Mechanism of heat transport in nanofluids

We have calculated thermal conductivity of alumina nanofluids (with water and ethylene glycol as base fluids) using temperature as well as concentration-dependent viscosity, η. The temperature profile of η is obtained using Gaussian fit to the available experimental data. In the model, the interfacial resistance effects are incorporated through a phenomenological parameter α. The micro-convection of the alumina nanoparticle (diameter less than 100 nm) is included through Reynolds and Prandtl numbers. The model is further improved by explicitly incorporating the thermal conductivity of the nanolayer surrounding the nanoparticles. Using this improved model, thermal conductivity of copper nanofluid is calculated. These calculations capture the particle concentration-dependent thermal conductivity and predict the dependence of the thermal conductivity on the size of the nanoparticle. These studies are significant to understand the underlying processes of heat transport in nanofluids and are crucial to design superior coolants of next generation.     

Thermal Conductivity of Standard Sands. Part I. Dry-State Conditions

A comprehensive thermal conductivity (λ) database of three dry standard sands (Ottawa C-109, Ottawa C-190, and Toyoura) was developed using a transient line heat source technique. The database contains λ data representing a variety of soil compactions and temperatures (T) ranging from 25 °C to 70 °C. The tested standard sands, due to their repeatable physical characteristics, can be used as reference materials for validation of thermal probes applied to similar dry granular materials. The measured data show an increasing trend of thermal conductivity at dryness (λ_dry) against T in spite of declining quartz λ with T. The air content (porosity) controls the λ of dry sands by acting as a very effective thermal insulator around solid soil particles. As a result, a diminutive increase of λ_dry with T is driven by increasing λ of air. The experimental λ data of dry sands were exceptionally well predicted by de Vries and Woodside–Messmer models, and also by a thermal conductance model, a product of λ of solids and the thermal conductance factor.     

Thermophysical Properties of Heterogeneous Structures Measured by Pulse Transient Method

This paper discusses differences in thermophysical parameters (thermal conductivity λ, thermal diffusivity a, and specific heat c) that can be found when experimental methods with different measuring regimes are used. Two classes of methods are compared, namely, classical methods using steady-state, equilibrium, and dynamic measuring regimes and transient methods. The data consistency formula λ = acρ gives a picture on data reliability when single-parameter methods are used. Results of analysis are verified on published, recommended, and measured data by transient methods considering homogenous materials (stainless steel A 310, BK 7, Perspex) and heterogeneous materials (composite C/C–SiC, aerated autoclaved concrete). Satisfactory agreement on data for the thermophysical parameters was found on homogenous materials only. Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22–27, 2003, Boulder, Colorado, U.S.A.     

Thermal Conductivity of Small Nickel Particles

The thermal conductivity of nanoscale nickel particles due to phonon heat transfer is extrapolated from thin film results calculated using nonequilibrium molecular dynamics (NEMD). The electronic contribution to the thermal conductivity is deduced from the electrical conductivity using the Wiedemann–Franz law. Based on the relaxation time approximation, the electrical conductivity is calculated with the Kubo linear-response formalism. At the average temperature of T=300 K, which is lower than the Debye temperature Θ_D=450 K, the results show that in a particle size range of 1.408–10.56 nm, the calculated thermal conductivity decreases almost linearly with decreasing particle size, exhibiting a remarkable reduction compared with the bulk value. The phonon mean free path is estimated, and the size effect on the thermal conductivity is attributed to the reduction of the phonon mean free path according to the kinetic theory.     

A new heat transfer model of inorganic particulate-filled polymer composites

Thermal conductivity is an important parameter for characterization of thermal properties of materials. Various complicated factors affect the thermal conductivity of inorganic particulate-filled polymer composites. The heat transfer process and mechanisms in an inorganic particulate-filled polymer composite were analyzed in this article. A new theoretical model of heat transfer in these composites was established based on the law of minimal thermal resistance and the equal law of the specific equivalent thermal conductivity, and an relevant equation of effective thermal conductivity (K _eff) for describing a relationship between K _eff and filler volume fraction as well as other thermal parameters were derived based on this model. The values of K _eff of aluminum powder-filled phenol–aldehyde composites and graphite powder-filled phenol–aldehyde composites were estimated by using this equation, and the calculations were compared with the experimental measured data from these composites with filler volume fraction from 0 to 50% in temperature range of 50–60 °C and the predictions by Maxwell–Eucken equation and Russell equation. The results showed that the predictions of the K _eff by this equation were closer to the measured data of these composites than the other equations proposed in literature.     

