Trend Of Thermal Conductivity Research Articles

Electron–electron scattering limits thermal conductivity of metals under extremely high electron temperatures

We report on the thermal transport properties of noble metals (gold, silver and copper) under conditions of extremely high electron temperatures (that are on the order of the Fermi energy). We perform parameter-free density functional theory calculations of the electron temperature-dependent electron–phonon coupling, electronic heat capacities, and thermal conductivities to elucidate the strong role played by the excitation of the low lying d-bands on the transport properties of the noble metals. Our calculations show that, although the three metals have similar electronic band structures, the changes in their electron–phonon coupling at elevated electron temperatures are drastically different; while electron–phonon coupling decreases in gold, it increases in copper and, it remains relatively unperturbed for silver with increasing electron temperatures of up to ∼60 000 K (or 5 eV). We attribute this to the varying contributions from acoustic and longitudinal phonon modes to the electron–phonon coupling in the three metals. Although their electron–phonon coupling changes with electron temperature, the thermal conductivity trends with electron temperature are similar for all three metals. For instance, the thermal conductivities for all three metals reach their maximum values (on par with the room-temperature values of some of the most thermally conductive semiconductors) at electron temperatures of ∼6000 K, and thereafter monotonically decrease due to the enhanced effect of electron–electron scattering for electronic states that are further away from the Fermi energy. As such, only accounting for electron–phonon coupling and neglecting electron–electron scattering can lead to large over-predictions of the thermal conductivities at extremely high electron temperatures. Our results shed light on the microscopic understanding of the electronic scattering mechanisms and thermal transport in noble metals under conditions of extremely high electron temperatures and, as such, are significant for a plethora of applications such as in plasmonic devices that routinely leverage hot electron transport.

Alloying Effects on the Transport Properties of Refractory High-entropy Alloys

Additive Manufacturing (AM) has opened new frontiers for the design of refractory high-entropy alloys (HEAs) for high-temperature applications. The thermal conductivity of the AM feedstock is among the most important thermo-physical properties that control the melting and solidification process. Despite its significance, there remains a notable gap in both computational and experimental research concerning the thermal conductivity of HEAs. Here, we use density functional theory (DFT) to systematically investigate the alloying effects on the transport properties of Ti-Cr-Mo-W-V-Nb-Ta RHEAs, including electrical and thermal conductivities and Seebeck coefficient. The relaxation time of charge carriers is a key underlying parameter determining thermal conductivity that is exceedingly challenging to predict from first principles alone, and we thus follow the approach by Mukherjee, Satsangi, and Singh [Chem Mater 32, 6507 (2022)] to optimize the relaxation time for RHEAs. We validated thermal conductivity predictions on elemental solids, binary and ternary alloys, and RHEAs and compared them against thermodynamic (CALPHAD) predictions and our experiments with good correlations. To understand observed trends in thermal conductivity, we assessed the phase stability, electronic structure, phonon, and intrinsic- and tensile strength of down-selected RHEAs. Our electronic structure and phonon results connect well with the observed compositional trends for thermal transport in RHEAs. Our DFT assessment and CALPHAD predictions provide a unique design guide for RHEAs with tailored thermal conductivity, a critical consideration for AM and thermal-management applications.

Assessing the thermal conductivity of amorphous SiN by approach-to-equilibrium molecular dynamics.

First-principles molecular dynamics combined with the approach-to-equilibrium molecular dynamics methodology is employed to calculate the thermal conductivity of non-stoichiometric amorphous SiN. This is achieved by implementing thermal transients in five distinct models of different sizes along the direction of the heat transport. Such models have identical structural features and are representative of the same material, thereby allowing for a reliable analysis of thermal conductivity trends as a function of the relevant cell dimension. In line with the known physical law of heat propagation at short scale, the thermal conductivity increases in size with the direction of heat transport. The observed behavior is rationalized accounting for previous results on crystalline and amorphous materials, thus providing a unified description holding for a large class of materials and spanning a wide range of heat propagation lengths.

