Total Effective Thermal Conductivity Research Articles

Probing the Thermal and Electrical Properties of Ultrawide Bandgap Nitrogen‐Polar AlGaN Heterostructures

AbstractUltra‐wide bandgap semiconductor AlGaN is a promising candidate for high‐power and high‐frequency electronics. AlGaN‐heterostructures with nitrogen (N)‐polarity can offer added benefits of low‐leakage and large drive current. However, electro‐thermal transport in such heterostructures remains unexplored, although they are essential for electronic device functionality. Here, the thermal and electrical properties of N‐polar AlxGa1‐xN‐channel heterostructures (Al percentage, x = 15–90%) are explored and compared with their GaN counterpart. The thermal measurements uncover that the effective thermal resistance of the thin channel and barrier layers are similar in magnitudes for N‐polar‐ AlGaN and GaN heterostructures, however, the total effective thermal conductivity in N‐polar AlGaN heterostructure is ≈4× smaller. This reduction originates from the larger thermal resistance of the thick Al0.15Ga0.85N buffer layer within the AlGaN stack. N‐polar AlxGa1‐xN stack displays a thermal conductivity almost independent of temperature, measured from room temperature up to 200 °C. Hall measurements of an N‐polar Al0.30Ga0.70N‐channel heterostructure further reveal that electrical properties such as resistivity, carrier density, and mobility remain nearly unchanged with temperature, indicating the dominance of alloy‐phonon scattering in such material systems. These results offer important insights into material‐device co‐design and reliability of N‐polar AlGaN heterostructures.

Thermal conduction model of asymmetric structural aramid nanofiber aerogel membranes based on fractal theory

Asymmetric structural aramid nanofiber aerogel membranes (ASAAMs) have been considered ideal thermal insulators due to their unique characteristics, such as dense surface layers and nanoscale 3D fibrous body components. Fractal theory has been used in studying the pore size distribution of fibrous aerogels with symmetrical structures but is rarely used in studying the thermal conductivity of asymmetric structural aerogels. In this work, two basic fractal units are used to simulate the pore size distribution of ASAAMs. The models are transformed into series and parallel fractal resistance networks using the equivalent resistance method. Additionally, a marginal weighting function is proposed to modify the heat transfer model, which is applied to calculate the total effective thermal conductivity of ASAAMs. Results showed that: (1) The correlation between the porosity and the effective thermal conductivity of ASAAMs is negative. (2) The basic fractal units of 7 × 7 size selected in this paper could be described the pore size distribution of ASAAMs well. (3) The modified model demonstrates only 2.58% error, which is closer to the experimental data.

Pressure dependent effective thermal conductivity of pure and SiC-opacified expanded perlite between 293 K and 1073 K

The effective thermal conductivity of pure and opacified expanded perlite is investigated at gas pressures between 10−4 hPa and 103 hPa and temperatures between 293 K and 1073 K by guarded hot plate and transient hot wire measurements. The examined materials are a low-density (ρ = 56 kg m−3) and a high-density (ρ = 180 kg m−3) commercial expanded perlite powder, denoted as P1.5 and P0.14, respectively, as well as a mixture of P0.14 with 40 weight-% SiC as opacifier, denoted as P0.14_O (ρ = 263 kg m−3). To obtain the gas pressure dependent contribution of the measured total effective thermal conductivity, the thermal conductivity in the fully evacuated state is determined experimentally and subtracted. A model for the gas pressure dependent contribution is developed, which takes into account all temperature dependencies of the occurring gas-kinetic parameters and successfully reproduces all measurement data within the experimental uncertainty (ca. 5%). The model includes four structural parameters determined by fitting, which are the effective pore diameters both inside and between the grains as well as the respective porosities. The obtained values agree well with the results of structural analysis by SEM and optical microscopy. Furthermore, the model contains an improved description of the coupling effect between solid-body and gas heat conduction by means of a single novel coupling parameter, which expresses the exceedance of the gas pressure dependent contribution of the effective thermal conductivity relative to the thermal conductivity of the gas inside the pores. At ambient pressure and 673 K mean temperature, the effective thermal conductivity of the opacified powder mixture amounts to 0.087 W m−1 K−1, thus being competitive with commercial high temperature insulation materials like calcium silicate, but at a lower price (ca. 2–3 € kg−1). Experiments with the transient hot wire method at ambient pressure yield a temperature dependent overestimation of the effective thermal conductivity by 4–22% compared to the guarded hot plate method, which is traced back to the pressure dependent contribution and discussed in appropriate terms of the difference between the coupling parameters obtained from both methods.

