A dilatometric method to measure the thermal diffusivity of nonmetallic liquids

A new method to measure the thermal diffusivity of liquids is presented. It requires determination of the time dependence of the thermal expansion of the liquid when it is subjected to a heat source at the top of the cell containing the liquid. The high accuracy of the method (about 3%) is due to an essential reduction of convective currents and also to the absence of temperature detectors, which generally introduce unwanted perturbations on the thermal Field.Nomenclature Thermal conductivity - c Specific heat - Density - c = specific heat x density - h Newton coefficient - Thermal diffusivity - T, 0 Temperature - tV Electric signal - Calibration coefficient - _exp, _th Volume change of the liquid     

A Universal Laser-Pulse Apparatus for Thermophysical Measurements in Refractory Materials at Very High Temperatures

This paper presents a new experimental technique enabling thermophysical measurements to be carried out at very high temperatures in a very simple and small pressurized vessel in which the sample is heated by a continuous wave laser, and subsequently subjected to a short temperature pulse. The adopted method is essentially an extension of the laser-flash technique, widely used for thermal diffusivity measurements, whereby, in addition, the heat capacity and, hence, the thermal conductivity, , are simultaneously evaluated from the pulse analysis. Results are presented for the thermal diffusivity and heat capacity of graphite, zirconia, and uranium dioxide up to temperatures above 3000 K.     

Anisotropic Thermal Properties of Solid Polymers

This paper discusses the thermal conduction anisotropy in polymers by reviewing currently available theories and experimental methods for studying oriented polymers. The anisotropic thermal conductivity and diffusivity of oriented polymers originate from the difference between the thermal energy transport mechanisms parallel and perpendicular to their molecules. Recent progress in the development of experimental techniques for studying the thermal conduction anisotropy of polymer films with thicknesses near 1 m is discussed in connection with modern microelectronics applications. The data obtained from these techniques are expected to serve for developing sophisticated thermal conduction theories that account for the polymer anisotropy and for performing precise thermal design of organic electronic devices that incorporate highly oriented polymer structures.     

Low-temperature anisotropy of thermal conductivity of tin single crystals doped with zinc

The thermal conductivity of tin single crystals with zinc admixtures has been measured in the temperature range 3.5–25 K for concentrations up to 0.1 wt%. The anisotropy of thermal conductivity for two orientations, [001] and [010], has been determined. It was found that the influence of zinc admixture on the thermal conductivity anisotropy is of a complex, temperature-dependent character.Nomenclature T ₁ T ₂ Temperature differences in the specimen - Thermal conductivity coefficient - W Thermal resistivity - A, B, C Constants in Eq. (1) - T Temperature - ^th Residual electrical resistivity calculated from W-F law - ₀ Residual electrical resistivity from measurements - L ₀ Lorenz constant - _th Anisotropy coefficient of thermal conductivity - _el Anisotropy coefficient of electrical conductivity - c Admixture concentration     

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.     

Measurement of temperature in a non-steady-state gas flow

A method is described for measuring the temperature of a non-steady-state gas flow with a thermocouple which is an inertial component of the first order.Notation T*_f non-steady-state gas flow temperature - T_t thermosensor temperature - thermal inertia factor of thermosensor - time - C total heat capacity of thermosensor sensitive element - S total heat-exchange surface between sensitive element and flow - heat-liberation coefficient - temperature distribution nonuniformity coefficient in sensitive element - Re, Nu, Pr, Bi, Pd hydromechanical and thermophysical similarity numbers - P^* total flow pressure - P static flow pressure - T^* total flow temperature - d_t sensitive element diameter - w gas flow velocity - flow density - flow viscosity - _f flow thermal conductivity - k gas adiabatic constant - R universal gas constant - M Mach number - T thermodynamic flow temperature - _o, _o and values at T=288°K - A, m, n, p, r coefficients - _c heat-liberation coefficient due to colvection - _r heat-liberation coefficient due to radiation - _b emissivity of sensitive element material - Stefan-Boltzmann constant - T_e temperature of walls of environment - _c, _r, _tc thermosensor thermal inertia factors due to convective, radiant, and conductive heat exchange - L length of sensitive element within flow - a thermal diffusivity of sensitive element material - _t thermal conductivity of sensitive element material Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 59–64, July, 1984.     

