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.     

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.     

Measurement of thermophysical properties of molten salts: Mixtures of alkaline carbonate salts

The purpose of this study is to develop measuring methods for the thermal diffusivity, the specific heat capacity, and the density of molten salts, as well as to measure these properties of mixtures of alkaline carbonate salts. The thermal diffusivity is measured by the stepwise heating method. The sample salt is poured into a thin container, and as a result, a three-layered cell is formed. The thermal diffusivity is obtained from the ratio of temperature rises at different times measured at the rear surface of the cell when the front surface is heated by the stepwise energy from an iodine lamp. The specific heat capacity is measured using an adiabatic scanning calorimeter. The density is measured by Archimedes' principle. Thermal conductivity is determined from the above properties. Measured samples are Li₂CO₃-K₂CO₃ (42.7–57.3, 50.0-50.0, and 62.0-38.0 mol%).Invited paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Experimental determination of the thermal conductivity of molten pure salts and salt mixtures

The thermal conductivity of some molten salts was measured at atmospheric pressure, using the coaxial cylinder method. The pure compounds NaCO₃, KNO₃, and NaNO₂, the equimolar mixture NaNO₃-KNO₃, and HITEC, which is a three-component mixture, NaNO₃-NaNO₂-KNO₃ (0.07-0.40-0.53 in weight), were investigated. For mixtures, it was found that the experimental thermal conductivity coefficients are in agreement with calculated values using a simple linear mixing law. The thermal diffusivity was calculated and compared with experimental data.     

Experimental determination of the thermal diffusivity of molten alkali halides by the forced Rayleigh scattering method. I. Molten LiCl,NaCl, KCl,RbCl, and CsCl

As a series of experimental determinations of the thermal diffusivity of molten alkali halides, this paper describes measurements on five molten alkali metal chlorides (LiCl, NaCl, KCl, RbCl, and CsCl) in the temperature range up to 1440 K by the forced Rayleigh scattering method. K₂Cr₂O₇ is employed as a dye substance to color the transparent molten salts. The accuracy is estimated to be ± 4 to ±11 % depending on the measured salts. In comparison with the present results converted into thermal conductivity, most of the previous experimental data obtained by steady-state methods show larger values, up to about five times, which may be due to the systematic error caused by the presence of convection and radiation. It is found that the thermal conductivity of these series of molten alkali metal chlorides decreases with increasing molecular weight, and their temperature coefficients are weakly negative.     

Thermal diffusivity and conductivity of Li2ZrO3 using the modulated electron beam technique

Thermal diffusivity and thermal conductivity of three Li₂ZrO₃ specimens with two different density values, 82.6 and 87% theoretical density, have been measured between 350 and 900°C. The modulated electron beam thermal diffusivity method was used. Heating the specimens above some 850°C but below 900°C results in a reversible increase in both the diffusivity and the conductivity. When heating to higher temperatures generally still higher increases are noticed but measurements become rapidly unstable and irreversible.     

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 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.     

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.     

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.     

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.     

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 of gaseous HFC-134a,HFC-143a,HCFC-141b,and HCFC-142b

The thermal conductivity of new environmentally acceptable fluorocarbons HFC-134a (CH₂FCF₃), HFC-143a (CH₃CF₃), HCFC-141b (CH₃CCl₂F), and HCFC-142b (CH₃CCl₂F) in the gaseous phase has been measured in the temperature range 293–353 K at pressures up to 4 MPa. The thermal conductivity has been measured with a coaxial-cylinder cell on a relative basis. The apparatus was calibrated with He, Ne, Ar, Kr, N₂, CH₄, and SF₆ as reference fluids. The uncertainty of the experimental data obtained is estimated to be within 2% except for the uncertainty associated with the reference thermal-conductivity values. The excess thermal conductivity has been correlated satisfactorily as a function of density.     

Measurement of transport properties of high-temperature fluids

High-temperature fluids often show interesting behavior and have important industrial applications, however, their thermophysical properties are extremely difficult to measure. Sometimes there are no measuring methods available, despite the fact that the great industrial demand for data on these property data at high temperatures is intense in recent years. In the present paper, five examples of approaches to measure transport properties of high temperature fluids are described. They include measurements of the viscosity of high-temperature melts by the oscillating-cup method, of the viscosity of vapors of H₂O and D₂O by the capillary method, of the thermal conductivity of molten salts by the transient hot-wire method, and of the thermal diffusivity by the optical method and of the thermal conductivity of high temperature gases by the shocktube method.     

Thermal conductivity and heat capacity of liquid toluene at temperatures between 255 and 400 K and at pressures up to 1000 MPa

The thermal conductivity and heat capacity c _p of liquid toluene have been measured by the ac-heated wire method up to 1000 MPa in the temperature range from 255 to 400 K. The total error of thermal conductivity measurements is estimated to be about 1 %, and the precision 0.3 %. The heat capacity per unit volume, pc _p, obtained directly from the experiment is uncertain within 2 or 3%. The vs p isotherms are found to cross one another at approximately 700 MPa. The minima in the pressure (or volume) dependence of c_p of toluene are evident at all temperatures investigated.     