Thermal transport characterization of monolayer GaN nanoribbon doped with group IV materials: An equilibrium molecular dynamics study

Bulk gallium nitride (GaN) has been considered as one of the prominent materials for a long time in the application of laser, LED and transistors. Due to its superior electrical characteristics, its low-dimensional hexagonal counterpart is currently drawing attention like graphene. In this study, we have investigated the effect of impurity atoms on the heat energy conduction within this honeycomb nanostructure of GaN to explore its scope of applications. The room temperature thermal conductivity of zigzag GaN nanoribbon (ZGaNNR) is found to be ∼ 11 Wm−1K−1 using the molecular dynamics approach with the Green-Kubo formulation. Various group IV elements namely- carbon, silicon, germanium and tin, have been incorporated within the pristine structure in four distinct doping patterns; like- point (Type-I and Type-II), pair and delta doping, to explore the thermal transport in chemically doped nanostructures. A gradual enhancement in the thermal conductivity is observed for the increasing concentration of carbon and silicon as dopants. On the other hand, selection of germanium and tin as impurity atoms suppresses the heat conduction within the crystal due to the increased low frequency phonon scattering. In all cases, Type-I point doping affects the thermal transport of ZGaNNR significantly. The narrower ribbons impede the phonon transportation due to the strong boundary effects resulting in a lower thermal conductivity. Moreover, phonon transportation is largely suppressed, and heat energy is observed to flow at a slower rate as the temperature of the ribbon rises. We have also studied these doped structures under the influence of point, edge and pair vacancies and observed a decreasing trend in thermal conductivity for each type of vacancy defect patterns introduced in the crystal. Such a study would promote the rising interest in properly characterizing the heat transport of low dimensional nanostructures and it can be an effective technique to tune the thermal conductivity of ZGaNNR for improving thermoelectric performance and thermal management in nanoscale devices.

Thermal Conductivity of MoS2 and Graphene/MoS2 Heterojunction

With the development of the miniaturization of electronic devices, controlling heat dissipation has become a key factor, which affects the service life of devices and energy utilization efficiency. Therefore, it is particularly important to study the heat conduction mechanism of nanomaterials inside microelectronic devices. Herein, the thermal conductivity of MoS2 and graphene/MoS2 heterojunctions using the bond‐order–length–strength theory and the local bond average method is quantitatively analyzed; the functional relationship between the thermal conductivity and the number of layers, temperature, and pressure is established; and the variation trend of thermal conductivity of materials with these factors is studied. The results show that the thermal conductivity of MoS2 and graphene/MoS2 heterojunctions is inversely proportional to the number of layers and temperature, proportional to the pressure. The work provides a simple and effective method for the study of thermal transport properties of 2D materials and heterojunction systems from the perspective of chemical bonding changes at the atomic level.

Achieving high thermal conductivity of Al–50Si alloy through heat treatment and its microstructural evolution

Al–50Si alloys were prepared by powder extrusion and characterized for electronic packaging. The optimization of powder size, extrusion temperature, and heat treatment parameters was performed to enhance the microstructure and thermo-physical properties. The alloy exhibits a high relative density >99 %, a low coefficient of thermal expansion (CTE) < 10 × 10−6/K, and a good thermal conductivity (TC) ∼117 Wm−1K−1 achieved by employing a large size powder and high extrusion temperature during the extrusion process. Subsequent heat treatment of the optimized alloy at 550 °C for various time reveals a fluctuating increasing trend in TC during the heat treatment process. The TC values exhibit periodic fluctuations as they alternate between increments and decrements, primarily resulting from the recrystallization and secondary recrystallization of Al grains during heat treatment process. Notably, the maximum TC value (∼159.1 Wm−1K−1) at room temperature is obtained after heating the alloy to 550 °C for 26 h. Compared to the as-extruded alloy, the TC of heat-treated alloy increases by approximately 36 %, which can be attributed to the elimination of eutectic Si and growth of Si and Al grains within the alloy. The study may shed light on the mechanism underlying the improvement in thermal conductivity of Al–50Si alloy by microstructural evolution.

Anomalous Thermal Transport across the Superionic Transition in Ice

Superionic ices with highly mobile protons within stable oxygen sub-lattices occupy an important proportion of the phase diagram of ice and widely exist in the interior of icy giants and throughout the Universe. Understanding the thermal transport in superionic ice is vital for the thermal evolution of icy planets. However, it is highly challenging due to the extreme thermodynamic conditions and dynamical nature of protons, beyond the capability of the traditional lattice dynamics and empirical potential molecular dynamics approaches. By utilizing the deep potential molecular dynamics approach, we investigate the thermal conductivity of ice-VII and superionic ice-VII″ along the isobar of P = 30 GPa. A non-monotonic trend of thermal conductivity with elevated temperature is observed. Through heat flux decomposition and trajectory-based spectra analysis, we show that the thermally activated proton diffusion in ice-VII and superionic ice-VII″ contribute significantly to heat convection, while the broadening in vibrational energy peaks and significant softening of transverse acoustic branches lead to a reduction in heat conduction. The competition between proton diffusion and phonon scattering results in anomalous thermal transport across the superionic transition in ice. This work unravels the important role of proton diffusion in the thermal transport of high-pressure ice. Our approach provides new insights into modeling the thermal transport and atomistic dynamics in superionic materials.

