Maxwell Eucken Research Articles

Calculation model and influence factors of thermal conductivity of composite cement-based materials for geothermal well

The use of cement-based composites (CBC) with high thermal conductivity for geothermal well cementing is extremely important for the efficient development and use of geothermal energy. Accurate prediction of thermal conductivity can save a lot of experimental costs and time. At present, there is no specific calculation model for the thermal conductivity of CBC. In this study, the microstructure, thermal conductivity model and influencing factors of CBC were investigated by experimental tests, theoretical analysis and numerical simulation. The results showed that the cement-based material could be simplified into a two-layer structure of hydrated and unhydrated layers. Mathematical and numerical models based on the coupled Series model and the Maxwell–Eucken model were established to calculate the thermal conductivity for CBC. The mathematical and numerical models were found to be more accurate by comparison with the conventional models and experimental test results. The cubic packing was more favorable than the spherical packing to improve the thermal conductivity of CBC. The plate material had significant anisotropy. The thermal conductivity of CBC showed a rapid decrease followed by a slow decrease, a decrease followed by a slow increase and finally a rapid decrease, a rapid increase followed by an up and down fluctuation and finally a plateau, respectively, with the increase of filler particle diameter, spacing and curing temperature. Based on these results, the effective methods and future research directions were proposed to maximize the thermal conductivity of geothermal well cementing materials in actual engineering applications. The research findings can provide some technical references for the efficient development of geothermal energy and research on CBC with high thermal conductivity.

Improving the Sierpinski carpet model arithmetic to accurately predict the thermal conductivity of fatty acid/carbon composite phase-change materials

The effective thermal conductivity is an important physical parameter of composite phase-change materials (PCMs). In this study, a new analytic expression of the dimensionless thermal conductivity is proposed to predict the dimensionless thermal conductivity of fatty acid–carbon materials composite PCMs based on the Sierpinski carpet model and the thermal resistance network model of a fractal geometry combined with the principle of the weighted average. The new analytical expression can be used to overcome the issue of the predicted values deviating considerably from the experimental results when the fractal series n is too small. At the same time, an accurate solution for the dimensionless ratio (t+) of the width of the carbon materials to the side length of the Sierpinski carpet is presented. Compared with the general solution algorithm proposed by Song, the commonly used quadratic parallel (QP) prediction model, and the Maxwell–Eucken model, this algorithm is more reliable. The proposed prediction model can be used to predict the effective thermal conductivity of fatty acid–carbon materials.

X‐ray Computed Tomography Characterization of Slag Crust and the Effect of Bubbles and Metallic Iron in Slag on Heat Transfer to Copper Stave

Understanding the heat transfer properties of the slag crust is critical to the safe operation of copper staves. The distribution of metallic iron and bubbles in the slag crust is detected by X‐ray computed tomography. The thermal conductivity of the slag crust is modified based on an effective thermal conductivity model and laser thermal conductivity measurements to predict the effect of metallic iron and bubbles on the heat transfer in the slag crust. The results show that the average volume fractions of metallic iron and air bubbles in the slag crust are 3% and 4.5%, respectively. The measured value is consistent with the trend of the effective thermal conductivity calculation model, and the calculation result of the Maxwell–Eucken effective thermal conductivity model is very accurate. Variations in the volume fraction of metallic iron in the slag crust have a greater effect on the thickness of the slag crust, while variations in the volume fraction of bubbles have a smaller effect on the thickness of the slag crust. It is recommended to keep it between 10 and 30 mm in blast furnace production to help improve the operational life of the copper stave.

Polycarbonate/poly(methyl methacrylate)/silica aerogel blend composites for advanced transparent thermal insulations: Mechanical, thermal, and optical studies

AbstractUsing transparent thermal insulators, which are low heat conductors and good light transmitters, is a brilliant idea to preserve heat energy. In this regard, silica aerogels (SAs) have attracted immense attention these days because of their unique nanoporous networks, consisting of connective silica nanoparticles and high‐volume nanopores. The present study investigates the influence of incorporating 3 and 5 phr SAs on the mechanical properties, thermal conductivity (TC), and optical characteristics of polycarbonate/poly(methyl methacrylate) (PC/PMMA) (75/25, 50/50, and 25/75 w/w) blends. The scanning electron microscopy studies indicated that the PC/PMMA/SA (25/75/3) composite has the best dispersion. The highest improvements in tensile strength and Young's modulus were observed for the PC/PMMA/SA (75/25/5) composite. In addition, incorporating the SA resulted in a reduction in the impact strength of all the blends. The lowest TC was observed for the PC/PMMA/SA (75/25/5) blend composite. The TC results were compared with the data predicted by the Agari, Russell, Maxwell–Eucken, and Bruggeman models. It was found that the Agari logarithmic model has the best agreement with the experimental data. Except for PC, PMMA, PC/PMMA (25/75), and PC/PMMA/SA (25/75/3), no other samples showed optical transmittance. On average, PC/PMMA/SA (25/75/3) had 13% more light absorption than PC/PMMA (25/75).

