Theoretical study on the effective thermal conductivity of silica aerogels based on a cross-aligned and cubic pore model

Aerogel nanoporous materials possess high porosity, high specific surface area, and extremely low density due to their unique nanoscale network structure. Moreover, their effective thermal conductivity is very low, making them a new type of lightweight and highly efficient nanoscale super-insulating material. However, prediction of their effective thermal conductivity is challenging due to their uneven pore size distribution. To investigate the internal heat transfer mechanism of aerogel nanoporous materials, this study constructed a cross-aligned and cubic pore model(CACPM) based on the actual pore arrangement of Si O2aerogel. Based on the established CACPM, the effective thermal conductivity expression for the aerogel was derived by simultaneously considering gas-phase heat conduction, solid-phase heat conduction, and radiative heat transfer. The derived expression was then compared with available experimental data and the Wei structure model. The results indicate that, according to the model established in this study for the derived thermal conductivity formula of silica aerogel, for powdery silica aerogel under the conditions of T = 298 K, a_(2)= 0.85, D_1= 90 μm, ρ = 128 kg/m^(3), within the pressure range of 0–105Pa, the average deviation between the calculated values and experimental values is 10.51%. In the pressure range of 103–104Pa, the deviation between calculated values and experimental values is within 4%. Under these conditions, the model has certain reference value in engineering verification. This study also makes a certain contribution to the research of aerogel thermal conductivity heat transfer models and calculation formulae.

A Prediction Model of Effective Thermal Conductivity for Metal Powder Bed in Additive Manufacturing

In current research,many researchers propose analytical expressions for calculating the packing structure of spherical particles such as DN Model,Compact Model and NLS criterion et al.However,there is still a question that has not been well explained yet.That is:What is the core factors affecting the thermal conductivity of particles?In this paper,based on the coupled discrete element-finite difference(DE-FD)method and spherical aluminum powder,the relationship between the parameters and the thermal conductivity of the powder(ETC_(p))is studied.It is found that the key factor that can described the change trend of ETC_(p) more accurately is not the materials of the powder but the average contact area between particles(a_(ave))which also have a close nonlinear relationship with the average particle size d_(50).Based on this results,the expression for calculating the ETC_(p) of the sphere metal powder is successfully reduced to only one main parameter d_(50)and an efficient calculation model is proposed which can applicate both in room and high temperature and the corresponding error is less than 20.9%in room temperature.Therefore,in this study,based on the core factors analyzation,a fast calculation model of ETC_(p) is proposed,which has a certain guiding significance in the field of thermal field simulation.

A Novel Approach for the Effective Thermal Conductivity of Porous Ceramics

A new approach in combination of the effective medium theory with the equivalent unit in numerical simulation was developed to study the effective thermal conductivity of porous ceramics. The finite element method was used to simulate the heat transfer process which enables to acquire accurate results through highly complicated modeling and intensive computation. An alternative approach to mesh the material into small cells was also presented. The effective medium theory accounts for the effective thermal conductivity of cells while the equivalent unit is subsequently applied in numerical simulation to analyze the effective thermal conductivity of the porous ceramics. A new expression for the effective thermal conductivity, allowing for some structure factors such as volume fraction of pores and thermal conductivity, was put forward, and the results of its application was proved to be close to those of the mathematical simulation.

Random checkerboard based homogenization for estimating effective thermal conductivity of fully saturated soils

This paper proposes homogenization scheme for estimating the effective thermal conductivity of fully saturated soils. This approach is based on the random checkerboard-like microstructure. Two modeling scales and two modeling approaches are distinguished and used, i.e. microscale and mesoscale and 1-step and 2-step homogenizations, respectively. The 2-step homogenization involves sequential averaging procedure, i.e. first, at microscale, a mineralogical composition of soil skeleton is considered and averaging process results in estimation of the skeleton effective thermal conductivity, and then, at mesoscale, a random spatial packing of solid skeleton and pores via random checkerboard microstructure is modeled and leads to evaluation of the soil overall thermal conductivity. The 1-step homogenization starts directly at the mesoscale and homogenization procedure yields evaluation of the overall soil thermal conductivity. At the mesoscale, the distinct nature of soil skeleton, as composed of soil separates,is considered and random variability of soil is modeled via enriched random checkerboard-like structure.Both approaches, i.e. 1-step and 2-step homogenizations, interrelate mineralogical composition with the soil texture characterized by the volume fractions of soil separates, i.e. sand, silt and clay. The probability density functions(PDFs) of thermal conductivity are assumed for each of the separates. The soil texture PDF of thermal conductivity is derived taking into consideration the aforementioned functions. Whenever the random checkerboard-like structure is used in averaging process, the Monte Carlo procedure is applied for estimation of homogenized thermal conductivity. Finally, the proposed methodology is tested against the laboratory data from our measurements as well as those available from literature.