Study on designing measurement system of thermal conductivity based on one-dimensional steady-state method

Thermal conductivity has wide application in various fields such as in agricultural and food sectors. In a food industry, measuring the thermal conductivity is designed to optimize the thermal process such as drying, sterilization, and freezing. In this study, a system to measure thermal conductivity is designed according to one-dimensional steady state method through Fourier formula. The experiment uses samples consisting of rice-based product (rice grain, rice powder, rice flour, cooked rice) and whole milk powder. The analysis will be performed in the range of 15-30 minutes on its steady condition. The results are verified with the literature data and evaluated through degree equivalence calculation. As a result, the system can distinguish the samples which has different texture and composition. Furthermore, the system can figure the increasing trend of thermal conductivity with the raise of moisture content. However, in most case, thermal conductivities of the measured samples have higher value compared to the literature data (2-4 times higher). The disparity due to the variation of heating temperature, sample condition, measurement technique, and analysis. Several finding to gain more reliable system can be done by improving the insulation or evaluating the mathematical calculation into a two-dimension approximation. In general, the design of the system is plausible for measuring the thermal conductivity.

Effect of eggshell powder on the microstructural and thermal behavior of Al7075/waste eggshell surface composites produced by solid-state friction stir processing developed for potential thermal applications

Lightweight composite materials for potential thermal applications are the contemporary demand for manufacturing and aircraft industries where the possibility to improve and tailor the desired properties is based on the application. Carbonized eggshell powder is a solid lubricant with absorbent capability and has proven as a reinforcement for metallic base composites. In the present work, an attempt is made to investigate the effect of carbonized chicken eggshell powder (3 to 9% by weight) on the microstructural and thermal properties of Al7075 alloy processed by solid-state friction stir processing. An infrared thermography and three K-type thermocouples equipped with the base plate at three equal distances are used to measure the temperature with respect to time. The comparative study of microstructure and grain structure analysis has been done by light microscopy, scanning electron microscopy, and electron backscattered diffraction methods. The findings explored the dynamic recrystallization and grain recovery with a reduced grain size of 6.2 to 10.3 µm at a varying percentage of eggshell powder (3 to 9%) in the stir zone. The thermal conductivity and coefficient of thermal expansion (CTE) were measured for the temperature range of 50 to 400 °C. In addition to it, differential thermal analysis (DTA), thermo-gravimetric analysis (TGA), and derivative thermo-gravimetric analysis (DTG) are conducted for the temperature range of 25 to 900 °C to discuss the endothermic, exothermic nature, and degradation characteristics. The result revealed the decreasing trend of thermal conductivity, and CTE values were found in the range of 97 to 53 W/mK and 26.6 to 24 × 10−6 K−1 (heating cycle), 27.2 to 23.8 × 10−6 K−1(cooling cycle), respectively. Furthermore, the higher and lower thermal conductivity of 108 W/mK and 62 W/mK is observed at higher and lower terminal voltages, 250 V and 100 V, respectively. The DTA, TGA, and DTG curves explored the maximum weight loss, which varies up to 5.25% with exothermic peaks and decomposition steps for each surface composite.

Microencapsulated phase change material incorporated light transmitting gypsum composite for thermal energy saving in buildings

The increased energy consumption for specific applications, including heating, cooling, air conditioning and lighting of residential and commercial buildings accelerate the research efforts concentrated on developing thermal energy storage capacity of buildings materials in recent years. Likewise, the development of light-transmitting building elements is a novel energy-saving technique that enhances lighting efficiency in buildings. In light of these, the current study seeks to design an untried microencapsulated phase change material (MPCM) integrated glass fiber reinforced gypsum composite with sufficient light-transmitting properties and thermal energy storage capacity. In this research, a multi-scale investigation of light-transmitting gypsum composite was conducted experimentally with physical, mechanical, chemical, microstructural, thermal, light transmittance and solar thermoregulation tests. The gypsum composite is formed from α-gypsum, water, polymer admixture, alkali-resistant glass fiber (AR-GF), several concentrations of MPCM, and plastic optical grids to allow light to transmit through the board. Although higher fractions of MPCM yielded an apparent decrease in mechanical strength test results, 5 wt% introduction of MPCM to the reference matrix reduced the compressive and flexural strength of specimens by 1 and 8 %, respectively. The results verified a reduction trend in thermal conductivity of composites with MPCM loading. DSC investigations revealed that the melting temperature and the regarding latent heat storage capacity of gypsum composite with 15 wt% of MCPM are 17.76 °C and 19.2 J/g, respectively. Light-transmitting gypsum composites showed up to ~10 % light transmittance, that can greatly increase the efficiency of lighting in buildings. The produced gypsum composites with MPCM kept the test room cooler during the highest temperature, while it provided a warmer room during the nighttime for an extended time. The study's findings are applicable to increase thermal comfort by reducing the significant temperature variations in buildings and improving artificial lighting efficiency, encouraging the design of sustainable building applications.

