Thermal Conductivity Of Solid Materials Research Articles

Automated system for measuring thermal conductivity of solid materials

Automated system for measuring thermal conductivity of solid materials

Integral solution method of the laminar conjugated natural convection heat transfer from a hollow cylinder

The laminar conjugated natural convection heat transfer from a hollow cylinder is a common problem in engineering. The accurate calculation of the hot-spot temperature helps to monitor and evaluate the operating status of the equipment. In this paper, first, a mathematical model of the conjugated natural convection from a hollow cylinder is established. The boundary layer integral equations under arbitrary heat flux distribution on the surface are derived, and the optimal velocity and temperature profiles corresponding to different Prandtl numbers are determined. By combining the integral equations and the thermal network model, the hot-spot temperature and the average surface temperature of a hollow cylinder are solved iteratively. Subsequently, a computational fluid dynamic (CFD) simulation based on finite volume method is carried out to verify the accuracy of the integral solution method. The maximum relative error of the computed results of the two methods is 1.35%. The integral solution method performs much better in computation speed, increasing by 90 times. It is also found that as the thermal conductivity of solid materials decreases, although the hot-spot temperature increases, the average surface temperature remains basically unchanged. Finally, based on the lumped thermal equivalent circuit, the correlation of the Nusselt number corresponding to the hot-spot temperature is predicted. The parameters in the correlation are estimated by regression orthogonal design. The results show that under a wide range of solid thermal conductivity and fluid Prandtl numbers, the maximum error of the correlation is 6.02%. Therefore, this novel method is feasible and significant for calculating hot-spot temperature.

Three-sensor 2ω method with multi-directional layout: A general methodology for measuring thermal conductivity of solid materials

Anisotropic thermal transport plays a key role in both theoretical study and engineering practice of heat transfer, but accurately measuring anisotropic thermal conductivity remains a significant challenge. To address this issue, we propose the three-sensor 2ω method in this study, which is capable of accurately measuring the isotropic or anisotropic thermal conductivity of solid materials. In this method, several three-sensor groups following the design guidelines are fabricated upon the sample along different characteristic directions, and each group consists of three parallel metal sensors with unequal widths and distances optimally designed based on sensitivity analysis. Among the three sensors, the outer two serve as AC heaters and the middle one as a DC detector. The 2ω voltage signals across the detector in each three-sensor group are measured, and then the data are processed by the proposed Intersection Method to derive thermal conductivities along directions of interest. The application of the detector's 2ω instead of the heater's 3ω voltage signals eliminates errors introduced by the uncertainties of thermal resistance in superficial structures (metal layer, insulation layer, interface, etc.). Meanwhile, by replacing the fitting algorithm with the Intersection Method, the local optimum trap of multivariate fitting is avoided. To verify the accuracy and reliability, four typical monocrystalline semiconductors, i.e., Si, GaN, AlN, and β-Ga2O3, are measured, and the results are consistent with the literature. This method will provide a comprehensive and versatile solution for the thermal conductivity measurements of solid materials.

Low-cost portable system for measuring thermal conductivity of building

The developed system allows to measure the thermal conductivity of solid materials used as thermal insulators in building bioclimatic houses on high Andean zones. A unidirectional heat flow model through a sample of dimensions 4.0 cm x 4.2 cm x 1.35 cm has been considered. K-type thermocouples were used to measure the temperature’s gradient. The obtained values were: 0.97 Wm−1°C−1 for glass, 0.38 Wm−1°C−1 in the ignimbrite, 0.58 Wm−1°C−1 for the roof brick and 0.34 Wm−1°C−1 in the adobe with Stipa ichu. These materials have been evaluated considering their abundance and use in house building on the Arequipa department high zones.