Thermal rectification enhancement of bi-segment thermal rectifier based on stress induced interface thermal contact resistance

Thermal rectification is the phenomenon that heat flows much easier from forward direction than reverse direction across the structure. Materials with temperature-dependent thermal conductivity and/or variable cross section area segments are always adopted to utilize obvious thermal rectification effect. Previous studies often ignored the effect of thermal contact resistance between the two segments of traditional bi-segment thermal rectifier. Since interface thermal contact resistance also contributes significantly to the total effective thermal conductivity of the rectifier, the present paper proposed a finite element scheme to simulate the thermomechanical coupling problem caused by the stress-dependent thermal contact resistance. The proposed method is verified and validated with analytical and experimental examples respectively, and numerical results show the effect of thermal contact resistance on the optimization of thermal rectification ratio. Several key parameters such as the initial gap between the two segments and the thermal contact resistance model parameters are investigated numerically, and the present paper provide a novel approach and design guidance to manipulate heat flux through stress-dependent thermal contact resistance.

Numerical and experimental study of stagnant effective thermal conductivity of a graphite pebble bed with high solid to fluid thermal conductivity ratios

In this work, a numerical method combining conduction and radiation is used to study the stagnant effective thermal conductivity of a simple cubic packed bed with high solid to fluid thermal conductivity ratios. The experiment is designed to verify the numerical model and the numerical results agree well with the experimental results. It is found that the effective thermal conductivity accounting for conduction and radiation declines first until 690 K as the temperature rises and then increases. This trend is a result of the interactions between different heat transfer components. Compared with the numerical values and experimental values, the ZBS correlation with a proper value for the empirical parameter φ selected is capable of predicting the stagnant effective thermal conductivity in the bulk region. Lastly the different heat transfer components caused by the solid/fluid conduction, contact conduction and radiation are extracted from the total effective thermal conductivity and their individual contributions are analyzed. The contact conduction makes a major contribution to the effective thermal conductivity but gets weaker as temperature rises. The radiation overtakes contact conduction after 920 K. The solid/fluid conduction has little influence on the effective thermal conductivity.

Investigation of Effective Thermal Conductivity for Ordered and Randomly Packed Bed with Thermal Resistance Network Method

In the present paper, the effective thermal conductivities of Li4SiO4-packed beds with both ordered and random packing structures were investigated using thermal resistance network methods based on both an Ohm’s law model and a Kirchhoff’s law model. The calculation results were also validated and compared with the numerical and experimental results. Firstly, it is proved that the thermal resistance network method based on the Kirchhoff’s law model proposed in the present study is reliable and accurate for prediction of effective thermal conductivities in a Li4SiO4-packed bed, while the results calculated with the Ohm’s law model underestimate both ordered and random packings. Therefore, when establishing a thermal resistance network, the thermal resistances should be connected along the main heat transfer direction and other heat transfer directions as well in the packing unit. Otherwise, both the total heat flux and effective thermal conductivity in the packing unit will be underestimated. Secondly, it is found that the effect of the packing factor is remarkable. The effective thermal conductivity of a packed bed would increase as the packing factor increases. Compared with random packing at similar packing factor, the effective thermal conductivity of packed bed would be further improved with an ordered packing method.