Estimating the thermal conductivity of plutonic rocks from major oxide composition using machine learning

SUMMARY The accurate estimation of temperature distribution in the earth's crust and modelling of heat-related processes in geodynamics requires knowledge of the thermal conductivity of plutonic rocks. This study compiled an extensive data set of 530 representative plutonic rock samples, including thermal conductivity, major oxide composition and (for two subsets of data) modal mineralogy. For the first time, three machine learning algorithms (ML; i.e. support vector regression, random forest and extreme gradient boosting) were employed to estimate the thermal conductivity of plutonic rocks using the major oxide composition feature as input variables. The performance of these ML-based models was evaluated against a geochemically compositional model and eight mineral-driven physically based empirical mixing models. Results show that the means of predicted thermal conductivity by the ML-based models and the geochemically compositional model are not significantly different from the measured thermal conductivity at a significance level of 5 per cent. However, the ML-based models outperformed the best-performing non-ML model, the geochemically compositional model. The highest prediction accuracy was achieved by extreme gradient boosting, which reduced the mean absolute percentage error and root mean square error by more than 50 per cent. Furthermore, SiO2 is confirmed as the most important independent variable, followed by Al2O3, TiO2, CaO and K2O. The turning point observed in the thermal conductivity trend with SiO2 wt per cent may be primarily attributed to variations in mineral composition within the subgroup of igneous rock types classified based on SiO2 wt per cent. This study explores, for the first time, the use of ML algorithms to estimate the thermal conductivity of plutonic rocks from their major oxide composition.

Cellulose nanocrystal-assisted processing of nanocomposite filaments for fused filament fabrication

This study introduces a scalable processing technique where cellulose nanocrystals (CNCs) are used to integrate pristine multi-walled carbon nanotubes (CNTs) into acrylonitrile butadiene styrene (ABS) polymer without functionalization, solvents, or surfactants. A synergy between the nanomaterials and printed road angle was discovered, with angle ply orientation optimizing mechanical properties and longitudinal orientation improving thermal conductivity. Mechanical properties improved up to 81% in tensile strength and 95% in elastic modulus, while a 102% increase in interlaminar strength was exhibited. The thermal conductivity trend showed an anisotropy between radial and axial directions, where one could be increased while the other was diminished, with as much as 807% increase in the transverse sample. By optimizing print orientation and nanoparticle content, tailored material properties are achievable.

Process-dependent anisotropic thermal conductivity of laser powder bed fusion AlSi10Mg: impact of microstructure and aluminum-silicon interfaces

