Numerical prediction of the thermal conductivity of fibers

The need to determine the thermal conductivity of fibers for design purposes of new composite materials and the inherent difficulties in the direct measurement of the thermal conductivity of fibers motivated the present work due to its importance for energy conservation purposes. In this work, a correlation formula is developed to predict the thermal conductivities of fiber as function of the effective thermal conductivity of a fiber-reinforced composite laminates and their constituents which are easy to measure. The parallel and series thermal models of composite walls have been utilized in developing this correlation equation. The coefficients of this formula can be given as functions of the voids volume fraction for each fiber to resin volume ratio considered. The validity of the models is verified through finite element analysis. This model also shows excellent agreement with the available experimental values.     

The direct effect of interfacial nanolayers on thermal conductivity of nanofluids

One of the most important features of nanofluids is their thermal conductivity. In this article, a new model for thermal conductivity is proposed based on the combination of a statistical model and thermal convection caused by Brownian motion of nanoparticles with considering the effect of interfacial nanolayers among nanoparticles and base fluids. This model is compared with Al₂O₃ in deionized water and CuO in deionized water (based nanofluids of spherical particles) using a number of theoretical and experimental thermal conductivity models, after that the experimental results have been made available in the open literature. In this model, an interfacial nanolayer is influenced directly on both parts of static and dynamic effective thermal conductivity. The present model shows good agreement with the experimental result of nanofluids and gives better predictions compared to models used for nanofluids in this article. This model is purely theoretical and in order to achieve it, experimental results have no effect.     

Prediction of the thermal conductivity of the constituents of fiber reinforced composite laminates

Three empirical formulas are developed to predict the thermal conductivities of fiber-reinforced composite laminates (FRCL) and its constituents. The inherent two or three-dimensional problem that is common in composites is simplified to a one-dimensional problem. The validity of the models is verified through finite element analysis. This method utilizes the parallel and series thermal models of composite walls. The models are tested at different fiber-to-resin volume ratios (30:70–75:25) and various fiber-to-resin thermal conductivity ratios (0.2–5). The predicted thermal conductivity of the fiber can be accurately predicted throughout the spectrum via two models. The first model is a first-order formula (R ² = 0.94) while the second model is a second-order formula (R ² = 0.976). These two models can be used to predict the fiber thermal conductivity based on the easily measured resin and laminate values. A third model to predict the overall laminate thermal conductivity is introduced. The thermal conductivity of the composite panel is predicted with very high accuracy (R ² = 0.995). The thermal conductivity predicted via the use of these models has an excellent agreement with the experimental measurements. Another use of these models is to determine the fiber-to-resin volume ratio (if all thermal conductivities of fiber, resin and laminate are known).     

Universal bounds on the electrical and elastic response of two-phase bodies and their application to bounding the volume fraction from boundary measurements

Universal bounds on the electrical and elastic response of two-phase (and multiphase) ellipsoidal or parallelopipedic bodies have been obtained by Nemat-Nasser and Hori. Here we show how their bounds can be improved and extended to bodies of arbitrary shape. Although our analysis is for two-phase bodies with isotropic phases it can easily be extended to multiphase bodies with anisotropic constituents. Our two-phase bounds can be used in an inverse fashion to bound the volume fractions occupied by the phases, and when the volume fraction is asymptotically small reduce to those of Capdeboscq and Vogelius, for electrical conductivity, and Capdeboscq and Kang, for elasticity. Other volume fraction bounds derived here utilize information obtained from thermal, magnetic, dielectric or elastic responses. One bound on the volume fraction can be obtained by simply immersing the body in a water filled cylinder with a piston at one end and measuring the change in water pressure when the piston is displaced by a known small amount. This bound may be particularly effective for estimating the volume of cavities in a body. We also obtain new bounds utilizing just one pair of (voltage, flux) electrical measurements at the boundary of the body.     