Development of correlations for effective thermal conductivity of a tetrakaidecahedra structure in presence of combined conduction and radiation heat transfer

The variations in the total effective thermal conductivity (keff,t) of a tetrakaidecahedra unit cell structure as functions of porosity (ϕ), thermal conductivity of the solid phase (ks) and the average temperature of the medium (Tavg), in the presence of combined conduction and radiation heat transfer, are presented in this article. For this purpose, the governing energy conservation equation is numerically solved using the blocked-off region approach based on the finite volume method. In addition, the variations in the radiative properties of the structure as functions of surface reflectivity (ρs), pore density (PPC) and ϕ are investigated, for which, a pure radiation heat transfer based numerical model is developed and used. From the detailed numerical simulations, three different correlations for keff,t are proposed. Correlation 1 is developed by fitting the raw simulated data, although its form does not respect some of the limiting conditions. Particularly for ks<5W/mK and in the absence of thermal radiation, it under-predicts the effective thermal conductivity due to pure heat conduction (keff,PC). Correlation 2, on the other hand, satisfies all possible limiting conditions, although it requires one additional simulation or correlation for keff,PC. Finally, correlation 3 is obtained by superposing the effective thermal conductivities due to pure radiation (keff,R) and keff,PC, while introducing an adjustable coefficient in order to account for the coupling between them. From the investigation on radiative properties, it is observed that the extinction coefficient increases with the decrease in ϕ and with the increase in PPC as well as ρs and hence keff,t as well as keff,R is expected to decrease for these conditions.

A theoretical model for the effective thermal conductivity of silica aerogel composites

In the present paper, a complete engineering calculation procedure for fast evaluations of the effective thermal conductivity of the silica aerogel composites is developed as follows. First, the spherical hollow model is adopted to calculate the conductive thermal conductivity of pure silica aerogels. Then, a mixing model is used to consider the conduction enhancement effects of doped opacifiers and fibers. Next, the Mie theory is adopted to calculate the temperature-dependent Rosseland mean extinction coefficient of the aerogel composites, and the radiative thermal conductivity is obtained according to the Rosseland equation. Finally, the superposition of the conductive thermal conductivity and radiative thermal conductivity gives the total effective thermal conductivity of aerogel composites. To validate the accuracy of the present model, some corresponding experimental measurements are conducted based on the Hot Disk thermal constant analyzer, and the experiment data agree well with the theoretical calculation values. The maximum deviation is about ±10%. The influences of the temperature, pressure and the structure parameters on the prediction of the effective thermal conductivity are then investigated. To determine the dominant factor of the effective thermal conductivity, the contributions of gas, solid and radiation to the total effective thermal conductivity are investigated individually and some significant results are obtained.

OPTIMIZATION OF THE FRACTAL-LIKE ARCHITECTURE OF POROUS FIBROUS MATERIALS RELATED TO PERMEABILITY, DIFFUSIVITY AND THERMAL CONDUCTIVITY

In this study, the optimization of the fractal-like architecture of porous fibrous materials related to permeability, diffusivity, and thermal conductivity was analyzed by applying the established theoretical models. It was observed that the ratio of dimensionless permeability over dimensionless effective diffusivity decreased with the decrease of porosity and tortuosity fractal dimension, respectively, which implied that lower porosity and tortuosity fractal dimension were beneficial to wind/water resistant fabric, as it reduced the ratio of dimensionless permeability over dimensionless effective diffusivity. Besides, it was found that the ratio of the dimensionless total effective thermal conductivity over dimensionless effective diffusivity increased with tortuosity fractal dimension, which implied lower tortuosity fractal dimension was beneficial to clothing insulation, as it reduced the ratio of dimensionless total effective thermal conductivity over dimensionless effective diffusivity. The optimization results indicated that fabrics with more aligned fibers were preferred for protective clothing, as the low tortuosity fractal dimension implied fibers in the fibrous materials should be more aligned.