A THEORY OF EFFECTIVE THERMAL CONDUCTIVITY FOR MATRIX-INCLUSION-MICROCRACK THREE-PHASE HETEROGENEOUS MATERIALS BASED ON MICROMECHANICS

The effective thermal conductivity of matrix-inclusion-microcrack three-phase heterogeneous materials is investigated with a self-consistent micromechanical method (SCM) and a random microstructure finite element method(RMFEM). In the SCM, microcracks are assumed to be randomly distributed and penny-shaped and inclusions to be spherical, the crack effect is accounted for by introducing a crack density parameter, the effective thermal conductivity is derived which relates the macroscopic behavior to the crack density parameter. In the RMFEM, the highly irregular microstructure of the heterogeneous media is accurately described, the interaction among the matrix-inclusion-microcracks is exactly treated, the inclusion shape effect and crack size effect are considered. A Ni/ZrO2 particulate composite material containing randomly distributed, penny-shaped cracks is examined as an example. The main results obtained are: (1) the effective thermal conductivity is sensitive to the crack density and exhibits essentially a linear relationship with the density parameter: (2) the inclusion shape has a significant effect on the effective thermal conductivity and a polygon-shaped inclusion is more effective in increasing or decreasing the effective thermal conductivity than a sphere-shaped one; and (3) the SCM and RMFEM are compared and the two methods give the same effective property in the case in which the matrix thermal conductivity A, is greater than the inclusion one lambda(2). In the inverse case of lambda(1) < lambda(2), the two methods as the as the inclusion volume fraction and crack density are low and differ as they are high. A reasonable explanation for the agreement and deviation between the two methods in the case of lambda(1) < lambda(2) is made.

Numerical Predictions of the Effective Thermal Conductivity of the Rigid Polyurethane Foam

A reconstruction method is proposed for the polyurethane foam and then a complete numerical method is developed to predict the effective thermal conductivity of the polyurethane foam. The finite volume method is applied to solve the 2D heterogeneous pure conduction. The lattice Boltzmann method is adopted to solve the 1D homogenous radiative transfer equation rather than Rosseland approximation equation. The lattice Boltzmann method is then adopted to solve 1D homogeneous conduction-radiation energy transport equation considering the combined effect of conduction and radiation. To validate the accuracy of the present method, the hot disk method is adopted to measure the effective thermal conductivity of the polyurethane foams at different temperature. The numerical results agree well with the experimental data. Then, the influences of temperature, porosity and cell size on the effective thermal conductivity of the polyurethane foam are investigated. The results show that the effective thermal conductivity of the polyurethane foams increases with temperature; and the effective thermal conductivity of the polyurethane foams decreases with increasing porosity while increases with the cell size.

Analytical design of effective thermal conductivity for fluid-saturated prismatic cellular metal honeycombs

A comparative optimal design of fluid-saturated prismatic cellular metal honeycombs （PCMHs） having different cell shapes is presented for thermal management applications. Based on the periodic topology of each PCMH, a unit cell （UC） for thermal transport analysis was selected to calculate its effective thermal conductivity. Without introducing any empirical coefficient, we modified and extended the analytical model of parallel-series thermal-electric network to a wider porosity range （0.7 ~ 0.98） by considering the effects of two-dimensional local heat conduction in solid ligaments inside each UC. Good agreement was achieved between analytical predictions and numerical simulations based on the method of finite volume. The concept of ligament heat conduction efficiency （LTCE） was proposed to physically explain the mechanisms underlying the effects of ligament configuration on effective thermal conductivity （ETC）. Based upon the proposed theory, a construct strategy was developed for designing the ETC by altering the equivalent interaction angle with the direction of heat flow： relatively small average interaction angle for thermal conduction and relatively large one for thermal insulation.

