Dependence Of Effective Thermal Conductivity Research Articles

Molecular simulation of steady-state evaporation and condensation of water in air

It was shown in recent experiments and molecular dynamics (MD) simulations that Schrage equation predicts evaporation and condensation rates of water in the absence of a non-condensable gas with good accuracy. However, it is not clear whether Schrage equation is still accurate or even valid for quantifying water evaporation and condensation rates in air. In this work, we carry out MD simulations to study steady-state evaporation and condensation of water at a planar water-air interface. The simulation results show that the evaporation and condensation fluxes of water in the presence of air are still in a good agreement with the predictions from Schrage equation. From Schrage equation and Stefan's law of mass diffusion, we derive an analytical expression for the effective thermal conductivity of a planar heat pipe. The analytical prediction of the dependence of effective thermal conductivity on heat pipe length and density of non-condensable gas is corroborated by our MD simulation results and recent experimental data.

Microstructure Dependence of Effective Thermal Conductivity of EB-PVD TBCs.

Microstructure dependence of effective thermal conductivity of the coating was investigated to optimize the thermal insulation of columnar structure electron beam physical vapor deposition (EB-PVD coating), considering constraints by mechanical stress. First, a three-dimensional finite element model of multiple columnar structure was established to involve thermal contact resistance across the interfaces between the adjacent columnar structures. Then, the mathematical formula of each structural parameter was derived to demonstrate the numerical outcome and predict the effective thermal conductivity. After that, the heat conduction characteristics of the columnar structured coating was analyzed to reveal the dependence of the effective thermal conductivity of the thermal barrier coatings (TBCs) on its microstructure characteristics, including the column diameter, the thickness of coating, the ratio of the height of fine column to coarse column and the inclination angle of columns. Finally, the influence of each microstructural parameter on the mechanical stress of the TBCs was studied by a mathematic model, and the optimization of the inclination angle was proposed, considering the thermal insulation and mechanical stress of the coating.

Effects of structure characteristics and fluid on the effective thermal conductivity of sintered copper foam

Heat exchangers with excellent heat transfer performance are highly demanded as the development of the powerful chips and integrated circuit. Due to the large surface area and good thermal conductivity, porous metal has become a potential candidate material for the future heat exchangers. A powder metallurgy-based method was used to manufacture copper foam samples with highly controllable particle size, porosity and pore size in this study. The effects of particle size, porosity and natural convection on the so-called effective thermal conductivity (ETC) of the copper foam and the heat transfer mechanism of copper foam-fluid system were experimentally investigated. The effect of natural convection was studied by comparing the ETC of the copper foam, copper foam-air and copper foam-water system. Results show that the thermal conductivity of sintered copper sample was strongly affected by the particle size of the starting copper powder. The medium particle size (45–70 μm) was ideal for obtaining the best thermal conductivity. The dependence of ETC on porosity can be properly described by the Power Law model. A linear correlation was also proposed to describe the effects of porosity and pore size on the contribution of the fluid to the metal foam–fluid system.

Numerical investigation on effective thermal conductivity of fibrous porous medium under vacuum using Lattice-Boltzmann method

Up to now, the application of fibrous porous medium (FPM) has gained considerable attention within the field of adiabatic materials, especially in the field of vacuum insulation panels (VIP). In the present study, a holistic numerical approach that combined with a modified 3D fibrous porous structure generation method and a D3Q19-BGK Lattice-Boltzmann method (LBM) is developed to investigate the dependence of effective thermal conductivity (ETC) on the microstructure of FPM under vacuum condition. The modified generation approach can effectively avoid fiber interpenetration. Model is validated with experimental and theoretical data. Influences of different microstructure parameters such as fiber diameter and fiber orientation angle are presented in detail. Results indicated that FPM structure with finer diameter leads to smaller pore size and has a more excellent ability to maintain the lower effective thermal conductivity under higher pressure. Besides, the more the length direction of fiber is inconsistent with the heat transfer direction, the better the insulation performance is. In addition, coupling effect is existed between the fiber diameter and orientation angle under high vacuum. These results are of great significance for the core material optimization of vacuum insulation panels.