Measurement of thermal properties of iron oxide pellets

The thermal properties of iron oxide pellets of different porosity and prepared by reduction at different rates were investigated in the range of room temperature to about 800°C. The thermal diffusivity a was measured by a laser flash method and the specific heat C _p was measured by adiabatic scanning calorimetry. The thermal conductivity was calculated from the relation =aC p, where is the density of the specimen.For nonreduced iron oxide pellets, the thermal diffusivity and thermal conductivity decreased with increase in temperature and porosity. The specific heat increased with increasing temperature and there was a transformation point at which the specific heat reached a maximum. In prereduced iron oxide pellets, the thermal diffusivity and thermal conductivity were very small compared with the nonreduced pellets and they gradually increased with increasing temperature. The specific heat had a minimum and a maximum at about 300 and 600°C, respectively, and the scale of these features became smaller with increase in the reduction rate.Paper presented at the Fourth Japan Symposium on Thermophysical Properties, October 20–22, 1983, Yokohama, Japan.     

Thermal Conductivity of Sm3S4 System with Mixed Valence Sm Ions

The thermal conductivity () and electrical resistivity () of mixed-valence compound Sm₃S₄ have been measured in the temperature range 5 to 300 K. The present results and those presented previously [1] for the thermal conductivity between 80 to 850 K are interpreted in terms of the temperature-dependent fluctuating valence of Sm ions. Sm₃S₄ crystallizes in the cubic Th₃P₄ structure, and the cations with different valences occupy equivalent lattice sites. Divalent and trivalent Sm ions are randomly distributed in the ratio of 1:2 over all possible crystallographic cation positions (Sm²⁺ ₂Sm³⁺ ₂S^2– ₄). The behavior of the Sm₃S₄ lattice thermal conductivity _ph is extraordinary since valences of Sm ions are fluctuating (Sm³⁺Sm²⁺) with a temperature dependent frequency. In the interval 20 to 50 K (low hopping frequencies), _ph of Sm₃S₄ varies as _ph T ^–1 (it is similar to materials with static distribution of cations with different valences): at 95 to 300 K (average hopping frequencies 10⁷ to 10¹¹ Hz), _ph changes as _ph T ^–0.3 (it is similar to materials with defects). Defects in Sm₃S₄ appear because of local strains in the lattice by the electrons hopping from Sm²⁺ ions (with big ionic radii) to Sm³⁺ ions (with small ionic radii) and back (Sm²⁺Sm³⁺), at T>300 K (high hopping frequencies), _ph becomes similar to materials with homogenous mixed valence states [1].     

Measurement of thermal diffusivity of diamond by the light-induced thermal lattice method

The thermal diffusivity coefficient of natural diamonds is measured by optical induction of thermal diffraction lattices.Notation gc thermal conductivity coefficient - thermal diffusivity coefficient - diffraction efficiency - I_dif diffracted radiation intensity - I_Probe probe radiation intensity - probe radiation wavelength - c specific heat - Q surface energy density - thermal lattice relaxation time - thermal lattice period Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 745–748, May, 1989.     

A Multiscale Model for the Effective Thermal Conductivity Tensor of a Stratified Composite Material

Thermal modeling of composites has three essential objectives: (i) comprehension of their thermal behavior; (ii) composite scaling in order to satisfy specific requirements; and (iii) optimal analysis of experimental results from thermal characterization. For a complete study of the material, each of these three points must be taken into account at the fiber scale ( 10m), the yarn scale ( 1 mm), and the composite scale ( 10 cm). This work presents multi-scale modeling of the effective thermal conductivity tensor of a stratified composite material made from carbon fibers, phenolic resin, and carbon loads. The longitudinal and transverse thermal conductivities of the yarn are computed from optical microscopic imaging of the material. The isotropic thermal conductivity of the loaded matrix is computed by the Bruggeman model. Then, the thermal conductivity tensor is determined by a finite element method taking into account the morphology of the fabric. Computed values are close to experimental values measured by classical methods. Finally, analytical relations are proposed to obtain an efficient model which can be used in a multiphenomenon simulation of the composite structure.Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22--27, 2003, Boulder, Colorado, U.S.A.     