A Tensile Split Hopkinson Bar for Testing Particulate Polymer Composites Under Elevated Rates of Loading

A tensile split Hopkinson bar apparatus is developed for testing high strain rate behavior of glass-filled epoxy. The apparatus uses a specimen gripping configuration which does not require fastening and/or gluing and can be readily used for castable materials. Details of the experimental setup, design of grips and specimen, specimen preparation method, benchmark experiments, and tensile responses are reported. Also, the effects of filler volume fraction (0–30%) and particle size (11–42 μm) are examined under high rates of loading and the results are compared with the ones obtained from quasi-static loading conditions. The results indicate that the increase in the loading rate contributes to a stiffer and brittle material response. In the dynamic case lower ultimate stresses are seen with higher volume fractions of filler whereas in the corresponding quasi-static cases an opposite trend exists. However, the absorbed specific energy values show a decreasing trend in both situations. The results are also evaluated relative to the existing micromechanical models. The tensile response for different filler sizes at a constant volume fraction (10%) is also reported. Larger size filler particles cause a reduction in specimen failure stress and specific energy absorbed under elevated rates of loading. In the quasi-static case, however, the ultimate stress is minimally affected by the filler size.     

Experimental investigations and theoretical determination of thermal conductivity and viscosity of Al2O3/water nanofluid

Experimental investigations and theoretical determination of effective thermal conductivity and viscosity of Al₂O₃/H₂O nanofluid are reported in this paper. The nanofluid was prepared by synthesizing Al₂O₃ nanoparticles using microwave assisted chemical precipitation method, and then dispersing them in distilled water using a sonicator. Al₂O₃/water nanofluid with a nominal diameter of 43 nm at different volume concentrations (0.33–5%) at room temperature were used for the investigation. The thermal conductivity and viscosity of nanofluids are measured and it is found that the viscosity increase is substantially higher than the increase in thermal conductivity. Both the thermal conductivity and viscosity of nanofluids increase with the nanoparticle volume concentration. Theoretical models are developed to predict thermal conductivity and viscosity of nanofluids without resorting to the well established Maxwell and Einstein models, respectively. The proposed models show reasonably good agreement with our experimental results.     

The effect of real viscosity on the heat transfer of water based Al2O3 nanofluids in a two-sided lid-driven differentially heated rectangular cavity

The heat transfer and fluid flow behavior of water based Al₂O₃ nanofluids are numerically investigated inside a two-sided lid-driven differentially heated rectangular cavity. Physical properties which have major effects on the heat transfer of nanofluids such as viscosity and thermal conductivity are experimentally investigated and correlated and subsequently used as input data in the numerical simulation. Transport equations are numerically solved with finite volume approach using SIMPLEC algorithm. It was found that not only the thermal conductivity but also the viscosity of nanofluids has a key role in the heat transfer of nanofluids. The results show that at low Reynolds number, increasing the volume fraction of nanoparticles increases the viscosity and has a deteriorating effect on the heat transfer of nanofluids. At high Reynolds number, the increase in the viscosity is compensated by force convection and the increase in the volume fraction of nanoparticles which results in an increase in heat transfer is in coincidence with experimental results.     

Comparison of geometry dependent resistance models with conventional models for estimation of effective thermal conductivity of two-phase materials

The geometry dependent resistance models are used to estimate the effective thermal conductivity of two-phase materials based on the unit cell approach. The algebraic equations are derived based on isotherm approach for various geometries. The effective thermal conductivity of the above models are found and compared with experimental data with a minimum and maximum deviation of ±3.976 and ±19.55%, respectively. The present models are good agreement with experimental results.     