Thermal conduction in open-cell metal foams: Anisotropy and Representative Volume Element

It is well known that the manufacturing process of open-cell foams slightly elongates their struts in one direction, thus making them anisotropic; in turn, anisotropy affects foam characteristics. Furthermore, actual foams can be characterized with reference to a Representative Volume Element (RVE), defined as the cubic sub-volume having the same characteristics as those of the whole foam. An appropriately chosen RVE is very helpful to pass simulation data from a micro-to a macro-scale. The important role played by RVE in characterizing foams performance suggests further research in its determination, in order to reduce computational power and to allow to apply the volume-averaging technique to open-cell foams. In this paper, anisotropy and RVE for the effective thermal conductivity of open-cell metal foams are numerically analyzed. After scanning with Computed Tomography (CT) and postprocessing four open-cell aluminum foams with different porosities and the same Pores Per Inch (PPI) value, their morphologies are investigated in order to evaluate the effects of porosity on cells anisotropy. Foam cell elongation is quantified by an anisotropy ratio. Simulations are performed on CT data with a finite-element method to compute the effective thermal conductivities along three orthogonal directions, and results are compared with data published in the literature. A new correlation between effective thermal conductivity, porosity and direction is presented. The dependence of effective thermal conductivity on cells elongation is also pointed out. RVE sizes for different porosities, directions and inaccuracy thresholds are then investigated. Finally, an existing analytical model is suitably adapted to reliably predict the RVE size with a new correlations which accounts for the directionally-averaged effective thermal conductivity.

Thermal conductivity model of open-cell foam suitable for wide span of porosities

In this work, an effective thermal conductivity (ETC) model of open cell foam composite is proposed based on regular pentagonal dodecahedron geometrical model, considering the realistic shape of ligaments, hollowness in ligaments and ligament orientations. Compared with other ETC models, this model exhibits higher accurate predictions with respect to the available experimental data in a wide span of porosities spanning from about 0.6 up to 1. Results show that the ETC of foam composites will increase with increase of the hollowness of ligaments at the same foam porosity. For a high porosity, the influence of the hollowness of ligaments on the ETC is negligible when the foam material has a high TC. The ETC of copper foam-paraffin composite predicted by our model agrees well with that obtained by experimental methods carried out in this work, both suggest that the ETC almost linearly depend on the melting degree of paraffin. According to the linear dependence of ETC on the melting degree of paraffin, the melting degree of the paraffin in copper foam-paraffin composite can be roughly obtained by fitting our model to the experimental ETC. The model developed in this work is expected to give an accurate prediction of open cell foam composites, and also could be applied to evaluate the melting degree of phase change materials in open cell foam composites.

A new semi-analytical model for effective thermal conductivity of nanofluids

ABSTRACTA new theoretical model for thermal conductivity of nanofluids is developed incorporating effective medium theory, interfacial layer, particle aggregation and Brownian motion-induced convection from multiple nanoparticles/aggregates. The predicated result using aggregate size, which represents the particle size in the actual condition of nanofluids, fits well with the experimental data for water-, R113- and ethylene glycol (EG)-based nanofluids. The present model also gives much better predictions compared to the existing models. A parametric analysis, particularly particle aggregation, is conducted to investigate the dependence of effective thermal conductivity of nanofluids on the properties of nanoparticles and fluid. Aggregation is the main factor responsible for thermal conductivity enhancement. The dynamic contribution of Brownian motion on thermal conductivity enhancement is surpassed by that of static mechanisms, particularly at high volume fraction. Predication also indicated that the viscosity increases faster than the thermal conductivity, causing the highly aggregated nanofluids to become unfavourable, especially for df = 1.8.

Superdiffusive heat conduction in semiconductor alloys. I. Theoretical foundations

Semiconductor alloys exhibit a strong dependence of effective thermal conductivity on measurement frequency. So far this quasi-ballistic behaviour has only been interpreted phenomenologically, providing limited insight into the underlying thermal transport dynamics. Here, we show that quasi-ballistic heat conduction in semiconductor alloys is governed by L\'evy superdiffusion. By solving the Boltzmann transport equation (BTE) with ab initio phonon dispersions and scattering rates, we reveal a transport regime with fractal space dimension $1 < \alpha < 2$ and superlinear time evolution of mean square energy displacement $\sigma^2(t) \sim t^{\beta} (1 < \beta < 2)$. The characteristic exponents are directly interconnected with the order $n$ of the dominant phonon scattering mechanism $\tau \sim \omega^{-n} (n>3)$ and cumulative conductivity spectra $\kappa_{\Sigma}(\tau;\Lambda)\sim (\tau;\Lambda)^{\gamma}$ resolved for relaxation times or mean free paths through simple relations $\alpha = 3-\beta = 1 + 3/n = 2 - \gamma$. The quasi-ballistic transport inside alloys is no longer governed by Brownian motion, but instead dominated by L\'evy dynamics. This has important implications for the interpretation of thermoreflectance (TR) measurements with modified Fourier theory. Experimental $\alpha$ values for InGaAs and SiGe, determined through TR analysis with a novel L\'evy heat formalism, match ab initio BTE predictions within a few percent. Our findings lead to a deeper and more accurate quantitative understanding of the physics of nanoscale heat flow experiments.