Calculating the effective thermal conductivity of gray cast iron by using an interconnected graphite model

A new theoretical model of gray cast iron taking into account a locally interconnected structure of flake graphite was designed,and the corresponding effective thermal conductivity was calculated using the thermal resistance network method.The calculated results are obviously higher than that of the effective medium approximation assuming that graphite is distributed in isolation.It is suggested that the interconnected structure significantly enhances the overall thermal conductivity.Moreover,it is shown that high anisotropy of graphite thermal conductivity,high volume fraction of graphite,and small aspect ratio of flake graphite will cause the connectivity effects of graphite to more obviously improve the overall thermal conductivity.Higher graphite volume fraction,lower aspect ratio and higher matrix thermal conductivity are beneficial to obtain a high thermal conductivity gray cast iron.This work can provide guidance and reference for the development of high thermal conductivity gray cast iron and the design of high thermal conductivity composites with similar locally interconnected structures.

Effective thermal conductivity of wire-woven bulk Kagome sandwich panels

Thermal transport in a highly porous metallic wire-woven bulk Kagome （WBK） is numerically and analytically modeled. Based on topology similarity and upon introducing an elongation parameter in thermal tortuosity, an idealized Kagome with non-twisted struts is employed. Special focus is placed upon quanti- fying the effect of topological anisotropy of WBK upon its effective conductivity. It is demonstrated that the effective conductivity reduces linearly as the poros- ity increases, and the extent of the reduction is significantly dependent on the orientation of WBK. The governing physical mechanism of anisotropic thermal transport in WBK is found to be the anisotropic thermal tortuosity caused by the intrinsic anisotropic topology of WBK.

Achieving thermal magnification by using effective thermal conductivity

thermal magnification device is proposed by using effective thermal conductivity. Different fromtransformation optics method, the magnification design is realized analytically by enforcingequality of effective thermal conductivity on the magnification device and the reference case inspecified domains. The validity of theoretical analysis is checked by numerical simulation results,which demonstrates the magnifying effects of the proposed design. The device only needsisotropic and homogeneous materials that are easy to obtain in nature. It is also shown that theobtained magnifying conditions are the same as those derived by separation of variables. But theproposed method proves more flexible for multilayered materials and simpler for non-sphericalobjects under non-uniform thermal fields. It can also be extended to other fields and applicationsgoverned by Laplace equation.

A composite sphere assemblage model for porous oolitic rocks:Application to thermal conductivity

The present work is devoted to the determination of linear effective thermal conductivity of porous rocks characterized by an assemblage of grains(oolites) coated by a matrix. Two distinct classes of pores, i.e.micropores or intra oolitic pores(oolite porosity) and mesopores or inter oolitic pores(inter oolite porosity), are taken into account. The overall porosity is supposed to be connected and decomposed into oolite porosity and matrix porosity. Within the framework of Hashin composite sphere assemblage(CSA)models, a two-step homogenization method is developed. At the first homogenization step, pores are assembled into two layers by using self-consistent scheme(SCS). At the second step, the two porous layers constituting the oolites and the matrix are assembled by using generalized self-consistent scheme(GSCS) and referred to as three-phase model. Numerical results are presented for data representative of a porous oolitic limestone. It is shown that the influence of porosity on the overall thermal conductivity of such materials may be significant.

Two-step homogenization for the effective thermal conductivities of twisted multi-filamentary superconducting strand

For the accurate prediction of the effective thermal conductivities of the twisted multi-filamentary superconducting strand,a two-step homogenization method is adopted.Based on the distribution of filaments,the superconducting strand can be decomposed into a set of concentric cylinder layers.Each layer is a two-phase composite composed of the twisted filaments and copper matrix.In the first step of homogenization,the representative volume element(RVE)based finite element(FE)homogenization method with the periodic boundary condition(PBC)is adopted to evaluate the effective thermal conductivities of each layer.In the second step of homogenization,the generalized self-consistent method is used to obtain the effective thermal conductivities of all the concentric cylinder layers.The accuracy of the developed model is validated by comparing with the local and full-field FE simulation.Finally,the effects of the twist pitch on the effective thermal conductivities of twisted multi-filamentary superconducting strand are studied.