Numerical simulation of the nanoparticle diameter effect on the thermal performance of a nanofluid in a cooling chamber

The thermal performance of a nanofluid in a cooling chamber with variations of the nanoparticle diameter is numerically investigated. The chamber is filled with water and nanoparticles of alumina (Al₂O₃). Appropriate nanofluid models are used to approximate the nanofluid thermal conductivity and dynamic viscosity by incorporating the effects of the nanoparticle concentration, Brownian motion, temperature, nanoparticles diameter, and interfacial layer thickness. The horizontal boundaries of the square domain are assumed to be insulated, and the vertical boundaries are considered to be isothermal. The governing stream-vorticity equations are solved by using a secondorder central finite difference scheme coupled with the mass and energy conservation equations. The results of the present work are found to be in good agreement with the previously published data for special cases. This study is conducted for the Reynolds number being fixed at Re = 100 and different values of the nanoparticle volume fraction, Richardson number, nanofluid temperature, and nanoparticle diameter. The results show that the heat transfer rate and the Nusselt number are enhanced by increasing the nanoparticle volume fraction and decreasing the Richardson number. The Nusselt number also increases as the nanoparticle diameter decreases.     

Comparison of the effects of measured and computed thermophysical properties of nanofluids on heat transfer performance

This article reports a comparison of the differences between using measured and computed thermophysical properties to describe the heat transfer performance of TiO₂–water nanofluids. In this study, TiO₂ nanoparticles with average diameters of 21 nm and a particle volume fraction of 0.2–1 vol.% are used. The thermal conductivity and viscosity of nanofluids were measured by using transient hot-wire apparatus and a Bohlin rotational rheometer, respectively. The well-known correlations for calculating the thermal conductivity and viscosity of nanofluids were used for describing the Nusselt number of nanofluids and compared with the results from the measured data. The results show that use of the models of thermophysical properties for calculating the Nusselt number of nanofluids gave similar results to use of the measured data. Where there is a lack of measured data on thermophysical properties, the most appropriate models for computing the thermal conductivity and viscosity of the nanofluids are the models of Yu and Choi and Wang et al., respectively.     

Experimental measurement of thermophysical properties of oxide-water nano-fluids down to ice-point

This paper presents the measurement of the thermal conductivity and the dynamic viscosity of Al₂O₃-water (1-4% particle volume fraction) and TiO₂-water (1-6% particle volume fraction) nano-fluids carried out at atmospheric pressure in the temperature range from 1 to 40 °C, which is particularly interesting for the application of nano-fluids as thermal medium in refrigeration and air-conditioning.The thermal conductivity measurement was performed by using a Transient Hot Disk TPS 2500S apparatus instrumented with a 7577 probe (2.001 mm in radius) having a maximum uncertainty (k = 2) lower than ±5.0% of the reading. The dynamic viscosity measurement and the rheological analysis were carried out by a rotating disc type rheometer Haake Mars II instrumented with a single cone probe (60 mm in diameter and 1° angle) having a maximum uncertainty (k = 2) lower than ±5.0% of the reading.The thermal conductivity measurements of the tested nano-fluids show a great sensitivity to particle volume fraction and temperature and a weak sensitivity to cluster average size: TiO₂-water and Al₂O₃-water nano-fluids show a thermal conductivity enhancement (with reference to pure water) from −2 to 16% and from −2 to 23% respectively.TiO₂-water and Al₂O₃-water nano-fluids exhibit a Newtonian behaviour in all the investigated ranges of temperature and nano-particle volume fraction. The relative viscosity shows a great sensitivity to particle volume fraction and cluster average size and no sensitivity to temperature: TiO₂-water and Al₂O₃-water nano-fluids show a dynamic viscosity increase with respect to pure water from 17 to 210% and from 15 to 150% respectively.Al₂O₃-water nano-fluid seems to be more promising as thermal medium than TiO₂-water nano-fluid, particularly at low thermal level (between ambient temperature and ice point) where TiO₂-water is not suitable showing worse performance than pure water.Present experimental measurements were compared both with available measurements carried out by different researchers and computational models for thermophysical properties of suspensions.     