Thermal conductivity prediction by atomistic simulation methods: Recent advances and detailed comparison

Atomistic simulation methods, including anharmonic lattice dynamics combined with the Boltzmann transport equation, equilibrium and non-equilibrium molecular dynamics simulations, and Landauer formalism, are vital for the prediction of thermal conductivity and the understanding of nanoscale thermal transport mechanisms. However, for years, the simulation results using different methods, or even the same method with different simulation setups, lack consistency, leading to many arguments about the underlying physics and proper numerical treatments on these atomistic simulation methods. In this perspective, we review and discuss the recent advances in atomistic simulation methods to predict the thermal conductivity of solid materials. The underlying assumptions of these methods and their consequences on phonon transport properties are comprehensively examined. Using silicon and graphene as examples, we analyze the influence of higher-order phonon scatterings, finite-size effects, quantum effects, and numerical details on the thermal conductivity prediction and clarify how to fairly compare the results from different methods. This perspective concludes with suggestions on obtaining consistent thermal conductivity prediction of different material systems and also provides perspective on efficient and accurate simulations of thermal transport in more complex and realistic conditions.

Mechanisms of Heat Transfer in Thermoelectric Materials

The analysis of methods for calculating the components of thermal conductivity of solid materials is carried out. The problems of using these methods are identified and their assessment is given from the point of view of obtaining reliable results. Experimental data on the temperature dependences of thermoelectric parameters of the main thermoelectric materials (TEMs) used for the manufacturing of Peltier and Seebeck thermoelements are presented. Using the obtained data, we calculated the main components of the thermal conductivity of TEMs (phonon, electronic, and bipolar) in the temperature range from 250 to 1200 K for solid solutions based on Bi, Sb, Pb, and Ge chalcogenides, as well as SiGe obtained by various methods of directional crystallization. The relationship between the mechanisms of heat transfer in TEMs and the temperature dependences of electrical conductivity and thermoelectric power has been established. It is shown that the use of nanostructured TEMs is promising for increasing the thermoelectric figure of merit.

Finite Element Method and Cut Bar Method-Based Comparison Under 150°, 175° and 310 °C for an Aluminium Bar

Analyses were developed using a finite element method of the experimental measurement system for thermal conductivity of solid materials, used by the Centro Nacional de Metrología (CENAM), which operates under a condition of permanent heat flow. The CENAM implemented a thermal conductivity measurement system for solid materials limited in its operating intervals to measurements of maximum 300 ° C for solid conductive materials. However, the development of new materials should be characterised and studied to know their thermophysical properties and ensure their applications to any temperature conditions. These task demand improvements in the measurement system, which are proposed in the present work. Improvements are sought to achieve high-temperature measurements in metallic materials and conductive solids, and this system may also cover not only metallic materials. Simulations were performed to compare the distribution of temperatures developed in the measurement system as well as the radial heat leaks, which affect the measurement parameters for an aluminium bar, and uses copper bars as reference material. The simulations were made for measurements of an aluminium bar at a temperature of 150 ° C, in the plane and 3D, another at 175 ° C and one more known maximum temperature reached by a sample of the aluminium bar with a new heater acquired at 310 ° C.

Reconstruction of elastic properties and thermal conductivity of solid materials from their small fragments

The absence of direct measurement of physical properties on the rock cuttings necessitates the use of theoretical approaches. One of the most promising is the use of methods of effective medium theory. In this work we apply the generalized singular approximation of effective medium theory to solve this problem. We construct a parametric mathematical model of effective physical properties of a composite material made from rock cuttings to link the effective properties of the composite material with its compositional and microstructure parameters. The list of unknown parameters includes those characterizing the elastic and thermal properties of rocks. We develop a technique for manufacturing the composite samples that are compacted mixtures of fine-grained wax and rock cuttings. We propose a method to restore the velocities of elastic waves (compressional and shear) and thermal conductivity of rocks from experimental data on the respective physical properties of composites based on the constructed model. This method is tested on fifteen composite samples made from four rocks of different types (two sandstones, quartz glass and white marble). The theoretical values characterizing the elastic and thermal properties of rocks are compared with respective experimental data obtained in independent experiments performed for these rocks. The average difference in the elastic wave velocities and thermal conductivity does not exceed 10%, whereas the maximum difference in the respective properties varies from 14 to 23%.

