Microstructures and macroscopic conductivity of randomly packed and uniaxially pressed sphere compacts

The present paper deals with simulation of microstructures and macroscopic conductivity of randomly packed, uniaxially pressed and sintered particles. Random packings of identical spheres are constructed by using a sequential deposition method and their microgeometry after the compaction in sintering is geometrically created by proportional reduction in distances between the sphere centers only in the vertical direction and by mass addition around overlapped necks. Some of microgeometrical characteristics of the created compacts are statistically examined. Using the data on the packings and geometrical models, macroscopic thermal conductivities of the compacts are estimated. It is found that the conductivities are greatly different from those of simple cubic packings, although both the packings have almost the same coordination number, and that anisotropy in the conductivity is induced by the compaction in addition to gravity. The conductivities are expressed as a function of the compaction and sintering degrees for practical purposes.     

Effect of fabrication parameters on the thermophysical properties of sintered wicks for heat pipe applications

Porous wicks for use in a loop heat pipe were sintered from copper and Monel powder. These wicks are characterized in terms of their porosity, liquid permeability, capillary pressure and thermal conductivity. The effect of fabrication parameters (particle size and sintering conditions) on these properties is studied. The experimentally measured values of permeability and capillary pressure were compared with correlations available in the literature. The Kozeny–Carman correlation was found to overpredict the experimental values of permeability; while the modified Young–Laplace equation was found to predict within 5% of the measured capillary pressure. Additionally, a model for predicting the thermal conductivity of sintered wicks is developed. First, the ‘two-sphere model’ is used to relate the sintering conditions to the size of the connection (the ‘neck’) between two particles. Then, a finite element simulation is used to determine the thermal resistance of the bonded particles as a function of the neck between them. This thermal resistance is integrated in a random 3D resistor network as a means to model the multiple connections between spheres in a wick and to calculate the effective thermal conductivity of the wick. Results of the model are compared with experimental measurements of thermal conductivity of sintered copper wicks. Agreement between the model and the experimental measurements is good (within 15%) for sintering temperatures below 550 °C, and within 26% for sintering temperatures up to 950 °C. Finally, a generalized thermal conductivity chart is presented, which can be used to estimate the sintering temperature and time required to achieve the desired thermal conductivity.     

Models for metal hydride particle shape,packing, and heat transfer

A multiphysics modeling approach for heat conduction in metal hydride powders is presented, including particle shape distribution, size distribution, granular packing structure, and effective thermal conductivity. A statistical geometric model is presented that replicates features of particle size and shape distributions observed experimentally that result from cyclic hydride decrepitation. The quasi-static dense packing of a sample set of these particles is simulated via energy-based structural optimization methods. These particles jam (i.e., solidify) at a density (solid volume fraction) of 0.671 ± 0.009 – higher than prior experimental estimates. Effective thermal conductivity of the jammed system is simulated and found to follow the behavior predicted by granular effective medium theory. Finally, a theory is presented that links the properties of bi-porous cohesive powders to the present systems based on recent experimental observations of jammed packings of fine powder. This theory produces quantitative experimental agreement with metal hydride powders of various compositions.     

Permeability and effective thermal conductivity of bisized porous media

In the region of minimum porosity of particulate binary mixtures, heat exchange and permeability were found to be higher than the ones obtained with a mono-size packing built with the same small size particles used in the binary packing. This effect was noticed in the range of the particles size ratio 0.1–1.0.The obtained improvement on thermal performance is related to the increase of effective thermal conductivity (ETC) in the binary packing and to the increase in transversal thermal dispersion due to the porosity decrease and tortuosity increase.Permeability can increase by a factor of two, if the size ratio between small and large spheres of a loose packing stays in the range 0.3–0.5.     

Contact thermal conductivity of a powder bed in selective laser sintering

Estimation of the temperature field in the powder bed in selective laser sintering process is a key issue for understanding the sintering/binding mechanisms and for optimising the technique. Heat transfer may be strongly affected by formation and growth of necks between particles due to sintering when the contact conductivity becomes predominant in the powder bed effective thermal conductivity. The necks often remain small as compared to the particle size. To calculate the effective contact conductivity of such structures a model of independent small thermal contacts is proposed. The conductivity of the considered cubic-symmetry lattices and the random packing of equal spheres depends on the three structural parameters: the relative density, the coordination number, and the contact size. The present model agrees with the known numerical calculations in the range of contact radius to particle radius ratio below 0.3. The strong dependence on the contact size is qualitatively confirmed by experimental data.     