The Thermal Conductivity, Thermal Diffusivity, and Specific Heat of Liquid n-Pentane

The thermal conductivity and thermal diffusivity of liquid n-pentane have been measured over the temperature range from 293 to 428 K at pressures from 3.5 to 35 MPa using a transient hot-wire instrument. It was determined that the results were influenced by fluid thermal radiation, and a new expression for this effect is presented. The uncertainty of the experimental results is estimated to be better than ±0.5% for thermal conductivity and ±2% for thermal diffusivity. The results, corrected for fluid thermal radiation, are correlated as functions of temperature and density with a maximum uncertainty of ±2% for thermal conductivity and ±4% for thermal diffusivity. Derived values of the isobaric specific heat are also given.     

Thermal conductivity of gaseous fluorocarbon refrigerants R 12, R 13, R 22, and R 23, under pressure

The thermal conductivity of four gaseous fluorocarbon refrigerants has been measured by a vertical coaxial cylinder apparatus on a relative basis. The fluorocarbon refrigerants used and the ranges of temperature and pressure covered are as follows: R 12 (Dichlorodifluoromethane CCl₂F₂): 298.15–393.15 K, 0.1–4.28 MPa R 13 (Chlorotrifluoromethane CClF₃): 283.15–373.15 K, 0.1–6.96 MPa R 22 (Chlorodifluoromethane CHClF₂): 298.15–393.15 K, 0.1–5.76 MPa R 23 (Trifluoromethane CHF₃): 283.15–373.15 K, 0.1–6.96 MPaThe apparatus was calibrated using Ar, N₂, and CO₂ as the standard gases. The uncertainty of the experimental data is estimated to be within 2%, except in the critical region. The behavior of the thermal conductivity for these fluorocarbons is quite similar; thermal conductivity increases with increasing pressure. The temperature coefficient of thermal conductivity at constant pressure, (/T) _p , is positive at low pressures and becomes negative at high pressures. Therefore, the thermal conductivity isotherms of each refrigerant intersect each other in a specific range of pressure. A steep enhancement of thermal conductivity is observed near the critical point. The experimental results are statistically analyzed and the thermal conductivities are expressed as functions of temperature and pressure and of temperature and density.     

Thermal Conductivity of a Simulated Fuel with Dissolved Fission Products

The thermal diffusivity of a simulated fuel with fission products forming a solid solution was measured using the laser-flash method in the temperature range from room temperature to 1673 K. The density and the grain size of the simulated fuel with the solid solutions used in the measurement were 10.49 g · cm⁻³ (96.9% of theoretical density) at room temperature and 9.5 μm, respectively. The diameter and thickness of the specimens were 10 and 1 mm, respectively. The thermal diffusivity decreased from 2.108 m² · s⁻¹ at room temperature to 0.626 m² · s⁻¹ at 1673 K. The thermal conductivity was calculated by combining the thermal diffusivity with the specific heat and density. The thermal conductivity of the simulated fuel with the dissolved fission products decreased from 4.973 W · m⁻¹ · K⁻¹ at 300 K to 2.02 W · m⁻¹ · K⁻¹ at 1673 K. The thermal conductivity of the simulated fuel was lower than that of UO₂ by 34.36% at 300 K and by 15.05% at 1673 K. The difference in the thermal conductivity between the simulated fuel and UO₂ was large at room temperature, and decreased with an increase in temperature. Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

The thermal conductivity of the molten NaNO3-KNO3 eutectic between 525 and 590 K

Molten salts are one of the few remaining classes of fluids for which standardquality (±1% accuracy) data on thermal conductivity have not hitherto been available. We have therefore developed a new apparatus based on the transient hot-wire technique to obtain reference-quality measurements of the thermal conductivity of molten salts at high temperatures. Liquid metal-filled quartz capillaries served as insulated hot wires in our method, and in addition, a two-wire technique was used in order to obtain absolute values of the thermal conductivity. New data for the NaNO₃-KNO₃ eutectic between 525 and 590 K are reported in this paper and comparisons with other recent measurements are shown.     

Thermal diffusivity measurement by the transient hot-wire technique: A reappraisal

The theory of the transient hot-wire technique for thermal conductivity measurements is reassessed in the special context of thermal diffusivity measurements. A careful examination of the working equation and an error analysis are employed to identify the principal sources of error. Notwithstanding earlier claims to the contrary, the best precision that can be attained in thermal diffusivity measurements is of the order of ±3%, while the accuracy is inevitably poorer. Experimental evidence is adduced from two different instruments that supports the analysis given here. Although the technique cannot yield values of the thermal diffusivity, k, as accurate as can be achieved by the use of the best possible individual values of ,, and C _p in the relation k=/C _p, the simplicity of the technique makes it attractive for many purposes. It is even possible to derive values of the isobaric heat capacity C _p for many fluids not available from other methods.