Estimation of thermal conductivity of low thermal conductive solid materials using the jet flush method

A novel and practical transient-type technique named as “Jet Flush” is proposed for measuring temperature-dependent thermal conductivity of solid materials with low thermal conductivity. In order to estimate thermal conductivity of the sample, its surface is exposed to an impinging air jet flow with higher (or lower) temperature than the sample for a short period of time, while an infrared thermometer records the heated (or cooled) surface temperature history. A nonlinear 1D inverse heat conduction problem with constant convective heat transfer coefficient on the boundary condition is then employed for determining the temperature-dependent thermal conductivity using the measured temperatures. As a requirement for solving the inverse problem, the convective coefficient on the surface of the sample is measured in a separate experiment with the same flow condition using a standard sample. Sensitivity and error analyses are performed to discuss the effects of the estimation points (the temperatures in which the thermal conductivity is to be estimated), and the simplification assumption of constant convective heat transfer coefficient (with respect to time) on the solution of the inverse problem and the accuracy of the estimated results. In order to demonstrate the applicability of the proposed method, the thermal conductivities of three polymer-type materials (HDPE, PMMA and PA6) are measured over the temperature range of ~22–62 °C, and the results are found to be in good agreement with literature data. Moreover, the uncertainty analysis performed in this study showed that the accuracy of the proposed method can be better than 5% for an appreciable temperature range.

Thermal Conductivity of Solid Materials

Thermal Conductivity of Solid Materials

An Acoustic Technique for the Analysis of Thermal Processes

A technique for experimental investigation of thermal processes in liquid media, which is based on putting the thermal source into contact with a solid rod, sounding the rod with a set of acoustic waves, and measuring the velocities of these waves under changing temperature, has been developed. The technique has been tested using the phase transition of the first order (evaporation of microdrops of a liquid) as an example. It has been shown that the technique makes it possible to measure temperature, time, velocity, heat of evaporation, and mass of the liquid sample. After an appropriate calibration, the technique is also applicable to determining the thermal conductivity of solid materials.

Anchoring mechanisms of methane/air premixed flame in a mesoscale diverging combustor with cylindrical flame holder

A mesoscale diverging combustor with a cylindrical flame holder is developed to improve the flame stabilization in present work for the first time. The experimental results show that the flame in the combustor with holder can remain symmetrically stable within a quite wide range of equivalence ratio. Then, the flame-anchoring mechanisms are analyzed systematically in terms of flow structure, conjugate heat exchange and preferential transport effect via numerical simulation. As the flame root and top attach to the flame holder and combustor, it can be deduced that the flow boundary layer very near the wall has the anchoring effect on the flame, so does the conjugate heat exchange. On the one hand, the upstream flame holder and combustor wall can preheat the incoming unburned mixture via conducting heat from the downstream solid walls, which provides a beneficial ignition condition. On the other hand, there are flame-wall coupling effects between the flame root/top and flame holder/combustor wall providing the suitable locations for flame anchoring. The anchoring locations of flame root and top show the almost same sensibility responding to the thermal conductivity of solid material. However, the anchoring temperature of flame top is more sensitive than that of flame root. In addition, the local equivalence ratios at the locations of the flame root and top are lower than the corresponding incoming equivalence ratio, which means that a better heat recirculation effect is not good for the flame-anchoring if only considering the preferential transport effect. In summary, the addition of flame holder can remarkably improve the flame stabilization and suppress the unstable flame in the combustor. This is beneficial for the application of the combustor with the diverging structure.

Influence of defects on the thermal conductivity of compressed LiF

Defect formation in LiF, which is used as an observation window in ramp and shock experi- ments, has significant effects on its transmission properties. Given the extreme conditions of the experiments it is hard to measure the change in transmission directly. Using molecular dynam- ics, we estimate the change in conductivity as a function of the concentration of likely point and extended defects using a Green-Kubo technique with careful treatment of size-effects. With this data, we form a model of the mean behavior and its estimated error; then, we use this model to predict the conductivity of a large sample of defective LiF resulting from a direct simulation of ramp compression as a demonstration of the accuracy of its predictions. Given estimates of defect densities in a LiF window used in an experiment, the model can be used to correct the observations of thermal energy through the window. In addition, the methodology we develop is extensible to modelling, with quantified uncertainty, the effects of a variety of defects on thermal conductivity of solid materials.