Thermal Diffusivity Measurement of Two-Layer Optical Thin-Film Systems Using Photoacoustic Effect1

In this study, we designed and developed two-layer antireflection (AR) optical coating samples on glass substrates, using different evaporation conditions of coating rates and substrate temperatures for two dielectric materials, MgF₂ and ZnS, with different refractive indices. The through-plane thermal diffusivity of these systems was measured using the photoacoustic effect. The optical thicknesses of MgF₂ and ZnS layers were fixed at 5/4 (=514.5 nm) and , respectively, and the thermal diffusivities of the samples were obtained from the measured amplitude of the photoacoustic signals by changing the chopping frequency of the Ar⁺ laser beam. The results demonstrated that the thermal diffusivity of the sample fabricated under the conditions of 10Å·s^–1 and 150°C had the maximum value and that the results were directly related to the microstructure of the film system.     

Measurement of the Thermal Diffusivity of Metallic Foils and Films by the Photoacoustic Method1

The thermal diffusivities of four kinds of metallic foils from 20 to 200m in thickness were measured by a photoacoustic method on the basis of the Rosencwaig and Gersho theory. The measured data for continuous foils of uniform microscopic structure almost agreed with the literature values. Measurements were also carried out on two kinds of metallic thin films with of 10m thickness produced by sputtering. The difference in thermal diffusivity between the foils and the sputtered films depended on the uniformity of the microscopic structure.     

Relations Between Transport Coefficients in Lennard–Jones Fluids and in Liquid Metals

Several simple approximate hard-sphere relations for transport coefficients are compared with the results of molecular dynamics (MD) simulations performed on Lennard–Jones (LJ) fluids. Typically the individual transport coefficients: self-diffusion coefficients, D, shear viscosity, _s, bulk viscosity, _B, and thermal conductivity, , agree within a factor of two of the exact results over the fluid and liquid parts of the phase diagram, which seems reasonable in view of the approximations involved in the models. We have also considered the ratio, /_s, and the product, D_s, for which simple analytic expressions exist in the hardsphere models. These two quantities also agree within a factor of two of the simulation values and hard sphere analytic expressions. Using time correlation functions, Tankeshwar has recently related the ratio /D to thermodynamic quantities, in particular, to the differences in specific heats, C _p – C _V, and to the isothermal compressibility, T. Using D and thermodynamic values taken solely from LJ MD simulations, his relation was tested and found to give typically better than ~20% agreement at liquid densities, deteriorating somewhat as density decreases into the gas phase. Finally liquid metals are considered. In this case, is dominated by its electronic contribution, which is related approximately to the electrical conductivity by the Wiedemann–Franz Law. Some theoretical results for the electrical conductivity of Na are referenced, which allow a semiquantitative understanding of the measured thermal conductivity of the liquid metal. Shear viscosity is also discussed and, following the work of Tosi, is found to be dominated by ionic contributions; Nevertheless, at the melting temperature of Na, a relation emerges between thermal conductivity, electrical resistivity and shear viscosity.     

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.     

The thermal conductivity of AISI 304L stainless steel

A compilation and critical analysis of the thermal conductivity () of AISI 304 stainless steel (SS) between 100 and 1707 K has been given in the literature. The author represented his recommended values of by an inflection in the A versus temperature relationship between 300 and 500 K. Because a physical mechanism had not been identified that would produce such a temperature dependence in of 304 SS, interest was generated in the possible existence of an as yet undiscovered phenomenon that might cause such an inflection. Consequently, experimental verification of the inflection was sought. The present paper presents recent measurements of , the electrical resistivity, and the absolute Seebeck coefficient of 304L SS from 300 to 1000 K and of the thermal diffusivity () from 297 to 423 K. The values computed from the a measurements were within ± 1.6% of the directly measured An inflection was not observed in the temperature dependence of between 300 and 500 K. After careful evaluation and because a physical mechanism still has not been identified which would produce such an inflection, the authors conclude that the inflection in the vs T relationship reported in the literature was caused by the data analysis technique.     

Thermal conductivity of dense and porous yttria-stabilized zirconia

The thermal conductivity of dense and porous yttria-stabilized zirconia (YSZ) ceramics has been measured as a function of temperature in the range 25 to 1000 °C. The dense specimens were either single crystal (8 mol% YSZ) or sintered polycrystalline (3 mol% and 8 mol% YSZ). The porous specimens (3 mol% YSZ) were prepared using the fugitive polymer method, where different amounts of polymer spheres (of two different average sizes) were included in the starting powders before sintering. This method yielded materials with uniformly distributed porosities with a tight pore-size distributions. A theory has been developed to describe the thermal conductivity of dense YSZ as a function of temperature. This theory considers the reduction in the intrinsic thermal conductivity due scattering of phonons by point defects (oxygen vacancies and solute) and by the hopping of oxygen vacancies. It also considers an increase in the effective thermal conductivity at high temperatures due to radiation. This theory captures the essential features of the observed thermal conductivity. The Maxwell theory has been used to analyze the thermal conductivity of the porous materials. An adequate agreement was found between the theory and experiment.     