PurposeAlSi10Mg alloy is commonly used in laser powder bed fusion due to its printability, relatively high thermal conductivity, low density and good mechanical properties. However, the thermal conductivity of as-built materials as a function of processing (energy density, laser power, laser scanning speed, support structure) and build orientation, are not well explored in the literature. This study aims to elucidate the relationship between processing, microstructure, and thermal conductivity.Design/methodology/approachThe thermal conductivity of laser powder bed fusion (L-PBF) AlSi10Mg samples are investigated by the flash diffusivity and frequency domain thermoreflectance (FDTR) techniques. Thermal conductivities are linked to the microstructure of L-PBF AlSi10Mg, which changes with processing conditions. The through-plane exceeded the in-plane thermal conductivity for all energy densities. A co-located thermal conductivity map by frequency domain thermoreflectance (FDTR) and crystallographic grain orientation map by electron backscattered diffraction (EBSD) was used to investigate the effect of microstructure on thermal conductivity.FindingsThe highest through-plane thermal conductivity (136 ± 2 W/m-K) was achieved at 59 J/mm3 and exceeded the values reported previously. The in-plane thermal conductivity peaked at 117 ± 2 W/m-K at 50 J/mm3. The trend of thermal conductivity reducing with energy density at similar porosity was primarily due to the reduced grain size producing more Al-Si interfaces that pose thermal resistance. At these interfaces, thermal energy must convert from electrons in the aluminum to phonons in the silicon. The co-located thermal conductivity and crystallographic grain orientation maps confirmed that larger colonies of columnar grains have higher thermal conductivity compared to smaller columnar grains.Practical implicationsThe thermal properties of AlSi10Mg are crucial to heat transfer applications including additively manufactured heatsinks, cold plates, vapor chambers, heat pipes, enclosures and heat exchangers. Additionally, thermal-based nondestructive testing methods require these properties for applications such as defect detection and simulation of L-PBF processes. Industrial standards for L-PBF processes and components can use the data for thermal applications.Originality/valueTo the best of the authors’ knowledge, this paper is the first to make coupled thermal conductivity maps that were matched to microstructure for L-PBF AlSi10Mg aluminum alloy. This was achieved by a unique in-house thermal conductivity mapping setup and relating the data to local SEM EBSD maps. This provides the first conclusive proof that larger grain sizes can achieve higher thermal conductivity for this processing method and material system. This study also shows that control of the solidification can result in higher thermal conductivity. It was also the first to find that the build substrate (with or without support) has a large effect on thermal conductivity.

Influence of point defects and multiscale pores on the different phonon transport regimes

A common strategy to tailor the thermal conductivity of a material is to introduce structural features that modulate phonon scattering, such as atomic-scale defects and nano- and macro-sized pores. However, particle-like and wave-like phonon transport and scattering during a crossover in thermal transport regimes is not well understood. Here, we perform a rigorous quantitative comparison of the thermal conductivity obtained from molecular dynamics simulations and phonon Boltzmann transport equations, taking graphene as an example. We observe a generally increasing trend in thermal conductivity when the pore size increases from point defect to nanopore, due to a transition from Rayleigh scattering to geometric scattering and reduced boundary density. The thermal conductivity further converges to the diffusive limit for macropores because of the dominant effect of phonon-phonon scattering over phonon-boundary scattering. Moreover, we identify a critical interpore distance for the crossover from dependent to independent phonon-pore scattering and a critical pore size for the crossover from point defect scattering to boundary scattering. This work provides a comprehensive understanding of phonon transport in materials containing defects and pores.

Investigation of thermal properties of graphene-silicone oil nanofluid

All electronic and mechanical devices are getting modified and modernized in compact sizes to increase performance. The thermal management of these systems is challenging because of the high heat rate from compact devices. Improper thermal management leads to short circuits in the electronics and poor performance in mechanical devices because the overheating and converting into waste pollutes the environment. This work attempts to prepare stable and homogeneous nanofluid with graphene nanoplatelets as the nanoparticles and silicone oil as the base fluid and evaluate the trend of thermal conductivity and viscosity of the prepared nanofluid for varying temperatures from 30 °C to 55 °C. Our attention is also on the ultrasonication time of prepared silicone oil graphene nanofluids. So, three ultrasonication times of 1 h, 2 h, and 3 h are chosen to check the effect of ultrasonication time on the nanofluid's thermodynamic properties (thermal conductivity and viscosity). In this work, nanofluids of particle concentrations 0.05 %, 0.1 %, and 0.15 % weight of 3 each for different ultrasonication times of 1 h, 2 h, and 3 h are prepared. The sodium lauryl sulphate was used as a surfactant for better stability of particles. The thermal conductivity test was conducted with thermal conductivity apparatus works on Debye's concept and calculated with a modified Bridgman equation. A rheometer was used for the viscosity measurement. This nanofluid is used as a coolant in transformers, automobile fan-clutch assemblies, and coolant in international space station radiators.

Dual effects of hetero-interfaces on phonon thermal transport across graphene/C[formula omitted]N lateral superlattices

Two-dimensional (2D) lateral superlattices, a typical artificial nano-phononic crystal, have stimulated widespread interests and potential application prospects in terms of their physically interesting features. Herein, we have found wave-particle crossover of phonon transport in the graphene (Gr)/2D polyaniline (C3N) lateral superlattices, which is an indication of a transition in the phonon transport mechanism from the incoherent to coherent regime. Due to the high structural similarity of C3N to Gr, the thermal conductivity of the Gr/C3N lateral superlattice can achieve an ultra-wide modulation range of about 500∼1100 W m−1 K−1, which is far beyond that of other superlattices. The analysis shows that an increase of the interface density will on the one hand weaken the thermal conductivity by increasing phonon-interface scattering, and on the other hand increase it by lowering the phonon transport barriers and allowing more long-wavelength phonons to participate in the transport. This determines the parabolic trend of thermal conductivity containing the minimum, and also reflects the dual effects of hetero-interfaces on phonon thermal transport. In addition, phonon calculations show that the above variation in thermal conductivity is entirely attributable to differences in the phonon mean free path for different interface densities and is not related to their group velocity.