Convective heat transfer of horizontal spherical particle layer heated from below and cooled from above Part II: Effect of thickness of particle layer

Convection heat transfer and pressure drop measurements were performed with a rectangular duct, having a cooled upper and a heated lower surface, which was packed with spherical particles. Air was used as the test fluid and four kinds of spherical particles having different diameters and thermal conductivities were used as the packing materials. The ratio of the diameter of the spherical particle to the distance between the cooled and heated surfaces, d/H, was varied from 0.173 to 1. The thermal conductivity of the particle layer was also measured under the still air condition. The thermal conductivity of the particle layer was not affected by the value of d/H. In the case of the one-stage arrangement of spherical particles (d/H = 1), the flow resistance took on a remarkably small value compared with the flow resistance of a homogeneous spherical particle layer. Moreover, the flow resistance of the particle layer formed with some layers of particles could be predicted by combining the flow characteristics of the one-stage particle layer and that of the homogeneous spherical particle layer. The heat transfer coefficient of the particle layer was larger than that of turbulent air flow on a flat plate. At a constant superficial air velocity, there existed a value of d/H which gave a maximum value of the average heat transfer coefficient. Nondimensional heat transfer correlation equations were derived in terms of parameters expressing the average characteristics of the spherical particle layers. © 1998 Scripta Technica, Heat Trans Jpn Res, 26(3): 176–192, 1997     

Determination of the thermal properties of ceramic sponges

The knowledge of thermal properties of technical components or internals in chemical reactors is often a key characteristic for planning and designing chemical engineering processes. As an alternative to packed beds or packings, sponges turned out to be used in new application fields in chemical and process engineering. Therefore an experimental study was performed to investigate the two-phase thermal conductivity of solid ceramic sponges made of alumina, mullite and oxidic-bonded silicon carbide (OBSiC) at moderate temperatures. A two-dimensional model is used for analysing the measured temperature profiles and for calculating the thermal conductivity. It can be observed, that the thermal conductivity increases with decreasing porosity and is nearly constant when the pore size (ppi number) is varied. The thermal conductivity data are modelled by an approach similar to the well known Krischer model. Compared to a packed bed of spherical particles, the values of the thermal conductivity of sponges turn out to be about five times higher.     

A particle-based model for predicting the effective conductivities of composite electrodes

This paper develops particle-resolved simulations to predict conductivity within porous composite electrodes. Hundreds of spherical particles (order fractions of a micron) are packed randomly into a cubical region (order of a few microns), using two alternative packing algorithms. The composite structures include both ion-conducting and electron-conducting particles. The particle network is discretized using tetrahedral meshes that fully resolve the interiors of the particles and their intersections. Charge-conservation equations are solved to predict current through the network. These simulations are used to derive the effective conductivities that are required for macroscale simulations at length scales much larger than the particle scale. Because the microstructures are synthesized via random particle packing, multiple realizations are needed to deliver statistically invariant results. The results show that a few hundred particles with a few hundred realizations is sufficient. Predicted coordination numbers, percolation probabilities, and three-phase-boundary lengths are consistent with percolation theory, but the predicted effective conductivities are significantly smaller than those predicted with conventional percolation theory. By adjusting the Bruggeman factor from the conventional value of 1.5-3.5 brings the percolation-theory prediction for effective conductivity in line with the fully resolved results.     

THERMAL STRESSES IN ISOTROPIC CELL-DIVIDED PARTICLE-MATRIX SYSTEM: SPHERICAL ANDCUBIC CELLS

Thermal stresses are studied in an isotropic particle-matrix system of homogeneously distributed spherical particles in an infinite matrix. The isotropic particle-matrix system is divided into cells containing the central spherical particle embedded in the matrix and is of dimensions equal to an interparticle distance. The cell surface is assumed to be acted on by nonzero stresses derived by a criterion of a minimum of the cell elastic energy of the thermal stresses. The thermal stresses originate during a cooling process as a consequence of the difference in thermal expansion coefficients between the matrix and the particle. The formulae for the thermal stresses acting in the isotropic cell-divided particle-matrix system for the ratio of a spherical particle volume to a cell volume v_p = 0 reduce to those for the isotropic particle-matrix system of one spherical particle embedded in an infinite matrix. The thermal stresses are derived for spherical and cubic cells, depending on the spherical particle distribution.     