Preparation of W-Plated Diamond and Improvement of Thermal Conductivity of Diamond-WC-Cu Composite

The tungsten (W)-plated diamond process was explored and optimized. A dense and uniform tungsten coating with a thickness of 900 nm was successfully prepared by the powder covering sintering method. The Diamond-WC-Cu composite with high density and high thermal conductivity were successfully prepared by cyclic vacuum pressure infiltration. The microstructure and composition of the W-plated diamond particles were analyzed. The effect of tungsten coating on the microstructure and thermal conductivity of the Diamond-WC-Cu composite was investigated. After calculation, the interface thermal resistance of the composite forming the tungsten carbide transition layer is 2.11 × 10−8 m2∙K∙W−1. The thermal conductivity average value of the Diamond-WC-Cu composite with a diamond volume fraction of 60% reaches 874 W∙m−1∙K−1, which is close to the theoretical prediction value of Hasselman-Johnson (H-J) model and differential effective medium (DEM) model. Moreover, the Maxwell-Eucken (M-E) model, H-J model, and DEM model were used to evaluate the thermal conductivity of the Diamond-WC-Cu composite.

Nonlinear finite element analysis of temperature-dependent functionally graded porous micro-plates under thermal and mechanical loads

In the present study, a displacement based nonlinear finite element model for functionally graded porous micro-plates is developed based on the general third-order shear deformation plate theory and the modified couple stress theory. The developed finite element model accounts for von Kármán nonlinear strains, a power-law variation of two material constituents through the plate thickness, and different distributions of porosity with a constant volume of voids on static bending of micro-plates are analyzed. The length scale dependency is captured using a single parameter of the modified couple stress theory. A power-law distribution is assumed to model the variation of the two material constituents, while the porosity distributions vary according to cosine functions. The temperature-dependent properties are obtained using a cubic-spline interpolation from experimental data. A one-dimensional steady-state heat conduction problem is solved using the effective thermal conductivity of the porous material based on the Maxwell–Eucken model to obtain temperature distribution through the plate thickness. The Newton–Raphson iteration scheme is used to solve the nonlinear system of equations. A parametric study is conducted to demonstrate the effects of material and porosity parameters, temperature and length scale dependencies, and boundary conditions on the deflections and stress distributions.

Two-different ways of synthesis for EG: Study of mechanical, thermal, and electrical properties of epoxy composite for TIMs

The current study reports the synthesis of expanded graphite (EG) in two different ways and its fabrication with epoxy matrix to form composite at various filler fractions (5, 10, 12.5). One type EG (EG-C) is prepared by the electrochemical process using natural graphite flake (NGF), concentrated sulfuric acid, and ammonium persulfate, while the other (EG-P) is just mixing and heating of NGF with zinc nitrate hexahydrate. The functional groups of synthesized EG were confirmed by Fourier transform infrared spectroscopy. The surface morphology and microstructure of synthesized filler (EG-C, EG-P) were studied using X-ray diffraction, scanning electron microscopy, and transmission electron microscopy. An optimum through-plane thermal conductivity (TC) of 2.04 and 2.22 W/mK was observed in the case of the composites containing 12.5 wt% of EG-C and EG-P, respectively. The obtained experimental TC was compared with three numerical thermal models, that is, inverse rule of mixture, Maxwell–Eucken model, and Agari model. Furthermore, the thermal stability of both composites was compared by using a thermogravimetric analyzer. The electrical resistivity of EG-P/epoxy composite at different formulations was higher than the EG-C-filled epoxy composites.

Thermal conductivity and diffusivity of carbon‐reinforced polyetherketoneketone composites

ABSTRACTHeat transfer properties play an important role in processing of polyetherketoneketone (PEKK)/carbon fiber (CF) composites. Accordingly, thermal conductivity and diffusivity of PEKK, PEKK/glassy carbon (GC), and PEKK/CF composites have been studied. Observed increase in conductivity and diffusivity with carbon filler addition was analyzed using the Maxwell–Eucken model. PEKK/GC composites with low carbon fraction indicated good fitting experimental points of the model, indicating good dispersion of particles. For PEKK/CF composites, the thermal conductivity and diffusivity increase is a reflection of a decrease in porosity. Results as observed from the model points to a homogenous dispersion within the PEKK/CF composites as well. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47975.