Dependence of effective thermal conductivity of composite materials on the size of filler particles

A well-known Maxwell’s model for evaluation of effective thermal conductivity has been modified incorporating a correction factor s. It is an important quantity, which influences the effective thermal conductivity of composite materials together with other parameters like volume fraction and thermal conductivities of the constituents. Parameter estimation technique is used to determine the value of s. Optimized value of s is used in the modified Maxwell’s model to estimate effective thermal conductivity of composite materials. The effective thermal conductivity of composite materials using an artificial neural network approach has also been calculated. Materials of different sizes of filler particles/matrix have been considered for calculation of the effective thermal conductivity. Results obtained using modified Maxwell’s model and artificial neural network technique have been compared with the experimental results available in the literature which shows a good fit.

Modeling the thermal conductivity of graphene nanoplatelets reinforced composites

An analytical model is developed for the effective thermal conductivity of the composites with graphene nanoplates (GNPs) within the framework of differential-effective-medium (DEM) theory. Results of the present model are compared to an effective-medium-approximation (EMA) based model and available experimental results. Predictions on the effective thermal conductivity of GNP/PA-6 and GNP/epoxy composites are in good agreement with the experimental data. Moreover, the present model can well describe the large thermal conductivity enhancement in GNP composites and, in particular, the nonlinear dependence of effective thermal conductivity on the volume fractions of GNPs, which is superior to the EMA model.

Understanding length dependences of effective thermal conductivity of nanowires

We have studied the length dependence of effective thermal conductivity of silicon nanowires by a thermon gas model and MD simulations. After modifications of the force term by considering the resistance enhancements from thermon gas interactions with the confined surfaces and the ends (inlet and outlet), the theoretical predictions of effective thermal conductivity agree well with the results of MD simulations in the length range of 4 to 550 nm. The result suggests that the resistance enhancement effect by thermon–boundary interactions, instead of the heat inertia, plays the dominating role in the non-Fourier heat conduction in silicon nanowires.

Determination of effective thermal conductivity and specific heat capacity of wood pellets

Effective thermal conductivity and specific heat capacity are important properties for studying the self-heating during wood pellets storage. A modified line heat source within a wood pellets container was used to determine the thermal conductivity and specific heat capacity of wood pellets with moisture content ranging from 1.4% to 9%w.b. A second order partial differential equation describing transient temperature distribution within the test container was numerically solved for temporal and spatial temperatures. The difference between experimental and numerical temperatures was minimized to estimate an effective thermal conductivity and specific heat capacity for the bulk pellets. The estimated thermal conductivity ranged from 0.146 to 0.192W/(mK) increasing with moisture content. An empirical relationship among effective thermal conductivity, moisture content and porosity was developed. The dependence of effective thermal conductivity on pellets size was negligible. The estimated specific heat capacity of pellets ranged from 1.074 to 1.253kJ/(kgK) in the tested range. A relation between specific heat capacity and moisture content was developed for general wood pellets.

Bulk composition and microstructure dependence of effective thermal conductivity of porous inorganic polymer cements

Experimental results and theoretical models are used to assess the effective thermal conductivity of porous inorganic polymer cements, often indicated as geopolymers, with porosity between 30 and 70. vol.%. It is shown that the bulk chemical composition affects the microstructure (grains size, pores size, spatial arrangement of pores, homogeneity, micro cracks, bleeding channels) with consequently the heat flow behaviour through the porous matrix. In particular, introduction of controlled fine pores in a homogeneous matrix of inorganic polymer cements results in an increase of pore volume and improvement of the thermal insulation. The variation of the effective thermal conductivity with the total porosity was found to be consistent with analytical models described by Maxwell-Eucken and Landauer.

Direct Simulation of Thermal Transport Through Sintered Wick Microstructures

Porous sintered microstructures are critical to the functioning of passive heat transport devices such as heat pipes. The topology and microstructure of the porous wick play a crucial role in determining the thermal performance of such devices. Three sintered copper wick samples employed in commercial heat pipes are characterized in this work in terms of their thermal transport properties––porosity, effective thermal conductivity, permeability, and interfacial heat transfer coefficient. The commercially available samples of nearly identical porosities (∼61% open volume) are CT scanned at 5.5 μm resolution, and the resulting image stack is reconstructed to produce high-quality finite volume meshes representing the solid and interstitial pore regions, with a conformal mesh at the interface separating these two regions. The resulting mesh is then employed for numerical analysis of thermal transport through fluid-saturated porous sintered beds. Multiple realizations are employed for statistically averaging out the randomness exhibited by the samples under consideration. The effective thermal conductivity and permeability data are compared with analytical models developed for spherical particle beds. The dependence of effective thermal conductivity of sintered samples on the extent of sintering is quantified. The interfacial heat transfer coefficient is compared against a correlation from the literature based on experimental data obtained with spherical particle beds. A modified correlation is proposed to match the results obtained.