A Numerical Technique for Computing Effective Thermal Conductivity of Fluid–Particle Mixtures

Periodic arrays of particles, foams, and other structures impregnated with a static fluid play an important role in heat transfer enhancement. In this article, we develop a numerical method for computing conduction heat transfer in periodic beds by exploiting the periodicity of heat flux and the resulting linear variation of mean temperature. The numerical technique is developed within the framework of an unstructured finite-volume scheme in order to enable the computation of effective thermal conductivity for complex fluid-particle arrangements. The method is applied to the computation of effective thermal conductivity of ordered as well as random beds of spheres and rods. The effects of varying surface area, aspect ratio, volume fraction, orientation, and distribution are studied for various solid-to-fluid conductivity ratios. Unlike classical theories which predict only a dependence on volume fraction, these direct simulations show that aspect ratio, distribution, and alignment of particles have an important influence on the effective thermal conductivity of the bed.     

Prediction of thermal conductivity and electrical resistivity of porous metallic materials

Thermal conductivity and electrical resistivity of porous materials, including 304L stainless steel Rigimesh, 304L stainless steel sintered spherical powders, and OFHC sintered spherical powders at different porosities and temperatures are reported and correlated. It was found that the thermal conductivity and electrical resistivity can be related to the solid material properties and the porosity of the porous matrix regardless of the matrix structure. It was also found that the modified Wiedemann-Franz-Lorenz relationship is valid for the porous materials under consideration. For high conductivity materials, the Lorenz function and the lattice component of conductivity depend on the material and are independent of the porosity. For low conductivity, the lattice component depends on the porosity as well.     

THE EFFECTIVE THERMAL CONDUCTIVITY OF PACKED BEDS OF SPHERES FOR A FINITE CONTACT AREA

The upper and lower bounds of the effective thermal conductivity range of packed beds of spheres is evaluated using the theoretical approach of the volume averaging method for a two-phase system. The solid mechanics and thermal problems are resolved by considering the effects of superficial roughness and pressure. The numerical solutions to the problem of thermal conduction through the periodic regular arrangement of stainless steel and aluminum spheres in the air are determined using the finite element method. As regards to the aluminum spheres, the influence of oxide stratum on the effective thermal conductivity is also considered. Finally, empirical equations are proposed for periodic regular arrangements of stainless steel and aluminum spheres.     

Thermal analysis of resin composites with ellipsoidal filler considering thermal boundary resistance

The effective thermal conductivity of composites with ellipsoidal fillers is analyzed by using a homogenization method that is able to represent the microstructure precisely. In this study, various parameters such as the volume fraction, shape, and distribution of the filler are quantitatively estimated to understand the mechanisms of heat transfer in the composite. First, thermal boundary resistance between resin and filler is important for obtaining composites with higher thermal conductivity. Second, the anisotropy of the effective thermal conductivity arises from contact between filler in the case of ellipsoidal filler and produces lower thermal resistance. Finally, the filler network and thermal resistance are essential for the heat transfer in composites because the path of thermal conduction is improved by contact between neighboring filler particles.     

Drastic enhancement of effective thermal conductivity of a metal hydride packed bed by direct synthesis of single-walled carbon nanotubes

Low heat conductivity restricts the rate of hydrogen absorption into a metal hydride, and this leads to a mismatch of the required absorption rate. The use of fin systems is standard in such cases, and the use of several different materials has been attempted. This includes high thermal conductivity carbon brushes and carbon nanotube. Unfortunately, such efforts have not been effective because the boundary thermal resistance has not been addressed. In this study, we focused on the direct synthesis of a single-walled carbon nanotube (SWCNT), which has high thermal conductivity, on particles in a packed bed, for reducing boundary thermal resistance and estimated effective thermal conductivity. Referring to Raman spectra, we succeeded in growing SWCNT on a metal hydride and effective thermal conductivity was estimated as a function of the filling ratios of the metal hydride and the SWCNT. Consequently, the effective thermal conductivity can satisfy the required value.     

SPHERE PACKING ALGORITHM FOR HEAT TRANSFER STUDIES

Sintering is an important process for most ceramic systems and optical fibers. Many of the defects, introduced at the sintering stage, are formed because of the thermal processes. As such, there has been significant interest in modeling the underlying thermal processes. However, because of the complexities involved, most of the existing analyses tended to utilize a porous medium assumption whereby the temperature is computed through some average thermal properties that are in turn related to the porosity of the structure. The assumption is that the porosity can describe uniquely the property of the structure. This has never been directly confirmed, as most of the existing packing algorithms cannot achieve sufficient microstructural control. In the present work, an algorithm is introduced to enable a greater degree of control on the microstructure of the packing (mean coordination number and mean contact area). The subsequent thermal analysis confirmed that packings with the same porosity could have different thermal conductivity values.     

