The effective thermal conductivity of a composite material with spherical inclusions

A new method is presented for calculating the effective thermal conductivity of a composite material containing spherical inclusions. The surface of a large body is assumed kept at a uniform temperature. This body is in contact with a composite material of infinite extent having a lower temperature far from the heated body. Green's theorem is then used to calculate the rate of heat transfer from the heated body to the composite material, yielding $$k_e /k = 1 + \frac{{3(\alpha - 1)}}{{[\alpha + 2 - (\alpha - 1)\phi ]}}\{ \phi + f(\alpha )\phi ^2 + 0(\phi ^3 )\} $$ where k _e is the effective thermal conductivity, k is the thermal conductivity of the continuous phase, α is the ratio of the thermal conductivity of the spherical inclusions to k, and φ is the volume fraction occupied by the dispersed phase. The function f(α) is presented in this work. Although a similar result has been found previously by renormalization techniques, the method presented in this paper has merit in that a decaying temperature field is used. As a result, only convergent integrals are encountered, and a renormalization factor is not needed. This method is more straightforward than its predecessors and sheds additional light on the basic properties of two-phase materials.     

An effective thermal conductivity model of nanofluids with a cubical arrangement of spherical particles

The theoretical investigation of the effective thermal conductivities of nanofluids, a new class of solid-liquid suspensions, is important in both predicting and designing nanofluids with effective thermal conductivities. We have developed a new thermal conductivity model for nanofluids that is based on the assumption that monosized spherical particles are uniformly dispersed in the liquid and are located at the vertexes of a simple cubic lattice, with each particle surrounded by a liquid layer having a thermal conductivity that differs from that of the bulk liquid. This model nanofluid with a cubical arrangement of nanoparticles gives a more practical upper limit of thermal conduction than a model nanofluid with a parallel arrangement of nanoparticles. The new model unexpectedly shows a nonlinear relationship of thermal conductivity with particle concentration, whereas the conductivity-concentration curve changes from convex upward to concave upward with increasing volume concentration. The effects of particle and layer parameters on the effective thermal conductivities are also analyzed. A comparison of predicted thermal conductivity values and experimental data shows that the predicted values are much higher than the experimental data, a finding that indicates that there is a potential to further improve the effective thermal conductivities of nanofluids with more uniformly dispersed particles.     

Thermal conductivity of a composite material reinforced by regularly distributed spheroidal particles

A rigorous solution of the problem of determining the effective thermal conductivity tensor of a composite material with regularly distributed spheroidal interstitials is presented.Institute of Superhard Materials, Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 4, pp. 497–504, April, 1994.     

Effective thermal conductivity of Cu/diamond composites containing connected particles

An analytical model for the thermal conductivity of Cu/diamond composites with connected particles is presented by replacement of a cluster of connected particles with an equivalent polycrystal subsequently using a multiple effective medium approach. By applying this model to the measured thermal conductivity of Cu/diamond composites prepared by high pressure high temperature sintering technique reported in the literature, we show that it quite well describes the observed thermal conductivity enhancement induced by the connected particles. We estimate the value of connected particle loading in real composites and show that large particles are easier to form the bonding contact than small particles. The present work also demonstrates that the sensitivity of thermal conductivity contribution from the connected particles strongly depends on the particle size, and their pronounced thermal conductivity enhancement should lie within the certain particle size range.     

A self-consistent approach to dynamic effective properties of a composite reinforced by distributed spherical particles

Summary A self-consistent approach to dynamic effective properties of a composite reinforced by randomly distributed spherical inclusions is studied. The coherent plane waves propagating through the particle-reinforced composite are of attenuation nature. It implies that there is an analogy between the particle-reinforced composite and the effective medium with complex-valued elastic constants from the viewpoints of wave propagation. A composite sphere consisting of the inclusion, the matrix and the interphase between them is assumed embedded in the effective medium. The effective wavenumbers of the coherent plane waves propagating through the particle-reinforced composite are obtained by the dynamic self-consistent conditions which require that the forward scattering amplitudes of such a composite sphere embedded in the effective medium are equal to zero. The dynamic effective properties (effective phase velocity, effective attenuation and effective elastic constants) obtained by the present dynamic self-consistent approach for SiC-Al composites are compared numerically with that obtained by the effective field approach at various volume concentrations. It is found that there is a good agreement between the two approaches at a relatively low frequency and low volume concentration but the numerical results deviate from each other at a relatively high frequency and high volume concentration.     