Thermal-Conductivity Characterization of Gas Diffusion Layer in Proton Exchange Membrane Fuel Cells and Electrolyzers Under Mechanical Loading

Accurate information on the temperature field and associated heat transfer rates is particularly important for proton exchange membrane fuel cells (PEMFC) and PEM electrolyzers. An important parameter in fuel cell and electrolyzer performance analysis is the effective thermal conductivity of the gas diffusion layer (GDL) which is a solid porous medium. Usually, this parameter is introduced in modeling and performance analysis without taking into account the dependence of the GDL thermal conductivity λ (in W · m⁻¹ · K⁻¹) on mechanical compression. Nevertheless, mechanical stresses arising in an operating system can change significantly the thermal conductivity and heat exchange. Metrology allowing the characterization of the GDL thermal conductivity as a function of the applied mechanical compression has been developed in this study using the transient hot-wire technique (THW). This method is the best for obtaining standard reference data in fluids, but it is rarely used for thermal-conductivity measurements in solids. The experiments provided with Quintech carbon cloth indicate a strong dependence (up to 300%) of the thermal conductivity λ on the applied mechanical load. The experiments have been provided in the pressure range 0 < p < 8 MPa which corresponds to stresses arising in fuel cells. All obtained experimental results have been fitted by the equation λ = 0.9log(12p + 17)(1 − 0.4e^−50p ) with 9% uncertainty. The obtained experimental dependence can be used for correct modeling of coupled thermo/electro-mechanical phenomena in fuel cells and electrolyzers. Special attention has been devoted to justification of the main hypotheses of the THW method and for estimation of the possible influence of the contact resistances. For this purpose, measurements with a different number of carbon cloth layers have been provided. The conducted experiments indicate the independence of the measured thermal conductivity on the number of GDL layers and, thus, justify the robustness of the developed method and apparatus for this type of application.     

Simultaneous measurements of thermal conductivity and thermal diffusivity of Se90?xTe5Sn5Inx (x?=?0, 3, 6, and 9) multi-component chalcogenide glasses

Measurements of thermal conductivity and thermal diffusivity of twin pellets of Se_90−x Te₅Sn₅In _x (x = 0, 3, 6, and 9) chalcogenide glasses were carried out at room temperature using transient plane source technique. The measured values of thermal conductivity and thermal diffusivity were used to determine the specific heat per unit volume of these glasses in the composition range of investigation. Results indicated that both values of thermal conductivity and thermal diffusivity were increased with addition of indium concentration at the cost of selenium, whereas the specific heat per unit volume was slightly decreases with increase of indium content. This compositional dependence behavior of the thermal conductivity and diffusivity can be explained in terms of the iono-covalent type of bonds, which In (indium) makes with Se as it is incorporated in the Se–Te–Sn glass.     

Thermal Properties of GaN Films Grown on Si Substrates

GaN films grown on Si substrates by molecular beam epitaxy with different nitridation times have been investigated. The GaN/Si structural and optical properties were evaluated by transmission electron microscopy, X-ray diffraction, atomic force microscopy, and photoluminescence. The effective thermal conductivity of the GaN/Si system was obtained using the photoacoustic technique, and from these results the nitridation time dependence of the interface thermal conductivity (η) can be evaluated using a two-layer model. An optimal nitridation time for which the GaN crystal quality can be improved was obtained. The variation of the parameter η for different nitridation times can be related to the interface phonon scattering process by the presence of disorder at the GaN/Si interface.     

Application of the Three-Omega Method to Measurement of Thermal Conductivity and Thermal Diffusivity of Hydrogen Gas

Preliminary investigations have been conducted to discuss the possibility of measuring the thermal conductivity of hydrogen gas by the three-omega method. A one-dimensional analytical solution for the 3ω component is derived which includes the effect of the wire heat capacity. It is shown that it is very important to take into account the wire heat capacity in the calculation to measure the thermal conductivity of gas by the three-omega method. In contrast, the wire heat capacity is less important for the thermal conductivity of the liquid or solid phase. The importance of the wire heat capacity is found to increase with increasing frequency and decrease if the sample thermal conductivity is high. In order to measure the thermal conductivity of hydrogen gas at atmospheric pressure, a wire of diameter less than 1μm is necessary if the properties of the wire are to be neglected.     