Discussion of proposed mechanisms of thermal conductivity enhancement in nanofluids

Based upon Green–Kubo linear response theory, we use the exact expression for the heat flux vector of the base fluid plus nanoparticle system to estimate the contribution of nanoparticle Brownian motion to thermal conductivity. We find that its contribution is too small to account for abnormally high reported values. The possibility of convection caused by Brownian particles is also found to be unlikely. We have estimated the mean free path and the transition speed of phonons in nanofluid through density functional theory. We found a layer structure can form around the nanoparticles and the structure does not further induce fluid–fluid phase transition in the bulk fluid. By analyzing the compressibility of the fluid, we have also investigated the sound speed in the nanofluid. For the models of an asymmetric hard sphere mixture representing the single spherical nanoparticles and a mixture of rods and hard spheres representing aggregates, both suspended in the fluid, we found that for the very low volume fraction cases, the compressibility changes little. This shows that the speed of phonon transition does not change due to the addition of nanoparticles of either type. Our results indicate that, besides the enhancement due to the high thermal conductivity of nanoparticles themselves, fluid molecules make no evident contribution to the enhancement of thermal conductivity attributable to the presence of the nanoparticles at volume fractions less than 5%.     

Effective thermal conductivity of wet particle assemblies

The effective thermal conductivity of mono- and poly-dispersed random assemblies of spherical particles and irregular crystals, both dry and partially or fully saturated by wetting and non-wetting liquids, has been determined computationally by numerical solution of the Fourier’s law on 3-D reconstructed media and experimentally by the transient hot wire method. The effect of spatial distribution and volume fractions of the vapour, liquid, and solid phases on effective thermal conductivity was systematically investigated. A power-law correlation for estimating the effective conductivity, valid over a wide range of phase volume fractions and relative conductivities of components, has been proposed.     

Prediction of pressure drop in a packed bed dehumidifier operating with liquid desiccant

In this paper a more rigorous model, which is valid for both structured and random packing columns, is used for predicting the irrigated pressure drop in a desiccant–air contact system. Calcium chloride solution is considered as the desiccant. Four different random packing materials and three different structured packing materials are considered in the present study. The effects of random packing shape and the type of structured packing on the hydraulic performance are studied. The model has been validated for a wide range of operating values available in the literature. It is found that the structured packing has the lower pressure drop and higher capacity compared with random packings. Among the random packing materials considered in the present study, Intalox saddles can provide the least irrigated pressure drop and among the structured packing materials the sheet-type Mellapak 250 Y has the lowest pressure drop.     

FORCED CONVECTION HEAT TRANSFER OF INTERACTING SPHERES

A basic understanding of the highly nonlinear interaction effects of closely spaced spheres on fluid mechanics and heat transfer parameters is important for improving the design of a variety of thermal fluid-particle systems. Fluid flow patterns, isotherms, as well as Nusselt number distributions and extended correlations are presented for steady laminar axisym-metric flow past a linear array of three spheres. A finite-element method is used to solve the complete Navier-Stokes and heat transfer equations for the system parameter ranges 1 Re_d  200 (Reynolds number) 2 d_ij10 ( particle spacings)and 0. 1  prRe_d 2000 (Piclet number). The verified computer simulation results indicate that convection heat transfer parameters of interacting spherical particles deviate significantly from solitary spheres for all Reynolds and Piclet numbers.     

Multi-artery heat-pipe spreader: Lateral liquid supply

We design and test a low thermal/hydraulic resistance, multi-artery heat-pipe spreader vapor chamber. Liquid (water) is supplied to a highly concentrated heat-source region through a monolayer evaporator wick and a set of lateral converging arteries, fabricated from sintered, spherical copper particles. The monolayer wick allows for a minimum evaporator resistance of 0.055 K/(W/cm²), which is related to a critical transition where the receding meniscus approaches the particle neck. Similar behavior is also observed in a monolayer-wick evaporator, partially submerged in liquid bath. After this minimum, local dryout occurs and increases the resistance. However, a continuous liquid supply through the lateral arteries does not allow for total dryout in the test limit of 580 W/cm². These thermal/hydraulic behaviors are predicted using the local thermal equilibrium and nonequilibrium models.