Flame propagation in nano-aluminum–water (nAl–H2O) mixtures: The role of thermal interface resistance

A detailed numerical analysis of flame propagation in nano-aluminum–water (nAl–H2O) mixture is performed. Emphasis is placed on investigating the role of particle thermal conductivity in the prediction of the burning properties of the mixture. Flame structure and burning characteristics are obtained by solving the energy equation using finite difference discretization and the Gauss–Seidel iteration method. Particle thermal conductivity is modeled using the temperature-dependent thermal conductivities of the aluminum core and oxide layer, as well as their interface resistance. The effective thermal conductivity of the mixture is modeled as a function of temperature, spatial coordinate, and local mixture composition, by means of the unified Maxwell–Eucken–Bruggeman model, accounting for random particle distribution and inter-particle interaction. Results indicate that the combined thermal resistance offered by the oxide layer and the interface constitute 95% of the total resistance of the particle. The calculated particle-size dependent linear burning rates show good agreement with experimental data, with only 5% error. Error in burning rate prediction increases, however, to 20% when interface resistance is excluded from the particle thermal conductivity model. It was also observed that burning rate varies as the inverse of particle size. Finally, an analysis of the sensitivity of burning rate to the individual components of the particle thermal conductivity model is also performed. Results suggest a 30% decrease in burning rate for two orders of magnitude reduction in both interface conductance and oxide thermal conductivity. The burning rate drops by only 15%, however, for a similar reduction in aluminum thermal conductivity. A heat conduction perspective on flame propagation in nanocomposites is presented, identifying the highest and the lowest conductive pathways for energy transport.

3D interconnected high aspect ratio tellurium nanowires in epoxy nanocomposites: serving as thermal conductive expressway

ABSTRACTHeat removal via thermal management materials is attracting more and more attention in the electronic industry. Conventional particle/polymer thermal conductive composites require a high filler loading ratio (>30 vol %), which cause severe thermal interfacial resistance and mechanical issue. In this work, we fabricate tellurium nanowires (NWs)/epoxy nanocomposites via a facile bar coating method. According to Agari model and Maxwell–Eucken model, the as‐synthesized ultra‐long NWs with high aspect ratio (>100) construct the 3D interconnected thermal conductive network better in resin matrix to facilitate the heat transfer process. The results show that at a low loading ratio of 2.4 vol %, this nanocomposite exhibits the out‐of‐plane and in‐plane thermal conductivity of 0.378 and 1.63 W m−1 K−1, respectively, which is 189 and 715% higher than that of pure epoxy resin. Importantly, good stability, and flexibility of nanocomposites are well maintained. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47054.

Influence of pore distribution on the equivalent thermal conductivity of low porosity ceramic closed-cell foams

The microstructures of porous alumina materials with different porosities were established by introducing the departure factor of pore position and acentric factor of pore diameter to describe the distribution of pores in space and in size, respectively. The contribution of radiation and influence of pore distribution on the equivalent thermal conductivity were discussed based on numerical simulations by the finite volume method (FVM) considering both thermal conduction and radiation. When the pore diameter was less than 10 µm, the radiation component was less than 2%, and radiation could be neglected. Radiative heat transfer played a dominant role for materials with high porosity and large pore size at high temperatures. For micro pore materials (< 100 µm), broad pore size and non-uniform pore space distribution decreased the thermal conductivity across the entire temperature range. For materials with macro pores (>1 mm), broad pore distribution decreased the thermal conductivity at low temperatures and increased it at high temperatures. The basic prediction model of effective thermal conductivity for a two-component material, the Maxwell–Eucken model (ME1) and its modified model were corrected by introducing the pore structure factor. The results from experiments prove that the numerical values were satisfactory.

Sludge disinfection using electrical thermal treatment: The role of ohmic heating

Electrical heating has been proposed as a potential method for pathogen inactivation in human waste sludge, especially in decentralized wastewater treatment systems. In this study, we investigated the heat production and E. coli inactivation in wastewater sludge using electrical thermal treatment. Various concentrations of NaCl and NH4Cl were tested as electrolyte to enhance conductivity in sludge mixtures. At same voltage input (18V), sludge treated with direct current (DC) exhibited slower ascent of temperature and lower energy efficiencies for heat production comparing to that using alternate current (AC). However, DC power showed better performance in E. coli inactivation due to electrochemical inactivation in addition to thermal inactivation. Greater than 6log10 removal of E. coli was demonstrated within 2h using 0.15M of NaCl as electrolyte by AC or DC power. The heat production in sludge was modeled using Maxwell–Eucken and effective medium theory based on the effective electrical conductivity in the two-phase (liquid and solid) sludge mixtures. The results showed that the water and heat loss is a critical consideration in modeling of sludge temperature using ohmic heating. The experimental data also suggested that the models are less applicable to DC power because the electrochemical reactions triggered by DC reduce the concentration of NH4+ and other ions that serve as electrolyte. The results of this study contribute to the development of engineering strategies for human waste sludge management.