Vacuum Insulation Panels – Exciting Thermal Properties and Most Challenging Applications

Vacuum insulation panels (VIPs) have a thermal resistance that is about a factor of 10 higher than that of equally thick conventional polystyrene boards. VIPs nowadays mostly consist of a load-bearing kernel of fumed silica. The kernel is evacuated to below 1 mbar and sealed in a high- barrier laminate, which consists of several layers of Al-coated polyethylene (PE) or polyethylene terephthalate (PET). The laminate is optimized for extremely low leakage rates for air and moisture and thus for a long service life, which is required especially for building applications. The evacuated kernel has a thermal conductivity of about 4 × 10⁻³ W · m⁻¹ · K⁻¹ at room temperature, which results mainly from solid thermal conduction along the tenuous silica backbone. A U-value of 0.2 W · m⁻² · K⁻¹ results from a thickness of 2 cm. Thus slim, yet highly insulating fa?ade constructions can be realized. As the kernel has nano-size pores, the gaseous thermal conductivity becomes noticeable only for pressures above 10 mbar. Only above 100 mbar the thermal conductivity doubles to about 8 × 10⁻³ W · m⁻¹ · K⁻¹, such a pressure could occur after several decades of usage in a middle European climate. These investigations revealed that the pressure increase is due to water vapor permeating the laminate itself, and to N₂ and O₂, which tend to penetrate the VIP via the sealed edges. An extremely important innovation is the integration of a thermo-sensor into the VIP to nondestructively measure the thermal performance in situ. A successful “self-trial” was the integration of about 100 hand-made VIPs into the new ZAE-building in Würzburg. Afterwards, several other buildings were super-insulated using VIPs within a large joint R&D project initiated and coordinated by ZAE Bayern and funded by the Bavarian Ministry of Economics in Munich. These VIPs were manufactured commercially and integrated into floorings, the gable fa?ade of an old building under protection, the roof and the facades of a terraced house as well as into an ultra-low-energy “passive house” and the slim balustrade of a hospital. The thermal reliability of these constructions was monitored using an infrared camera.Invited paper presented at the Seventh European Conference on Thermophysical Properties, September 5-8, 2005, Bratislava, Slovak Republic.     

Spectral Absorptivity and Thermal Conductivity of BGO and BSO Melts and Single Crystals

The present work describes the results of spectral absorptivity, α, and thermal conductivity, λ, studies for compound oxides Bi₄Ge₃O_12, Bi₁₂GeO_20, Bi₄Si₃O_12, and Bi₁₂SiO₂₀ in molten and monocrystalline states. The data for the spectral absorptivity were obtained by placing the sample onto a mirror and using the transmission method. To obtain the data on the thermal conductivity of crystals, the stationary method of two identical samples was used. The data for the thermal conductivity of melts were obtained by a new stationary relative method in which the thermal conductivity of the crystal is used as a reference. Special attention is focused on numerical and experimental error analysis at high temperature. The studies have shown that α in the range of a transmission band strongly depends on crystal purity. It varies from 0.0005 cm⁻¹ to 0.03 cm⁻¹ for Bi₄Ge₃O₁₂ and reaches 0.15 cm⁻¹ for Bi₄Si₃O₁₂. It was found that α is significantly greater for melts than for crystals, reaching (150 to 200) cm⁻¹ for the Bi₄Ge₃O₁₂ melt. The thermal conductivity of the melts under investigation was found to be much smaller than that of the corresponding crystals.     

Determining Thermal Conductivity and Thermal Diffusivity of Low-Density Gases Using the Transient Short-Hot-Wire Method

The transient short-hot-wire method for measuring thermal conductivity and thermal diffusivity makes use of only one thermal-conductivity cell, and end effects are taken into account by numerical simulation. A search algorithm based on the Gauss–Newton nonlinear least-squares method is proposed to make the method applicable to high-diffusivity (i.e., low-density) gases. The procedure is tested using computer-generated data for hydrogen at atmospheric pressure and published experimental data for low-density argon gas. Convergence is excellent even for cases where the temperature rise versus the logarithm of time is far from linear. The determined values for thermal conductivity from experimental data are in good agreement with published values for argon, while the thermal diffusivity is about 10 % lower than the reference data. For the computer-generated data, the search algorithm can return both thermal conductivity and thermal diffusivity to within 0.02 % of the exact values. A one-dimensional version of the method may be used for analysis of low-density gas data produced by conventional transient hot-wire instruments.     

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.     

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 and Thermal-Diffusivity Measurements of Nanofluids by 3<Emphasis Type="Italic">ω</Emphasis> Method and Mechanism Analysis of Heat Transport

A 3ω technique is developed for simultaneous determination of the thermal conductivity and thermal diffusivity of nanofluids. The 3ω measuring system is established, in which a conductive wire is used as both heater and sensor. At first, the system is calibrated using water with known thermophysical properties. Then, the thermal conductivity and thermal diffusivity of TiO₂/distilled water nanofluids at different temperatures and volume fractions and the thermal conductivity of SiO₂ nanofluids with different carrier fluids (water, ethanol, and EG) are determined. The results show that the working temperature and the carrier fluid play important roles in the enhancement of thermal transport in nanofluids. These results agree with the predictions for the temperature dependence effect by the Brownian motion model and the micro-convection model. For SiO₂ nanofluids, the thermal-conductance enhancement becomes strong with a decrease in the heat capacity of the carrier fluids. Finally, according to our results and mechanism analysis, a corrected term is introduced to the Brownian motion model for providing better prediction of heat transport performance in nanofluids.     