CFD studies on natural convection heat transfer of Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-water nanofluids

This work is focused on numerical simulations of natural convection heat transfer in Al₂O₃-water nanofluids using computational fluid dynamics approach. Fluent v6.3 is used to simulate water based nanofluid considering it as a single phase. Thermo-physical properties of the nanofluids are considered in terms of volume fraction and size of nanoparticles, size of base fluid molecule and temperature. The numerical values of effective thermal conductivity have also been compared with the experimental values available in the literature. The numerical result simulated shows decrease in heat transfer with increase in particle volume fraction. Computed result shows similar trend in increase of Nusselt number with Relayigh number as depicted by experimental results. Streamlines and temperature profiles are plotted to demonstrate the effect.     

Influence of the particle size and volume fraction on micro-damage of the composites

The bulk and shear modulus of metal matrix composites with various volume fractions of particles are modified based on the Eshelby’s equivalent inclusion method combined with self-consistent scheme. By introducing the modified modulus, a new model, which can predict the particle size effects on the stress–strain relation under interfacial debonding damage between matrix and particles, is established. The results obtained from the present investigation show a better agreement with the experimental data.     

Role of interfacial layer and clustering on the effective thermal conductivity of CuO-gear oil nanofluids

Copper oxide nanoparticles (∼40 nm) are dispersed in gear oil (IBP Haulic-68) at different volume fractions (0.005-0.025) with oleic acid added as a surfactant to stabilize the system. Prepared nanofluids are characterized by Fourier Transform Infrared spectroscopy (FTIR) and Dynamic light scattering (DLS) measurements. DLS data confirmed the presence of agglomerated nanoparticles in the prepared nanofluids. Thermal conductivity measurements are performed both as a function of CuO volume fraction and temperature between 5 and 80 °C. An enhancement in thermal conductivity at 30 °C of 10.4% with 0.025 volume fraction of CuO nanoparticle loading is observed. Measured volume fraction dependence of the thermal conductivity enhancement at room temperature is predicted fairly well considering contributions from both nanolayer at the solid-liquid interface and particle agglomeration in the suspension, as visualized by Feng et al.     

空心材料导热性能预测研究

本文建立了一种预测空心材料导热性的方法。研究了空心材料的导热性。用柱形空心材料分析了体分比和孔洞的排列方式对整体材料导热性的影响，用圆柱形、方柱形空心材料和含裂纹材料，分析了空心形状对材料导热性的影响。同他人的实验结果和某些现有的理论模型比较表明，本文方法是有效的。本文的结果能够很好地解释实验结果。     

Incorporating truncated fractal distribution into Maxwell model to quantify thermal conductivity and its uncertainty in heterogeneous multiparticle systems

An approach is developed to examine the mean and uncertainty of thermal conductivity of a heterogeneous multiparticle system, where the particle concentration or void fraction is treated as a truncated fractal distribution. The truncated fractal distribution is then integrated into the Maxwell model, which is equivalent to a cell model in which the multiparticle system is conceptualized as a spherical fluid cell that envelopes a solid particle. The developed mean thermal conductivity is compared with four experimental data sets of liquid-saturated media from the literature. The effect of fractal characteristics is quantified and discussed. Incorporating particle concentration or void fraction truncated fractal distribution can better capture scatters in the experimental results. The thermal conductivity and its standard deviation decrease with increasing fractal dimensions. When the void fraction is truncated fractal, the uncertainty increases mostly in the low mean void fraction range and drops more quickly with the increasing mean void fraction compared to the case where the particle concentration is truncated fractal. In a typical case of multiparticle system when the solid particles are more conductive than the fluid, the faster increase rate of standard deviation with the ratio of solid over fluid conductivities occurs when the mean void fraction is smaller.     