A thermal conductivity study of double-pore distributed powdered silica aerogels

Powdered nanoporous silica aerogel is a typical double-pore distributed material. This paper develops a total effective thermal conductivity model that considers the coupling effect between different forms of heat transfer for the microstructure features of powdered silica aerogel by using an ideal structure with nanoporous spheres arranged in a spatially periodic structure. Performance of the developed model is compared to experimental results, with the effects of various parameters on thermal conductivity analyzed. The results show that the thermal conductivity of powdered silica aerogel decreased with decreasing gas pressure, and stabilized at its lowest value at pressures below 20Pa. A turning point existed at approximately 103Pa when looking at the logarithmic scale of gas pressure. The thermal conductivity decreased quite slowly with decreasing pressure when p>103Pa, but more quickly when gas pressure was lower than 103Pa. The thermal conductivity reduced with increased specific surface area, but did not change with powder diameter D when the pressure was higher than 103Pa. On the other hand, the thermal conductivity increased with increasing powder diameter D, but did not change with specific surface area when the pressure was less than 103Pa. As the powder diameter D decreased, the lowest stable point of the thermal conductivity increased. The radiation heat transfer contribution was very small when the temperature was less than 400K. With elevating temperature, the thermal conductivity of powdered silica aerogel distinctly increased. Thus, silica aerogel samples with large macro pores achieve greater thermal conductivity at elevated temperatures.

Theoretical Analysis of Effective Thermal Conductivity for the Chinese HTR-PM Heat Transfer Test Facility

The Chinese high temperature gas-cooled reactor pebble bed module (HTR-PM) demonstration project has attracted increasing attention. In order to support the project, a large-scale heat transfer test facility has been constructed for pebble bed effective thermal conductivity measurement over the whole temperature range (0~1600 °C). Based on different heat transfer mechanisms in the randomly packed pebble bed, three different types of effective thermal conductivity have been theoretically evaluated. A prediction of the total effective thermal conductivity of the pebble bed over the whole temperature range is provided for the optimization of the test facility and guidance of further experiments.

Coupling of gaseous and solid thermal conduction in porous solids

Porous material systems are commonly used for thermal insulation due to their low total effective thermal conductivities. However, the prediction of this physical property is difficult for some porous materials, since there is no straightforward relation to describe the impact of coupling between solid and gaseous thermal conduction. Thus, the aim of this work was to get a better general understanding of the coupling effect. For this purpose, different carbon and organic (resorcinol-formaldehyde) aerogels were used as model system with high and low intrinsic backbone conductivity and were investigated by means of gas-pressure dependent hot-wire measurements in different gas atmospheres (Ar, N2, He and CO2) up to 10MPa. The thermal conductivity data received for all samples analyzed show a significant amount of thermal coupling between gas and solid phase: The experimental gas-pressure dependent thermal conductivities are up to a factor of 3.3 higher than the expected pure gaseous thermal conductivities.A simple theoretical approach (“scaling model”) is introduced providing a good description of the experimental gas-pressure dependent thermal conductivity data. Thus, this model is useful for easily estimating the mean pore sizes of porous samples. Moreover, applying the scaling model to the helium data reveals that the accommodation coefficient of helium must be close to one for all aerogel samples investigated.Furthermore, the coupling term for a simple layer system is analytically described by a series connection of the thermal resistances of the two phases, in order to analyze the impact of different parameters on the coupling term: coupling increases with the ratio of solid phase thickness to mean pore size and with the ratio of solid to gaseous thermal conductivity. Overall, the theoretical results are consistent with the experimental results.