Thermal and mechanical performance of gypsum composites with waste cellulose acetate fibres

The influence of waste cellulose acetate (CA) fibres in the physico-mechanical (i.e. density, surface hardness - Shore C, flexural and compressive strength) and thermal properties (i.e. thermal conductivity coefficient) of gypsum-based composites was evaluated in this study. Furthermore, complementary stereomicroscopy and scanning electron microscopy analysis were carried out. Lighter composites were obtained with ensuing incorporation of waste CA fibres. In comparison to the control material, an improvement on flexural and compressive strength, up to ∼9 % and ∼1 %, respectively was observed. Moreover, a slight declining trend in thermal conductivity was found with increasing replacement level (up to ∼16 % decrease).

Establishment of thermal conductivity model and analysis of enhancement mechanism in nanofluids: A molecular dynamics study

The requirements for high efficient heat exchange technology in many fields are gradually increasing. Nanofluids have attracted extensive attention due to their enhanced thermal conductivity. Revealing the mechanism of thermal conductivity enhancement is key to the preparation of high-efficiency nanofluids. In molecular dynamics (MD), the accuracy of simulation models is crucial to predict the thermal conductivity of nanofluids. Here, systems with various volume fractions were established by utilizing three different approaches. These approaches, denoted as Model 1, Model 2, and Model 3, involved changing the number of nanoparticles (NPs), the size of NPs, and the size of the simulation box as well as number of water molecules, respectively. The thermal conductivity values obtained from the simulations were validated using experimental data. The mechanism of thermal conductivity enhancement was explained by microscopic parameters. The results show that Model 1 was best able to capture the trends in thermal conductivity seen in the experimental data. Further, the thickness of the interfacial layer, estimated from the RDF and number density, was not affected by volume fraction and temperature, which instead determine the interactive forces between the NPs and the base fluid. The mechanism of enhancement of thermal conductivity may be attributed to the fact that the L-J potential energy of the Cu-O pair (−1.21 Kcal.mol−1) is stronger than that of the O-O pair (−0.15 Kcal.mol−1), thereby bringing water molecules into closer contact with the Cu NPs. As the volume fraction and temperature increase, the heat exchange between water molecules inside and outside the interfacial layer also increases, which accelerates the attainment of thermal equilibrium in the nanofluidic system.

Thermal response tests on deep boreholes through multiple ground layers

Distributed thermal response tests (DTRTs) on vertical boreholes estimate design parameters, which are used in the coupling of these boreholes to heat pumps. A semi-analytical model of a DTRT has been developed that includes multiple ground layers and the geothermal gradient for deep boreholes. The model is computationally efficient, which allows quick estimates of ground properties when the model is linked with parameter estimation techniques. The study focuses on coaxial boreholes, which are the more likely geometry for deep boreholes, although the model also handles boreholes with U-tubes. The proposed model is validated against previous DTRT simulations with an independent numerical model. In the cases studied, the model estimates the mean ground thermal conductivity within ± 5% of the exact value, while the uncertainty of the estimate is ± 10% or ± 0.2 W/(m‧K). The model identifies upward and downward increasing trends of thermal conductivity among ground layers. The estimates of ground thermal conductivity for individual layers have uncertainties as large as ± 0.65 W/(m‧K) under heat extraction cases in deep boreholes (800 m).

The influence of nitrogen doping on the thermal conductivity of diamond heat sink

During the epitaxial growth process of diamond heat sinks, nitrogen impurities are usually unintentionally introduced, which impact on the thermal conductivity. Therefore, the effect of nitrogen doping on the thermal conductivity of diamond heat sink is studied in this paper. The change of thermal conductivity conforms to the K = CT−1+A(B1/T)T5/2, which is attributed to the synergistic effects of phonons and carriers. With the increase of the nitrogen concentration, the downward trend of thermal conductivity gradually flattened and began to show a weak upward trend. This phenomenon is attributed to the anharmonic effect of lattice vibration rather than an increase in the number of conduction electrons.