Heat transfer performances of cryogenic fluids in offset strip fin-channels considering the effect of fin efficiency

This paper numerically explores the heat transfer behaviors of cryogenic fluids in offset strip fin (OSF) channels considering the important effect of fin efficiency that combines the factors of low thermal conductivity of fin material at cryogenic temperatures and the fin geometry. A series of numerical simulations, which involve three kinds of fin materials with different thermal conductivities and the cryogenic fluids including both gases and liquids of nitrogen, normal hydrogen and classic helium 4, are carried out with well-validated 3D models. The results show that lower thermal conductivity of solid material at cryogenic temperature causes a considerable reduction in heat transfer performance of OSF fins especially for the liquids with high Prandtl number. Further analysis of the results reveals that for different cryogenic fluids, Nusselt number is strongly related to Prandtl number and fin efficiency. In particular, Nusselt number is proportional to the Pr0.235ηf0.9 in laminar region, regardless of Reynolds number and fin geometries. The results for different fin geometries suggest that larger fin thickness-to-length ratio can help to improve the heat transfer performance, while smaller fin thickness-to-height ratio and higher fin density no longer contribute to higher j factor (or Nusselt number) of OSF fin, especially in the case of lower thermal conductivity of fin material. There exist optimum fin thickness-to-height ratio and fin density that correspond to the maximum value of j factor for the cryogenic fluids.

Thermal Conductivity Measurement of Solid Materials by Thermistor Direct Heating Method

Background. This work addresses the development of an experimental device and increasing the accuracy of determining the thermal conductivity of solid materials by thermistor direct heating method. Objective. The aim of the paper is to create the installation, conduct experimental studies to determine the value of the thermal conductivity of solid materials by thermistor direct heating method and to research destabilizing factors that affect the measurement error, and to suggest ways to increase the accuracy of measurements. Methods. Experimental device has been created, which work is based on the direct heating method of the thermistor and necessary researches have been carried out. The results of the measurement are given by setting the thermal conductivity coefficients of various materials, which make it possible to expand the scope of the method. Results. Rational operating modes and design of probes for measuring the thermal conductivity of solid materials depending on their TPC are proposed and justified. Ways to reduce the measurement error by thermistor direct heating method are presented. Investigation of destabilizing factors influencing the measurement error made it possible to determine means of reducing their influence on the results of determining the thermal conductivity of solid materials and to suggest ways to increase the accuracy of measurements. Conclusions . The experimental device has been tested experimentally and implemented in the research and production activities of “VIRCOM” and in the educational process of the Department of Instrumentation Design and Engineering of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” .

Recipe for optimizing a solid-state thermal rectifier

A thermal rectifier, i.e. a device in which the magnitude of the heat flux depends on the sign of the temperature gradient, has potential application in thermal logic systems, memory devices, and for long-term seasonal thermal energy storage. There is yet no clear guide for designing working rectifiers based on binary material systems. We use the analytical solution for thermal rectification in such a binary system that considers the local temperature dependence of the thermal conductivity to identify combinations that produce reasonable rectification. Often, between 200 and 400 K, the thermal conductivity of solid materials can be approximated as a linear function of temperature, κ=aT+b. The best binary material combinations occur when b/a approaches −Thot for one material and −Tcold for the other. Our results provide clarity for experimentalists regarding suitable combinations. Applying the method with a sample database shows that a Si-Ce system exhibits the largest rectification with R = 1.61 although, since Ce easily oxidizes in air, manufacturing a Si-Fused SiO2 rectifier with R = 1.37 may be more reasonable. We show that contacts made to a binary rectifier for either characterization or integration into a device can negatively impact device performance.