Fracture toughness and electrical conductivity of epoxy composites filled with carbon nanotubes and spherical particles

The attainment of both high toughness and superior electrical conductivity of epoxy composites is a crucial requirement in some engineering applications. Herein, we developed a strategy to improve these performances of epoxy by combining the multi-wall carbon nanotubes (MWCNTs) and spherical particles. Two different types of spherical particles i.e. soft submicron-rubber and rigid nano-silica particles were chosen to modify the epoxy/MWCNT composites. Compared with the binary composites with single-phase particles, the ternary composites with MWCNTs and spherical particles offer a good balance in glass transition temperature, electrical conductivity, stiffness and strength, as well as fracture toughness, exhibiting capacities in tailoring the electrical and mechanical properties of epoxy composites. Based on the fracture surface analysis, the complicated interactions between multiscale particles and the relative toughening mechanisms were evaluated to explain the enhancement in fracture toughness of the ternary composites.     

Effective thermal conductivity of a structured powder

The effective conductivity in a granular bed may be substantially dependent on the transport at granule contacts.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 1, pp. 122–130, July, 1988.     

From discrete particles to continuum fields near a boundary

An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents’ degrees of freedom and interaction forces. Starting point is the exact and general coarse graining formulation presented by Goldhirsch (Granul Mat 12(3):239–252, 2010), which is consistent with the continuum equations everywhere but does not account for boundaries. Our extension accounts for the boundary interaction forces in a self-consistent way and thus allows the construction of continuous stress fields that obey the macroscopic conservation laws even within one coarse-graining width of the boundary. The resolution and shape of the coarse-graining function used in the formulation can be chosen freely, such that both microscopic and macroscopic effects can be studied. The method does not require temporal averaging and thus can be used to investigate time-dependent flows as well as static or steady situations. Finally, the fore-mentioned continuous field can be used to define ‘fuzzy’ (very rough) boundaries. Discrete particle simulations are presented in which the novel boundary treatment is exemplified, including chute flow over a base with roughness greater than one particle diameter.     

Effective thermal conductivity coefficients of a grainy medium

An exact solution is presented for the problem of determination of effective thermal conductivity coefficients of a composite medium with regularly spaced spherical grains.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 2, pp. 336–344, February, 1981.     

Magnetic structure of a spherical cluster of monodomain particles

A numerical model is proposed for simulating the magnetic properties of a system (N-cluster) comprising a finite number N of monodomain particles uniformly distributed over a spherical surface. The calculation algorithm is based on the Monte Carlo method. In the absence of an external magnetic field, the magnetic moment of any spherical N-cluster vanishes due to the formation of vortex structures, with a measure of vorticity offered by the toroid moment Q. The results of model calculations show that the value of Q in N-clusters with 4 < N < 20 amounts to about 80% of the maximum and is virtually independent of N, while exhibiting weak even-odd oscillations.     

Hydriding behavior of spherical particles of a titanium-aluminum-tin alloy

The hydriding behavior of the VT5-1 alloy (92.05 wt % Ti + 4.52 wt % Al + 3.43 wt % Sn) in the form of spherical particles 0.1, 0.4, 0.6, and 0.8 mm in diameter was studied at temperatures from 820 to 973 K and hydrogen pressures from 1 to 6 MPa. The results indicate that the absorption capacity of VT5-1 is lower than that of titanium and that the thermal stability of the resultant mixed-metal hydride is lower than that of titanium dihydride.     