Investigation on the effective thermal conductivity of typical Pidgeon process briquette with a combined model

Experiments were conducted on the specific heat and thermal conductivity of a calcined dolomite briquette, a ferrosilicon sample, and a pre-reduction Pidgeon-processed briquette. The laser flash method was used in the measurement of thermal conductivity. Based on the results, a combination of the Series and Maxwell–Eucken 2 models was deduced to fit the effective thermal conductivity of a Pidgeon-processed briquette, which was demonstrated by an analysis of the briquette microstructure. In contrast to previous studies, the proposed study provided specific measured values of briquette density, specific heat, and thermal conductivity, which could be used in the calculation of the Pidgeon process. Moreover, this study offers new potential for the improvement of the numerical simulation accuracy of the Pidgeon process.

Porous metal produced by selective laser melting with effective isotropic thermal conductivity close to the Hashin–Shtrikman bound

Additive manufacturing may be a novel method for fabricating porous materials. These materials can achieve effective performance because of their internal geometries. Metal-additive manufacturing is expected to utilize thermal conduction materials and devices. We have developed a porous metal with effective isotropic thermal conductivity by using metal-selective laser melting additive manufacturing. The internal pore structure was designed by topology optimization, which is the most effective structural optimization technique to maximize effective thermal conductivity. The designed structure was converted to a three-dimensional STL model, which is a native digital format of additive manufacturing, and assembled as a test piece. Effective thermal conductivity was measured by a steady-state method in which the effective thermal conductivity was calculated from a one-dimensional temperature gradient and the heat flux of the test pieces. The test pieces showed an effective thermal conductivity close to the Hashin–Shtrikman or Maxwell–Eucken bound, which is the theoretical limit of effective performance with an error less than 10%.

Measurement and Modeling of Tissue Thermal Conductivity With Variable Water Content and Compression

The effects of water content and compression level on tissue thermal conductivity were studied. These effects are important in electrosurgery, as tissue is subjected to both compression and thermal heating. Ex vivo canine spleen tissue was used in this study. A thermal diffusion probe technique was employed to measure the tissue thermal conductivity in three different conditions. First, the tissue thermal conductivity with different water content levels was measured. The measured thermal conductivity decreased as the percentage of water within the tissue decreased. Second, the tissue thermal conductivity under compression, up to 77%, was measured and it showed a 9% reduction as the load was applied. Third, desiccated tissue was compressed, and the thermal conductivity was measured. The compression effect on thermal conductivity was less prominent in the desiccated tissue because less water was squeezed out due to compression. A three-phase Maxwell–Eucken model was developed to predict the tissue thermal conductivity for varying water content and compression levels. The model used the ratio of air, tissue fiber, and water to predict the thermal conductivity and showed a good agreement with the experimental data.

Modeling the effective thermal conductivity for disperse systems with high solid mass fractions

An analytical model was presented for calculating the effective thermal conductivity for disperse systems based on fractal theory and percolation theory. The shortcomings of previous models for the high mass fraction of solid particles can be overcome by the recent model. Experiments were conducted on liquid phase mixed aluminum powder, copper powder and graphite powder, and the experimental results were compared with the model results. The results indicate that the proposed model is in good agreement with the experimental results, whereas the Maxwell–Eucken model deviates from the test results at a high mass fraction. The new model also provides more structural models using the modeling procedure previously proposed by authors.

Analysis of the optical and thermal properties of transparent insulating materials containing gas bubbles

As a medium of low absorption and low thermal conduction, introducing gas bubbles into semitransparent mediums, such as glass and polycarbonate (PC), may simultaneously improve their light transmission and thermal insulation performances. However, gas bubbles can also enhance light scattering, which is in competition with the effect of the absorption decrease. Moreover, the balance between the visible light transmittance and the effective thermal conductivity should also be considered in the material design. Therefore, a radiative transfer model and the Maxwell–Eucken model for such material were employed to analyze the optical and thermal performances, respectively. The results demonstrate that the transmittance increases when the bubble radius (r) increases with a fixed volume fraction of the gas bubbles (fv) due to the increased scattering intensity. In addition, the effective thermal conductivity always decreases with increasing fv. Thus, to achieve both good optical and thermal performances, high fv with large r is preferred. When fv = 0.5, the transmittance can be kept larger than 50% as long as r ≥ 0.7 mm. To elucidate the application performance, the heat transfer of a freezer adopting the glass or PC with gas bubbles as a cover was analyzed and the energy saving can be nearly 10%.