Experimental study of effective thermal conductivity of stainless steel fiber felt

An experimental apparatus was designed to measure the effective thermal conductivity of porous stainless steel fiber felt under different operating pressures. The total effective thermal conductivity was studied by analyzing matrix heat conduction, air natural convection, and matrix thermal radiation at ambient pressure. The contribution of air natural convection was experimentally obtained by changing the ambient pressure to vacuum condition and the solid matrix heat conduction was evaluated using a theoretical model. The ratios of the three mechanisms to the total effective thermal conductivity were approximately 40%, 37.9%, and 22.1%, respectively. In addition, the effects of fiber diameter and porosity on the three mechanisms and on the total effective thermal conductivity were studied. The air natural convection was found to gradually intensify when the operating pressure increases from vacuum condition (15 Pa) to ambient pressure (1.0 × 105 Pa). With an increase in fiber diameter under fixed porosity, the solid matrix heat conduction remained unchanged, and air natural convection and thermal radiation decreased, thereby resulting in reduced effective thermal conductivity. With an increase in porosity under fixed fiber diameter, the air natural convection was almost unchanged, and solid matrix heat conduction and thermal radiation were reduced, thereby resulting in reduced effective thermal conductivity.

Coupling model for heat transfer between solid and gas phases in aerogel and experimental investigation

Abstract The coupling heat conduction between the aerogel solid and gas phases is of important contribution to the total effective thermal conductivity of aerogel. Based on the assumption of spherical particles in the aerogel backbone, a theoretical model is proposed to calculate the coupling thermal conductivity in aerogel which relates aerogel mean pore size, mean particle size, gaseous thermal conductivity and solid particle thermal conductivity. An experimental study on the thermal conductivity of silica aerogel is carried out to validate the coupling model, and good agreement between the measured data and the coupling model is found. The present coupling model is also verified by available data including experimental results, numerical results and theoretical predictions in the literature. The comparison among the coupling models shows that the present model is of high accuracy without complex and difficult calculations.

Thermal Transport in High-Strength Polymethacrylimide (PMI) Foam Insulations

Thermal transport in high-strength polymethacrylimide (PMI) foam insulations is described, with special emphasis on the density and temperature effects on the thermal transport performance. Measurements of the effective thermal conductivity are performed by a freestanding sensor-based method. A linear relationship between the density and the effective thermal conductivity is observed. Based on the analysis of the foam insulation morphological structures and the corresponding geometrical cell model, the quantitative contribution of the solid conductivity and the gas conductivity as well as the radiative conductivity to the total effective thermal conductivity as a function of the density and temperature is calculated. The agreement between the curves of the results from the developed model and experimental data indicate the model can be used for PMI foam insulating performance optimization.

A Theoretical Comparative Study Between Open Cell Foam and Conventional Packed Bed in Externally Cooled Multitubular Fixed-Bed Reactors for the C1 Chemistry

The open cell foams are likely to be the next generation of catalyst supports due to their interesting specific properties (large exchange area, easy control of external porosity, etc.). In multitubular packed-bed reactors used for the C1 chemistry which constitute the focus of this work, it is well known that the removal of the reaction heat and the pressure drop are the most critical aspects for planning and designing chemical engineering processes. In this context, the objective of the present work is to compare the 'conventional' SiC spherical particles bed and SiC open cell foam bed for the C1 chemistry. From simulations, this work allows observing and quantifying the influences of the fluid velocity and the type of catalyst used (foam or packed bed) on the properties of transport. The observed responses are the total effective thermal conductivity and the pressure drop. The results indicate that it will be necessary to tune the void fraction and morphological parameters of the open cell foam in order to obtain the best compromise between pressure drop and a good thermal behavior.

Heat Transport in Evacuated Perlite Powders for Super-Insulated Long-Term Storages up to 300 °C