Thermal Conductivity of Al2O3–ZrO2 Composite Ceramics

The Al2O3–ZrO2 composite ceramics were prepared by slip casting in plaster molds and sintering at 1350°C in air. The composition of prepared samples varied from pure alumina to doped zirconia (3Y‐TZP) with steps of 10 vol%. The relative density of the sintered samples varied from 94% to 98%, depending on the composition. Thermal diffusivity of sintered samples was measured by means of the xenon flash method at 100°C, 200°C, 400°C, 600°C, 800°C, and 1000°C and thermal conductivities were calculated based on measured bulk densities and specific heat data and finally corrected for porosity effects. As expected, the thermal conductivity decreased with increasing zirconia content, and in the case of samples with higher alumina content, it also decreased with increasing temperature. Effective thermal conductivities are close to the lower Hashin–Shtrikman bound and the recently proposed sigmoidal average. Empirical relations were used to fit the dependence of effective thermal conductivity of Al2O3–ZrO2 composite ceramics on both composition and temperature.

Theory for anisotropic thermal conductivity of magnetic nanofluids

Effective thermal conductivity tensor for magnetic nanofluids containing magnetizable nanoparticles suspended in a base liquid is theoretically investigated with a two-step homogenization method. First, we adopt differential effective medium theory to determine the equivalent thermal conductivity of magnetizable nanoparticle chains. Second, we generalize self-consistent anisotropic effective medium theory to study the effective thermal conductivity tensors of magnetic nanofluids. Numerical results show that the aspect ratio of chain-like aggregated clusters plays an important role in enhancement of anisotropic thermal conductivity. In addition, our theoretical results on the elements of thermal conductivity parallel to the fields K e z and perpendicular to the fields K e x are in good agreement with experimental data. Furthermore, we predict the nonmonotonic dependence of effective thermal conductivity on magnetic field strength, in accordance with experimental reports.

Thermal Conductivity Characterization of Hafnium Diboride‐Based Ultra‐High‐Temperature Ceramics

We evaluated the thermal conductivity of HfB2‐based ultra‐high‐temperature ceramics from laser flash diffusivity measurements in the 25°–600°C temperature range. Commercially available powders were used to prepare HfB2 composites containing 20 vol% SiC, some including TaSi2 (5 vol%) and Ir (0.5 or 2 vol%) additions. Samples were consolidated via conventional hot pressing or spark plasma sintering. Processing differences were shown to lead to differences in magnitude and temperature dependence of effective thermal conductivity. We compared results with measured values from heritage materials and analyzed trends using a network model of effective thermal conductivity, incorporating the effects of porosity, grain size, Kapitza resistance, and individual constituent thermal conductivities.

Size and frequency dependence of effective thermal conductivity in nanosystems

A single phenomenological expression is proposed to describe thermal transport in a wide variety of nanoscale devices. Size and frequency dependence is studied for some nanosystems from the diffusive to the ballistic regimes. In a single expression we obtain the effective thermal conductivity of cross-plane thin layer experiments where the device has a size limitation in the direction of the flux, and nanowire and in-plane experiments where the size limitation is in a transversal direction from the flux in terms of the effective size of the device. For nonzero frequencies, the size dependence has a maximum which becomes narrower at higher frequencies. For a given size, the effective thermal conductivity decreases for increasing frequency. These features may be limited in the design of nanoscale devices, because of the accumulation of dissipated heat.

Effective thermal and electrical conductivity of carbon nanotube composites

We generalize Bruggeman effective medium theory to investigate the effective electrical and thermal conductivity of carbon nanotube composites. Both the nonlinear dependence of effective thermal conductivity on the nanotube volume fraction in nanofluids and very low percolation threshold for carbon nanotube/polyimide composites are well predicted. Numerical results show that although single-walled carbon nanotubes possess a higher thermal conductivity than multi-walled nanotubes, they induce less effective conductivity due to interfacial resistance. Moreover, the non-spherical shape of carbon nanotubes helps to achieve a large enhancement of the effective conductivity, and the use of disc-shaped particles gives a larger conductivity than the use of needle-shaped particles.

Effective thermal conductivity in nanofluids of nonspherical particles with interfacial thermal resistance: Differential effective medium theory

By taking into account the interfacial thermal resistance across the solid particles and the host liquids, we present differential effective medium theory to estimate the effective thermal conductivity in nanofluids of nonspherical solid particles. It is found that high enhancement of effective thermal conductivity can be achieved when the nanoparticles’ shape is deviated much from the spherical one. On the other hand, increasing the interfacial thermal resistance results in an appreciable degradation in the thermal conductivity enhancement. To one’s interest, our theoretical results are in good agreement with recent experimental data on nanofluids. In particular, our theoretical predictions successfully show the nonlinear dependence of effective thermal conductivity on the volume fractions of nanotubes.