Effect of thermal conductivity on reaction front propagation during combustion synthesis of intermetalics

A mathematical model is developed to investigate the effect of thermal conductivity on the combustion synthesis of intermetallics. The governing equations are solved using a high-order-implicit numerical scheme capable of accommodating the steep spatial and temporal gradients of properties. A parametric study is then performed to elucidate reaction characteristics (propagation type, steady-state propagation velocity, peak temperature, etc.) in terms of the thermal conductivity ratio, κ=k_p/k_r. The predicted results appear plausible and consistent with the trends presented in the available literature.     

A noncontact method for measuring thermal conductivity and thermal diffusivity of anisotropic materials

A noncontact method for measuring the thermal conductivity and thermal diffusivity of anisotropic materials is proposed. This method is based on the fact that the surface temperature variation with time depends on the thermal properties of the material when its surface is heated locally. The three-dimensional transient heat conduction equation in the material is solved numerically. The dimensionless average surface temperature variations are obtained along each principal axis: that is, thex andy axes. The relation between the dimensionless temperature and the Fourier number is expressed by a polynomial equation and used as a master plot, which is a basic relation to be compared with measured temperature variation. In the experiments, the material surface is heated with a laser beam and the surface temperature profiles are measured by an infrared thermometer. The measured temperature variations with time are compared with the master plots to yield the thermal conductivity λ _x and thermal diffusivityx _v in thex direction and the thermal conductivity ratioE _xy (=λ _y λ _x ) simultaneously. To confirm the applicability and the accuracy of the present method, measurements were performed on multilayered kent-paper, vinyl chloride, and polyethylene resin film, whose thermal properties are known. From numerical simulations, it is found that the present method can measure the thermophysical properties λ _x , α _x andE _xy within errors of ±6, ±22, and ±5%, respectively, when the measuring errors of the peak heat flux, the heating radius, and the surface temperature rise are assumed to be within ±2, ±3%, and ±0.2 K, respectively. This method could be applied to the measurement of thermophysical properties of biological materials.     

Thermoelectric Power and Thermal Conduction Studies on the Gd Substituted BPSCCO (2234) Superconductors

Measurements of the electrical resistance (R-T), thermoelectric power (S-T) and thermal conductivity (κ-T) have been carried out on the superconductor Bi_1.7Pb_0.3-x Gd _x Sr₂Ca₃Cu₄O_12+y , (0.01 ≤ x ≤ 0.1). According to the XRD patterns the volume fraction of the Bi-2223 phase decreases in favor of Bi-2212. All the samples show normal metallic behavior down to their relevant transition temperature, T _c . T _c -values decrease significantly with increasing Gd concentration in the system. The hole concentration per Cu has been calculated by using the Presland method and found to decrease with increasing Gd content. The thermoelectric power values of the samples are positive and increase in magnitude with increasing the substitution level. The results obtained have been analyzed in terms of “Two band model with linear T-term” and “Xin’ s two band model”. A very good agreement between the first model and our thermoelectric power data was obtained, but the fit to the second model was poor. The substitution has considerable effect on the thermal conductivity, κ. The magnitude of κ is suppressed and a peak appears just below their T _c , values but becomes weaker and broader when the Gd concentration is increased.      

The use of an explicit method of identifying objects to solve problems of nonstationary heat conduction

The theoretical principles of an explicit method of identifying multidimensional objects with nonstationary thermal conductivity are described. The solution of problems of measuring nonstationary heat flux and thermal conductivity in the range λ = 0.03–800 W/(m·K), the thermal conductivity of one of the materials of a double-layer system, the temperature dependence of the thermal conductivity, and the combined “thermal conductivity and volume heat capacity” are presented. The results of investigations on thermal models are given. __________ Translated from Izmeritel’naya Tekhnika, No. 6, pp. 32–38, June, 2008.     

Influence of Temperature Gradients on Tunnel Junction Thermometry below 1 K: Cooling and Electron–Phonon Coupling

We have studied thermal gradients in thin Cu and AlMn wires, both experimentally and theoretically. In the experiments, the wires were Joule heated non-uniformly at sub-Kelvin temperatures, and the resulting temperature gradients were measured using normal metal–insulator–superconducting tunnel junctions. The data clearly shows that even in reasonably well-conducting thin wires with a short (~10 μm) non-heated portion, significant temperature differences can form. In most cases, the measurements agree well with a model which includes electron–phonon interaction and electronic thermal conductivity by the Wiedemann–Franz law. The online version of the original article can be found under