Effective elastic moduli of three-phase composites with randomly located and interacting spherical particles of distinct properties

A micromechanical analytical framework is presented to predict effective elastic moduli of three-phase composites containing many randomly dispersed and pairwisely interacting spherical particles. Specifically, the two inhomogeneity phases feature distinct elastic properties. A higher-order structure is proposed based on the probabilistic spatial distribution of spherical particles, the pairwise particle interactions, and the ensemble-volume homogenization method. Two non-equivalent formulations are considered in detail to derive effective elastic moduli with heterogeneous inclusions. As a special case, the effective shear modulus for an incompressible matrix containing randomly dispersed and identical rigid spheres is derived. It is demonstrated that a significant improvement in the singular problem and accuracy is achieved by employing the proposed methodology. Comparisons among our theoretical predictions, available experimental data, and other analytical predictions are rendered. Moreover, numerical examples are implemented to illustrate the potential of the present method.     

Isothermal adsorption by biporous spherical particles in a restricted volume

A finite-difference method is used in examining the isothermal one-component adsorption by spherical particles in a restricted volume on the assumptions of nonlinear equilibrium and nonlinearity in the diffusion coefficient.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 3, pp. 423–427, March, 1986.     

Effective conductivity of matrix composites

The effective-field method is generalized to the problem of the conductivity of microhomogeneous media having a random structure, with allowance for the binary interaction of inclusions. The calculations of the effective conductivity by various methods are compared with experiments on the electrical and moisture conductivity of composites.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 61, No. 2, pp. 305–312, August, 1991.     

A novel fiber-reinforced polyethylene composite with added silicon nitride particles for enhanced thermal conductivity

A novel thermally conductive plastic composite was prepared from a mixture of silicon nitride (Si₃N₄) filler particles and an ultrahigh molecular weight polyethylene–linear low density polyethylene blend. The effects of Si₃N₄ particle sizes, concentration, and dispersion on the thermal conductivity and relevant dielectric properties were investigated. With proper fabrication the Si₃N₄ particles could form a continuously connected dispersion that acted as the dominant thermally conductive pathway through the plastic matrix. By adding 0–20% Si₃N₄ filler particles, the composite thermal conductivity was increased from 0.2 to ～1.0 W m^?1 K^?1. Also, the composite thermal conductivity was further enhanced to 1.8 W m^?1 K^?1 by decreasing the Si₃N₄ particle sizes from 35, 3 and 0.2 μm, and using coupling agent, for the composites with higher filler content. Alumina short fibers were then added to improve the overall composite toughness and strength. Optimum thermal, dielectric and mechanical properties were obtained for a fiber-reinforced polyethylene composite with 20% total alumina–Si₃N₄ (0.2 μm size) filler particles.     

金刚石表面镀钨对铜/金刚石复合材料热导率的影响

利用粉末覆盖烧结法成功在金刚石表面镀覆W,并采用气体压力熔渗法制备Cu/diamond(W)复合材料。研究了不同镀覆温度对镀层微观结构以及复合材料热导率的影响。结果表明,金刚石表面镀钨有效的改善了界面结合,提高了复合材料热导率。镀层厚度随镀覆温度的提高而明显增加,复合材料热导率先增高再降低。当镀覆工艺为1 050℃保温15 min时,镀层厚度为2 000nm,复合材料热导率最高可达到670 W/mK。     

Low-temperature thermal conductivity of a glassy epoxy-epoxy composite

The thermal conductivities of epoxy resins filled with particles which are identical to the resin matrix have been measured from 0.025 to 9 K. The thermal conductivities of the filled epoxy resins are decreased slightly by the presence of the epoxy particles. This reduction for different epoxies, filling factors, and particle sizes is explained by an increase of about a factor of two in phonon scattering within a boundary layer between particle and matrix.     

Development of composite spherical bearing

Carbon–phenolic woven composite materials are employed in heavy-duty bearings due to their inherent self-lubricating properties and thermal stability. In this work, a composite spherical bearing (CSB) composed of carbon–phenolic composite race and steel ball is developed to solve the seizure of conventional metal–metal spherical bearings for the elevation driving mechanism (EDM) of a future battle tank. In order to eliminate machining and assembling processes of the composite race, the composite race was manufactured with precise compression molding on the ball surface directly. Several self-lubricating particles were embedded to improve the tribological properties of the inner surface of the composite race. Also the compressive strength of the carbon–phenolic composite with interior wrinkles which were induced during the compression molding was measured to verify the applicability of the carbon composite spherical bearing to the future battle tank.