The influence of neutron irradiation on the thermal conductivity of aluminum in the range 5–50 K

Measurements of thermal conductivity of 6N to 3N pure aluminum in the temperature range 5–50 K subjected to fast neutron irradiation, with exposures of 10¹³ and 10¹⁶ n · cm^–2, are reported. The thermal conductivity maximum was found to shift towards higher temperatures with an increase in the fast neutron irradiation exposure. At high temperatures, a departure from Wilson's theory was observed, which may be attributed to the existence of additional electron scattering mechanisms. An increase in both ideal and residual thermal resistivity components with an increase in the radiation exposure was noted.Nomenclature I ₅ (/t) Debye integral of the fifth order - –m slope of the straight line that crosses maximum thermal conductivity values - n exponent in ideal thermal resistivity component - T _m temperature corresponding to maximum thermal conductivity - W _e total electronic thermal resistivity - W _i ideal thermal resistivity - W ₀ residual thermal resistivity - ideal thermal resistivity coefficient in Eq. (4) - ideal thermal resistivity coefficient in Eq. (1) - constant related to the ideal part of thermal resistivity in Eq. (2) - () ideal thermal resistivity coefficient depending on irradiation exposure - () residual thermal resistivity coefficient depending on irradiation exposure - thermal conductivity - _m maximum thermal conductivity - Debye characteristic temperature - irradiation exposure     

Relationship between thermal conductivity,speed of sound,and isobaric heat capacity of liquids

Using two liquids-water and toluene — as an example, the author determines the dependence of the coefficient of thermal conductivity on the speed of sound and isobaric molar heat capacity for high state parameters.Notation coefficient of thermal conductivity - u speed of sound - _S same for a saturated liquid - c isobaric molar heat capacity - density - p_s same, for a saturated liquid - p pressure - p_s same, for a saturated liquid - R gas constant - T absolute temperature - x coefficient of thermal activity - x _s same, for a saturated liquid - L, constants in Eqs. (1) and (2) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 311–314, August, 1980.     

The thermal conductivity of α-plutonium between 3 and 100 K

The thermal conductivity of -plutonium has been measured over the range 3–100 K. For the highest purity material (50 ppm metallic impurities) a small peak in the conductivity is seen at 10 K, followed by a shallow minimum at 40 K. The maximum measured conductivity is 34.3 mW/K cm at 100 K. A decrease in conductivity occurs at low temperatures as a result of radioactive self-damage, which saturates with an exponential dependence. It is shown that most of the heat conduction is by phonons, electronic thermal conduction being small but rising with temperature.     

Theoretical fundamentals of the method for thermal diffusivity measurements from auto-oscillation parameters in a system with a thermal feedback

Theoretical fundamentals of the method to determine thermal diffusivity from auto-oscillation parameters in a control system, CS, with thermal feedback through the test specimen, are developed. The equation of a CS with a flat specimen and proportional controller (nonlinear boundary value problem of nonstationary heat conduction) is considered. Periodic solutions of the boundary value problem, which is linearized in the vicinity of the stationary solution, are analyzed. It is proved that, with a certain value of CS gain factor, excitation of auto-oscillations occurs. Their frequency _c is related to the thermal diffusivity as = C_c, where C is constant. By nonlinear analysis, it is revealed that the auto-oscillation excitation mode is soft and the frequency depends on the gain factor to a very weak degree. Formulas for calculation of the thermal diffusivity and the specimen temperature field are obtained.Nomenclature A Generalized gain factor - A _c Critical value of A - a Thermal diffusivity - b ₂, c₂ Lyapunov coefficients - K Controller gain - k Wavenumber - q Heat flux - R Heater resistance - S Heater surface area - T(x, t) Difference between specimen and thermostat temperatures - t Real time - u ₀ Reference voltage - u ₁,u₂ Voltage - x Coordinate - x ₀ Thermocouple coordinate - Thermo emf factor - Specimen thickness - Relative deflection of A from A _c - Thermocouple normalized coordinate - Thermal conductivity - v Temperature wave phase delay through the whole specimen - Auto-oscillation amplitude - Heaviside step function - Normalized time - ¢ Spatial part of phase - Frequency