimen. The signal is virtually free of thermal emf’s because no external bridge resistors are needed. Each single strip is meander-shaped to give it a higher resistivity and, additionally, segmented into a long and short part to compensate for the end effect. The THB closely meets the specific requirements of industry and research institutes for an easy to handle and accurate low cost sensor. As the key component of an instrument, it allows rapid thermal-conductivity measurements on solid and fluid specimens from 0.02 to 100 W· m⁻¹·K⁻¹ at temperatures up to 250°C. Measurements on some reference materials and thermal insulations are presented. These verify the preliminary estimated uncertainty of 2% in thermal conductivity.     

Thermal Diffusivity of Semitransparent Materials Determined by the Laser-Flash Method Applying a New Analytical Model

We have developed an analytical model to determine the thermal diffusivity of nonscattering materials from samples with low optical thickness and opaque boundaries with arbitrary emissivities. The paper outlines the new analytical model and describes measurements on two samples: a microscope slide glass and a high-grade fused quartz plate. Results show that the new model applied to measurements on gold- or graphite-coated samples leads to the same results as if a conventional model is used on gold-coated samples.