Prediction of Thermal Conductivity and Specific Heat of Native Maize Starch and Comparison with HMT Treated Starch

Specific heat(Cp)and effective thermal conductivity(λ)of native maize starch(NS)were measured by DSC and transient heat transfer method,respectively,at different moisture contents and temperatures.The dependency of temperature(T)and moisture content(W)on the two parameters were investigated.The thermophysical properties of treated starch(TS)by four hydrothermal processes(RP-HMT,IV-HMT,DV-HMT and FV-HMT)were measured and compared to native strach.Hydrothermal treatments were performed at 3 bars(133°C)for 10 min.For Cp andλmeasurements,moisture content varied for NS from 5 to 21.5%d.b.and from 8.8 to 25%d.b.,respectively,and was fixed at 6%d.b.for TS.Empirical models were developed to specific heat and effective thermal conductivity,using a multiple regression algorithm with subsequent statistical analysis.The proposed models for NS based on T and W predict Cp andλwith a mean absolute error of 3.5%and 1.3%,respectively.Large differences in specific heat were observed between TS and NS.In a temperature range of 40 to 160°C,Cp values varied from 1.964 to 2.699 for NS and 1.380 to 2.085(J.g-1.°C-1)for TS.In contrast,the conductivity of NS was almost identical to that of treated starch by FV-HMT,followed in an increasing order by those treated by DV-HMT,RP-HMT,and IV-HM processes.

Analysis of thermal conductivity in tree-like branched networks

Asymmetric tree-like branched networks are explored by geometric algorithms. Based on the network, an analysis of the thermal conductivity is presented. The relationship between effective thermal conductivity and geometric structures is obtained by using the thermal-electrical analogy technique. In all studied cases, a clear behaviour is observed, where angle （δ,θ） among parent branching extended lines, branches and parameter of the geometric structures have stronger effects on the effective thermal conductivity. When the angle δ is fixed, the optical diameter ratio β＋ is dependent on angle θ. Moreover, γand m are not related to β＊. The longer the branch is, the smaller the effective thermal conductivity will be. It is also found that when the angle θ〈δ2, the higher the iteration m is, the lower the thermal conductivity will be and it tends to zero, otherwise, it is bigger than zero. When the diameter ratio β1 〈 0.707 and angle δ is bigger, the optimal k of the perfect ratio increases with the increase of the angle δ; when β1 〉 0.707, the optimal k decreases. In addition, the effective thermal conductivity is always less than that of single channel material. The present results also show that the effective thermal conductivity of the asymmetric tree-like branched networks does not obey Murray＇s law.

Numerical and experimental evaluation for density-related thermal insulation capability of entangled porous metallic wire material

Entangled porous metallic wire material(EPMWM)has the potential as a thermal insulation material in defence and engineering.In order to optimize its thermophysical properties at the design stage,it is of great significance to reveal the thermal response mechanism of EPMWM based on its complex structural effects.In the present work,virtual manufacturing technology(VMT)was developed to restore the physics-based 3D model of EPMWM.On this basis,the transient thermal analysis is carried out to explore the contact-relevant thermal behavior of EPMWM,and then the spiral unit containing unique structural information are further extracted and counted.In particular,the thermal resistance network is numerically constructed based on the spiral unit through the thermoelectric analogy method to accurately predict the effective thermal conductivity(ETC)of EPMWM.Finally,the thermal diffusivity and specific heat of the samples were obtained by the laser thermal analyzer to calculate the ETC and thermal insulation factor of interest.The results show that the ETC of EPMWM increases with increasing temperature or reducing density under the experimental conditions.The numerical prediction is consistent with the experimental result and the average error is less than 4%.