Numerical simulation of an instrument to determine the thermal conductivity of conductive solids

In this paper the design of a cut bar system to determine the thermal conductivity of conductive solid materials is presented. The system works under the comparative method, therefore two reference samples with known thermal conductivity are needed. The thermal design consisted on defining the physical configuration of the thermal system, materials to use and their dimensions, in order to evaluate their thermal performance by varying these parameters to calculate the maximum percentage design error. Given that the thermal design was parametric, the finite volume method was used to solve the heat conduction equation in the cut bar system, which allowed us to vary the different parameters that make up the thermal system such as length and diameter of the bars, insulation thickness, type of reference material, etc. The numerical code developed was verified with one analytical solution. It was found that, the thermal design of a cut bar instrument to determine the thermal conductivity of solid materials within the interval 0.58 ⩽ λ ⩽ 429 W.m-1 .K-1 shows a maximum design error of 3.77% associated to the length of the sample material. The results in this paper allow one to kwon the error by design which can be taken into account as a source of uncertainty when determining the thermal conductivity of solid materials.

Influence of probe geometry on measurement results of non-ideal thermal conductivity sensors

Abstract. The thermal properties of the surface and subsurface layers of planets and planetary objects yield important information that allows us to better understand the thermal evolution of the body itself and its interactions with the environment. Various planetary bodies of our Solar System are covered by so-called regolith, a granular and porous material. On such planetary bodies the dominant heat transfer mechanism is heat conduction via IR radiation and contact points between particles. In this case the energy balance is mainly controlled by the effective thermal conductivity of the top surface layers, which can be directly measured by thermal conductivity probes. A traditionally used method for measuring the thermal conductivity of solid materials is the needle-probe method. Such probes consist of thin steel needles with an embedded heating wire and temperature sensors. For the evaluation of the thermal conductivity of a specific material the temperature change with time is determined by heating a resistance wire with a well-defined electrical current flowing through it and simultaneously measuring the temperature increase inside the probe over a certain time. For thin needle probes with a large length-to-diameter ratio it is mathematically easy to derive the thermal conductivity, while this is not so straightforward for more rugged probes with a larger diameter and thus a smaller length-to-diameter ratio. Due to the geometry of the standard thin needle probes they are mechanically weak and subject to bending when driven into a soil. Therefore, using them for planetary missions can be problematic. In this paper the thermal conductivity values determined by measurements with two non-ideal, ruggedized thermal conductivity sensors, which only differ in length, are compared to each other. Since the theory describing the temperature response of non-ideal sensors is highly complicated, those sensors were calibrated with an ideal reference sensor in various solid and granular materials. The calibration procedure and the results are described in this work.

Mixing Rules of Young’s Modulus, Thermal Expansion Coefficient and Thermal Conductivity of Solid Material with Particulate Inclusion

This review paper analyzed a Young’s modulus (E), a thermal expansion coefficient (TEC, β) and a thermal conductivity (κ) of the material with simple cubic particulate inclusion using two model structures: a parallel structure and a series structure of laminated layers. The derived β equations were applied to calculate the β value of the W-MgO system. The accuracy was higher for the series model structure than for the parallel model structure. Young’s moduli (Ec) of sintered porous alumina compacts were theoretically related to the development of neck growth of grain boundary between sintered two particles and expressed as a function of porosity. The series structure model with cubic pores explained well the increased tendency of Ec with neck growth rather than the parallel structure model. The thermal conductivity of the three phase system of alumina-mullite-pore was calculated by a theoretical equation developed in this research group, and compared with the experimental results. The pores in the sintered composite were treated as one phase. The measured thermal conductivity of the composite with 0.5-25% porosity (open and closed pores) was in accordance with the theoretical prediction based on the parallel structure model. Key words: Sintering, Porous ceramics, Thermal conductivity, Thermal expansion

Development of a single-sided guarded hot plate apparatus for thermal conductivity measurements

This work presents the development of an experimental setup for measurements on of thermal conductivity of solid materials, such as ceramics, polymers, rubbers, glasses, biological materials, etc. whose thermal conductivity lies in the approximate range between 0.1 and 2 Wm-1K-1. The setup was designed on the principle of the single-sided guarded hot plate method. In order to find the optimal design for generation of traceable one-dimensional heat flux through an investigated 300?300 mm2 specimen, a numerical heat transfer FEM analysis was performed. The principal components of the measuring apparatus, such as hot plate with thermopile, cold plate and auxiliary hot plate were constructed according to the obtained results of simulations. Software for the control of experiment and data acquisition was developed using the LabVIEW programming environment.