Electrical Conductivity of Cabbage and Daikon Radish as Affected by Electrical Voltage, Frequency, Salt Concentration and Temperature

AbstractShredded cabbage (50% v/v) and Daikon radish cubes (57% v/v) were mixed with different salt solutions (0.15, 0.5, 1, 1.5 and 1.85%), poured into a Teflon‐coated static Ohmic cell and heated from 30 to 70°C at different alternating current voltages (65, 80, 100, 120 or 135 V) and frequencies (60, 2,070, 5,030, 7,990 or 10,000 Hz). Voltage, current, time and temperature were measured to calculate electrical conductivities at different temperatures. For the modeling part, 750 g of a blended crude puree (particle size &lt; 0.5 mm) was used to fill the Ohmic cell. Daikon radish gave the highest value for electrical conductivity of 1.07 S/m at 30°C and 1.85%, 100 V and 5,030 Hz while cabbage gave a value of 0.81 S/m under the same conditions. For cabbage, the electrical conductivity values increased with increasing frequency at higher voltage, but decreased at low voltage levels. An opposite trend was observed for Daikon radish. Modeling indicated that electrical conductivity increased quadratically with temperature, salt concentration and electrical voltage. Response surface models revealed that linear, cross products, as well as quadratic effects were significant with R2 &gt; 0.98. The Maxwell–Eucken model, which describes solid particles dispersed in continuous liquid, showed good fit for the electrical conductivity data.Practical ApplicationsOhmic heating can be an alternative to conventional heat processing of food, reducing treatment time and improving quality. Ohmic heating has been generally recognized to provide uniform and rapid heating conditions. The electrical conductivity (EC) of food components is the key property in the Ohmic heating process and is dependent on many product and system‐dependent properties, especially the salt content. It is also the primary property needed for modeling the Ohmic heating effects of a system or product. This manuscript details the gathered data on electrical conductivity of cabbage and radish, and an appropriate modeling approach to describe their dependence on product and system properties. The study generates new data EC for the vegetables and how the EC is influenced by the two vegetables that differ significantly in structure.

Anisotropy of thermal conductivity and elastic properties of extruded clay-based materials: Evolution with thermal treatment

Kaolinite and muscovite are major clay mineral phases found in the raw materials used for tile and brick production. As phyllosilicates, the crystal structures are layered yielding anisotropic properties. The thermo-physical properties of an extruded clay material, essentially composed of kaolinite, quartz and muscovite have been investigated in the parallel and perpendicular directions to the extrusion axis. Texture is characterized by scanning electron microscopy observations and X-ray diffraction measurements. Values of effective thermal conductivity measured by the laser flash technique and Young's modulus measured with an ultrasonic pulse-echo method reveal an anisotropy factor of 2 for the material in the green body at the macroscopic scale. The thermal conductivity of the solid phases of the material without the quartz fraction was then estimated using an analysis based on the Maxwell–Eucken and Landauer relations. This yields an anisotropy ratio=3.5 for the clay phase, explained by the alignment of kaolinite and muscovite particles with the extrusion process. The elastic and thermal properties evolve as a function of the heat treatment temperature for the clay, resulting in isotropic behavior after treatment at 1300°C. These evolutions are concomitant with mineralogical transformations of kaolinite including the formation of mullite above 1000°C.

Modeling the effect of gas on the effective thermal conductivity of heterogeneous materials

The aim of this research is to study the effect of gas phase on the effective thermal conductivity of heterogeneous materials with high solid phase mass fraction. A general model based on Maxwell–Eucken model and Effective Medium Theory model was proposed first and compared with the previous models, showing some potential significance of the present model. The present model shows that the gas phase in heterogeneous materials is significantly affected by maximum volume fraction of solid phase. Then, the effect of the shape parameters of solid particle on the maximum volume fraction of solid phase was discussed. The results indicate the maximum volume fraction of solid phase tends to grow up by increasing the particle diameter or decreasing the particle diameter ratio. Finally, the effective thermal conductivity of heterogeneous materials predicted by the proposed model was compared with that by direct experiment, showing great agreement.