Numerical Analysis of the Thermal Properties of Ecological Materials Based on Plaster and Clay

Most of the energy savings in the building sector come from the choice of the materials used and their microphysical properties.In the present study,through numerical simulations a link is established between the thermal performance of composite materials and their microstructures.First,a two-phase 3D composite structure is modeled,then the RSA(Random Sequential Addition)algorithm and a finite element method(FE)are applied to evaluate the effective thermal conductivity of these composites in the steady-state.In particular,building composites based on gypsum and clay,consolidated with peanut shell additives and/or cork are considered.The numerically determined thermal conductivities are compared with values experimentally calculated using the typical tools of modern metrology,and with available analytical models.The calculated thermal conductivities of the clay-based materials are 0.453 and 0.301 W.m^(−1).K^(−1) with peanut shells and cork,respectively.Those of the gypsum-based materials are 0.245 and 0.165 W.m^(−1).K^(−1) with peanut shells and cork,respectively.It is shown that,in addition to its dependence on the volume fraction of inclusions,the effective thermal conductivity is also influenced by other parameters such as the shape of inclusions and their distribution.The relative deviations,on average,do not exceed 6.8%,which provides evidence for the reliability of the used approach for random heterogeneous materials.

Effects of Metal Absorber Thermal Conductivity on Clear Plastic Laser Transmission Welding

In our previous study, metals have been used as absorbers in the clear plastic laser transmission welding. The effects of metal thermal conductivity on the welding quality are investigated in the present work. Four metals with distinctly different thermal conductivities, i.e., titanium, nickel, molybdenum, and copper, are selected as light absorbers. The lap welding is conducted with an 808 nm diode laser and simulation experiments are also conducted. Nickel electroplating test is carried out to minimize the side-effects from different light absorptivities of different metals. The results show that the welding with an absorber of higher thermal conductivity can accommodate higher laser input power before smoking, which produces a wider and stronger welding seam.The positive role of the higher thermal conductivity can be attributed to the fact that a desirable thermal field distribution for the molecular diffusion and entanglement is produced from the case with a high thermal conductivity.

Thermal stretching in two-phase porous media: Physical basis for Maxwell model

An alternate yet general form of the classical effective thermal conductivity model （Maxwell model） for two-phase porous materials is presented, serving an explicit thermo-physicM basis. It is demonstrated that the reduced effective thermal conductivity of the porous media due to non-conducting pore inclusions is caused by the mechanism of thermal stretching, which is a combi- nation of reduced effective heat flow area and elongated heat transfer distance （thermal tortuosity）.

High Temperature Thermal Physical Properties of High-alumina Fibrous Insulation

The thermal properties of high-alumina fibrous insulation which filled in metallic thermal protection system were investigated. The effective thermal conductivities of the fibrous insulation were measured under an atmospheric pressure from 10^-2 to 10^5 Pa. In addition, the changes of the specific heat and Rosseland mean extinction coefficient were experimentally determined under various surrounding temperatures up to 973 K. The spectral extinction coefficients were obtained from transmittance data in the wavelength range of 2.5- 25 μm using Beer＇s law. Rosseland mean extinction coefficients as a function of temperature were calculated based on spectral extinction coefficients at various temperatures. The results show that thermal conductivities of the sample increase with increasing temperature and pressure. Specific heat increases as temperature increases, which shows that the capacity of heat absorption increases gradually with temperature. Rosseland mean extinction coefficients of the sample decrease firstly and then increase with increasing the temperature.

Thermal Behavior of Clay-Based Building Materials: A Numerical Study Using Microstructural Modeling

A large part of the energy savings in the building sector comes from the choice of materials used and their structures. We are interested, through a numerical study, in establishing the link between the thermal performance of composite materials and their microstructures. The work begins with the generation of a two-phase 3D composite structure, the application of the Random Sequential Addition (RSA) algorithm, and then the finite element method (FE) is used to evaluate, in steady-state, the effective thermal conductivity of these composites. The result of the effective thermal conductivity of composite building material based on clay and olive waste at a volume fraction of 10% obtained by simulation is 0.573 W·m?1·K?1, this result differs by 3.6% from the value measured experimentally using modern metrology methods. The calculated value is also compared to those of existing analytical models in the literature. It can be noticed also that the effective thermal conductivity is not only related to the volume fraction of the inclusions but also to other parameters such as the shape of the inclusions and their distribution. The small difference between the numerical and experimental thermal conductivity results shows the performance of the code used and its validation for random heterogeneous materials. The homogenization technique remains a reliable way of evaluating the effective thermal properties of clay-based building materials and exploring new composite material designs.