Numerical simulation and error analysis for thermal diffusivity measurements using laser-induced thermal grating technique

The laser-induced thermal grating technique has been used to determine the thermal diffusivity of liquids and liquid mixtures. But the dynamic behaviour of the transient thermal grating has not yet been thoroughly investigated, and the systematic errors, which result from the departures from one-dimensional heat conduction, have scarcely been studied quantitatively. In this paper. a three-dimensional numerical simulation and results of the transient thermal grating technique are presented, which enable a good understanding of the dynamic behaviour of the transient thermal grating. The results of this simulation are important for the proper design of the experimental setup to keep the systematic errors for the diffusivity measurement small. Based on the simulation method, the systematic errors were analyzed quantitatively. Here, the following effects were studied: (I) sample thickness, (2) intersection angle, (3) absorption, (4) Gaussian beam intensity distribution and focusing of heating laser beam, and (5) heating pulse duration and laser power. This error analysis makes it possible to specify the criteria for optimum measuring conditions, to correct the measured thermal-diffusivity values for systematic errors, and to estimate the accuracy of the measurements.     

Measurement of the thermal diffusivity and speed of sound of hydrothermal solutions via the laser-induced grating technique

We use the laser-induced grating technique to measure the thermal difusivity and speed of sound of hydrothermal solutions. In this noninvasive optical technique, a transient grating is produced in the hydrothermal solution by optical absorption from two crossed, time-coincident nanosecond laser pulses. The grating is probed by measuring the diffraction efficiency of a third laser beam. The grating relaxes via thermal diffusion, and the thermal diffusivity is determined by measuring the decay of the grating diffraction efficiency as a function of of the pump-probe delay time. In addition, intense pump pulses produce counterpropagating acoustic waves that appear as large undulations in the transient grating decay spectrum. The speed of sound in the sample is simply the grating fringe spacing divided by the undulation period. The cell is made from a commercial high-pressure fitting and is equipped with two diamond windows for optical access. Results are presented for dilute dye/water solutions withT=400° and pressures between 20 and 70 MPa.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Measurement of the thermal diffusivity of liquids with a laser-induced thermal-grating technique: An experimental investigation of systemtic errors

The laser-induced thermal-grating; technique has been developed to determine the thermal diffusivity of liquids and liquid mixtures. Here we report an experimental investigation of the systematic errors. which are caused by departures from one-dimensional heat conduction. In particular. the effects of cell wall and intersection angle of the heating beams have been thoroughly studied through measurements on toluene and methanol. A comparison has been made between experimental results and numerical predictions. The excellent agreement between experiments and theoretical predictions shows that the theoretical error analysis can be used for the estimation and accurate correction of systematic errors in measurements by this technique.     

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 of Aqueous Solutions of Magnesium Chloride in the Temperature Range from 294 to 371 K

The thermal diffusivity of aqueous solutions of magnesium chloride was determined in the temperature range 294 to 371 K and at atmospheric pressure. Using a noninvasive optical technique—laser-induced thermal grating (LTG)—the measurements were carried out in aqueous solutions of weight fractions of 5, 10, 15, and 20% magnesium chloride. The measurement results for the aqueous solutions are presented as a function of temperature and weight fraction.     

Measurement of the thermal diffusivity of molten KCl up to 1000°C by the forced Rayleigh scattering method

This paper describes measurement of the thermal diffusivity of molten KCl in the temperature range from 804 to 1030°C by the forced Rayleigh scattering method. In this contact-free optical measuring technique for the thermal diffusivity of liquids, a sample needs to be colored by the admixture of a dye for suitable absorption of a heating laser beam. The dye substances employed are CoCl₂ and NiCl₂, which were chosen through the experimental evaluation. The accuracy is estimated to be ±7% for molten KCl colored with NiCl₂. The results converted to thermal conductivity show one of the smallest values among other previous data; the difference is a factor of four. The present study demonstrates the promising applicability of the forced Rayleigh scattering method to the measurement of high-temperature molten salts, which has never be attained by other conventional methods.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Simultaneous measurement of thermal conductivity and thermal diffusivity of solids by the parallel-wire method

An improved parallel-wire technique for simultaneous measurement of thermal conductivity and thermal diffusivity is presented. The deviation between experimental results and recommended (or another author's) values is less than 5% for fused quartz and refractory brick.     

Absolute measurements of the thermal conductivity of mixtures of alcohols with water

New absolute measurements of the thermal conductivity of mixtures of methanol, ethanol, and propanol with water are presented. The measurements were performed in a tantalum-type transient hot-wire instrument at atmospheric pressure, in the temperature range 300–345 K. The overall uncertainty of the reported values is estimated to be less than ±0.5%, an estimate confirmed by measurements of the thermal conductivity of water. The mixtures with water studied have compositions of 25. 50, and 75%, by weight, of methanol and ethanol and 50%, by weight, of propanol. A recently proposed semiempirical scheme for the prediction of the thermal conductivity of pure liquids is extended to allow the prediction of the thermal conductivity of these mixtures from the pure components, as a function of both composition and temperature.     

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.     

Measurement of the thermal diffusivity by the thermal wave method using low-power heat sources

The errors in measuring the thermal diffusivity by the plane thermal wave method are considered as a function of the thermal flux power density. The minimum values of the thermal flux power density required for measurements with a specified error and the optimum parameters of the samples and of the heat source are determined. __________ Translated from Izmeritel’naya Tekhnika, No. 8, pp. 44–46, August, 2007.     