Vacuum super insulation (VSI) with expanded perlite powder is commonly used at cryogenic temperatures, but principally can also be adapted to applications at higher temperatures, such as the long-term storage of hot water in solar thermal systems. Due to the lack of experimental data in the respective temperature range, especially without external load, thermal conductivity measurements have been performed with commercial perlite powder up to 150°C mean sample temperature, corresponding to storage temperatures of around 300°C. Two different experimental geometries have been used: a guarded hot plate (GHP) setup and a cut-off concentric cylinder (CCC) apparatus. Furthermore, the radiative heat transport has been determined separately by extinction measurements using Fourier transform infrared (FTIR) spectroscopy. In addition to the laboratory experiments, a real-size prototype of a solar VSI-storage tank with 16.4 m3 water storage volume has been constructed, and the effective thermal conductivity of the perlite insulation has been determined from a heat loss measurement. The heat transport in evacuated perlite has also been treated theoretically using common models and approaches for gas heat conduction, solid-body conduction and heat transfer by thermal radiation. For the coupling between solid-body and gas conduction which occurs in the intergranular spaces of a powder material, a simple model has been developed. The total effective thermal conductivity λeff of a vacuum super insulation with dry, evacuated perlite powder (p≤0.01 mbar,ρ≈60 kg/m3) amounts to 0.007–0.016 W/mK for mean sample temperatures between 50°C and 150°C, compared to 0.003–0.005 W/mK at cryogenic temperatures. For the real-size storage prototype, the value λeff=0.009 W/mK has been obtained at T=90°C (storage temperature), p = 0.08 mbar and ρ=92.4 kg/m3, which compares to 0.03–0.06 W/mK for dry conventional storage insulations. With the applied theoretical models and approaches, the effective thermal conductivity of evacuated perlite and its individual contributions can successfully be described at different densities (55-95 kg/m3), compression methods, vacuum pressures (10-3-1000 mbar) and filling gases (air, Ar, Kr) up to mean sample temperatures of T=150°C. With regard to practical purposes, it has shown that vacuum super insulation with perlite is a suitable and economic method to achieve low thermal conductivities also at medium storage temperatures.

EFFECTIVE THERMAL CONDUCTIVITY OF FROST CONSIDERINGMASS DIFFUSION AND EDDY CONVECTION

A physical model for the effective thermal conductivity of water frost is proposed for application to the full range of frost density. The proposed model builds on the Zehner-Schlunder one-dimensional formulation for porous media appropriate for solid-to-fluid thermal conductivity ratios less than about 1000. By superposing the effects of mass diffusion and eddy convection on stagnant conduction in the fluid, the total effective thermal conductivity of frost is shown to be satisfactorily described. It is shown that the effects of vapor diffusion and eddy convection on the frost conductivity are of the same order. The results also point out that idealization of the frost structure by cylindrical inclusions offers a better representation of the effective conductivity of frost as compared to spherical inclusions. Satisfactory agreement between the theory and the measurements for the effective thermal conductivity of frost is demonstrated for a wide range of frost density and frost temperature.

Modeling of Transverse Direction Thermal Conductivity in Micro-nano Fiber-reinforced Composites

Analytical modeling for heat transfer behavior of micro-nano fiber-reinforced composites to determine the dimensionless effective thermal conductivity in the transverse direction has been performed. A hexagonal unit cell was developed that contained matrix, filler and interface (barrier) as the components. Thermal-electrical analogy method was used in the model. Models were developed with and without barrier effect. Filler ratios were taken to be between 10 and 30 %. Effects of barrier thickness and filler volume fraction on the dimensionless effective transverse thermal conductivity have been analyzed. The Rule of Mixtures and analytical modeling results have been compared. The model showed that increasing the volume fraction of the filler inside the matrix increased the total effective thermal conductivity values. When the barrier thickness increased, the dimensionless effective thermal conductivity value increased.

Thin film evaporation effect on heat transport capability in a grooved heat pipe

A theoretical model predicting the heat transfer performance occurring in a grooved heat pipe is developed. The model includes the effects of groove geometry, thin film evaporation, contact angle, and film condensation. The numerical results show that the groove geometry significantly affects the thin film evaporation and condensation. The thin film evaporation plays a key role in the total effective thermal conductivity and determines a limit for the maximum amount of heat transport through the micro regions for a given evaporator geometry. While the contact angle can influence the capillary limitation, it significantly affects the thin film evaporation and the total effective thermal conductivity of a groove heat pipe. In order to verify the theoretical analysis, an experimental investigation on a grooved heat pipe was conducted. The current investigation will result in a better understanding of thin film evaporation and its effect on the maximum heat transport in a grooved heat pipe.