Prediction of thermal conductivity of air voided-fiber-reinforced composite laminates part II: 3D simulation

Applying the fundamental definition of thermal conductivity to a unit cell of unidirectional fiber reinforced composite with air voids, one can deduce simple empirical formula to predict the thermal conductivity of the composite material with estimated air void volume percent. The inherent 3-D problem is modeled using finite element analysis. The model is tested at different fiber to resin volume ratios and various fibers to resin thermal conductivity ratios for three different air void volume percent. The air voids are modeled as cylindrical shapes with different lengths aligned with fiber direction. Two prediction schemes have been developed through the present work. One is to predict the longitudinal thermal conductivity and the other is to predict the transverse thermal conductivity of the fibers. Also, the model can be used to estimate the voids volume percent if the fiber thermal conductivity has been provided. Such expression can, also, serve as useful guides for quality and perfect bonding for material development.     

Rheological characterization of carbon nanotubes/poly(ethylene oxide) composites

Rheological properties of poly(ethylene oxide) nanocomposites embedded with carbon nanotubes (CNTs) were investigated in the present study. It was found that the CNT nanocomposites had a higher effective filler volume fraction than the real filler volume fraction, which yielded a drastic enhancement of shear viscosity. As the CNT loading in the nancomposites increases, non-Newtonian behavior was observed at the low-shear-rate region in the steady shear experiments. Oscillatory dynamic shear experiments showed that more addition of the CNTs led to stronger solidlike and nonterminal behaviors. To identify a dispersion state of the CNTs, field emission scanning electron spectroscopy and transmission electron microscopy were adopted and thermal analysis was also performed by using differential scanning calorimetry. The existence of percolated network structures of the CNTs even at a low CNT loading was verified by rheological properties and electrical conductivities.     

炭黑增强橡胶复合材料力学行为的三维数值模拟

本文基于炭黑填充橡胶复合材料具有周期性细观结构的假设,采用一种新的、改进的随机序列吸附算法建立了三维多球颗粒随机分布式代表性体积单元,并通过细观力学有限元方法对炭黑颗粒填充橡胶复合材料的力学行为进行了模拟仿真。研究结果表明：采用改进的随机序列吸附算法所建立的模型更加便于有限元离散化;模拟中周期性边界条件的约束,使其更加符合实际约束的真实情况;炭黑填充橡胶复合材料的有效模量明显高于未填充橡胶材料,并随着炭黑颗粒所占体积分数的增加而增大;通过比较发现,本文提出的多球颗粒随机分布式三维数值模型对复合材料的应力-应变行为和有效弹性模量的预测结果与实验结果吻合良好,证实了该模型能够用于炭黑颗粒增强橡胶基复合材料有效性能的模拟分析。     

Strain gradient solution for a finite-domain Eshelby-type anti-plane strain inclusion problem

A solution for the finite-domain Eshelby-type inclusion problem of a finite elastic body containing an anti-plane strain inclusion of arbitrary cross-sectional shape prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is derived in a general form using a simplified strain gradient elasticity theory (SSGET). The formulation is facilitated by an extended Betti’s reciprocal theorem and an extended Somigliana’s identity based on the SSGET and suitable for anti-plane strain problems. The disturbed displacement field is obtained in terms of the SSGET-based Green’s function for an infinite anti-plane strain elastic body. The solution reduces to that of the infinite-domain anti-plane strain inclusion problem when the boundary effect is not considered. The problem of a circular cylindrical inclusion embedded concentrically in a finite cylindrical elastic matrix undergoing anti-plane strain deformations is analytically solved by applying the general solution, with the Eshelby tensor and its average over the circular cross section of the inclusion obtained in closed forms. This Eshelby tensor, being dependent on the position, inclusion size, matrix size, and a material length scale parameter, captures the inclusion size and boundary effects, unlike existing ones. It reduces to the classical linear elasticity-based Eshelby tensor for the circular cylindrical inclusion in an infinite matrix if both the strain gradient and boundary effects are suppressed. Numerical results quantitatively show that the inclusion size effect can be quite large when the inclusion is small and that the boundary effect can dominate when the inclusion volume fraction is high. However, the inclusion size effect is diminishing with the increase of the inclusion size, and the boundary effect is vanishing as the inclusion volume fraction becomes sufficiently low.