The thermal diffusivity of argon in the critical region

In this paper experimental results on the thermal diffusivity of argon in the supercritical region are reported. Five isotherms were investigated at 150.90, 153.16, 163.15, 173.14, and 188.14 K, in the pressure range from 2 to 13 MPa, corresponding to density variations from 90 to 800kg · m^–3. The experimental thermal diffusivity data are compared with theoretical predictions. The corresponding thermal conductivity coefficients are calculated and correlated with respect to the spinodal curve.     

Measurements of the thermal conductivity of aqueous LiBr solutions at pressures up to 40 MPa

This paper describes absolute measurements of the thermal conductivity of aqueous LiBr solutions in the concentration range 5 to 15m (molality), the temperature range 30 to 100°C, and the pressure range 0.1 to 40 MPa. The measurements have been performed with the aid of a transient hot-wire apparatus employing a thin tantalum wire coated with an anodic tantalum pentoxide insulation layer. In using the tantalum wire, a modification of the bridge circuit has been made to keep the electric potential of the wire always higher than the ground level in order to protect the insulation layer from breakdown. The experimental data, which have an estimated accuracy of ±0.5%, have been correlated in terms of the polynomials of concentration, temperature, and pressure for practical use. Also, it has been found that the pressure coefficient of the thermal conductivity decreases with increasing concentrations.     

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.     

Measurement of transient behavior of the thermal diffusivity of flowing polymer melt

Molecular orientation of polymer molecules created by shear force due to the flow of the polymer melt in a duct rapidly relaxes after the change in the shear rate. This relaxation causes the changes in anisotropic behavior of mechanical. thermal, and optical properties which have strong effect in precision forming of casted polymer products. Among these properties, thermal diffusivity is one of the most difficult properties to measure by the conventional techniques. The present paper describes and discusses the subsecond measurement of relaxation characteristics in thermal dilfusivity anisotropy of flowing polymer melt in conjunction with measurements of some typical flow characteristics. The method used was the forced Rayleigh scattering method, an optical method which was developed and modified by the authors' group for applying to oriented polymer materials. The measuring lime of I ms can trace the relaxation occurred in the order of several seconds. Measured results of thermal diffusivity anisotropy were compared with transient characteristics of the now and quantitatively showed a good agreement with estimated behavior of oriented polymer molecules.Paper presented at the Fourth International Workshop on Subsecond Thermophysics, June 27–39, 1995, Köln, Germany.     

Thermal diffusivity and thermal conductivity of steam in the crossover region

In this paper, we present a comparison of the thermal diffusivity and thermal conductivity data of steam in the temperature range 0.02 K<T-T _c< 140 K with a recent formulation of crossover from singular to regular behavior of the transport properties of fluids. We have used two sets of experimental data previously obtained by the authors. The agreement between experimental and calculated data is good.     

Thermal diffusivity of solids with a low expansion coefficient: A dilatometric technique

A dilatometric method is presented, suitable to obtain both thermal diffusivity and conductivity of low-conducting solids with a low expansion coefficient. The repeatibility of the measurements of thermal conductivity is 3%, whereas that for diffusivity is 5 %. Data for fused silica at room temperature are given, consistent with those reported in the literature. Since the method is based on detecting the thermal expansion of a copper disk in thermal contact with the specimen, its range of applicability is linked to the sensitivity by which the dilation of copper can be measured: no difficulty arises between liquid nitrogen and 1000°C.     

Experimental apparatus for measuring the thermal diffusivity of pure fluids at high temperatures

Dynamic light scattering represents a suitable method for measuring the thermal diffusivity of optically transparent fluids. The classic application of the method is the immediate vicinity around the critical point due to its dependence upon the intensity of scattered light and its high sensitivity to undesired light scattering. By means of subsequent modifications of the experimental setup, we have been able to expand this region of applicability over the last 12 years and could systematically investigate numerous substances and their binary mixtures within a temperature range of 280 K<T<350 K. Our planned investigation of fluids suitable for ORC-HP-technology necessitates performing measurements at higher temperatures and pressures. The experimental apparatus newly designed for this purpose is capable of sustaining a relatively high temperature constance at temperatures up to 700 K. Factors restricting the measurable range of state and their influence on the design of the sample cell are discussed.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Measurement of thermal diffusivity and anisotropy of plasma-sprayed coatings

The thermal diffusivity of free-standing tungsten and zirconia plasma-sprayed coatings was measured in the directions parallel and perpendicular to their surface. The parallel thermal diffusivity was evaluated by a double-sensing Laplace-transform technique and compared to the perpendicular values obtained by the (lash technique. Ratios between the parallel and the perpendicular thermal diffusivity values were in the range of 1.1 to 1.5 for zirconia and 4 to 6 for tungsten. The results are discussed in terms of the coating thickness and microstructure.On leave from Laboratoire d'Énergetique et de Méchanique Théorique et Appliquée, B.P. 160, 54504 Vandoeuvre les Nancy, France.     

Experimental determination of the thermal diffusivity of molten alkali halides by the forced Rayleigh scattering method. II. Molten NaBr,KBr, RbBr,and CsBr

This is a companion to an earlier paper (on molten alkali metal chlorides) which gives experimental results for the thermal diffusivity of four molten alkali metal bromides: NaBr, KBr, RbBr, and CsBr. The measurements were performed with a forced Rayleigh scattering instrument at temperatures up to 1326 K. The overall uncertainty in the measured thermal diffusivity is estimated to be ±3 to ±11%, depending on the measured salts. The results converted to thermal conductivity show one of the smallest values among other earlier experimental data obtained mainly by the steady-state methods. It is also found that the temperature dependence of the thermal conductivity is weakly negative.     

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.