Thermal Conductivity Model Research Articles

An improved model for predicting the thermal conductivity of sand based on a grain size distribution parameter

Soil thermal conductivity is a critical parameter in various fields related to soil heat transfer, mainly affected by porosity and saturation. In this research, the thermal conductivity of three types of sands with different properties was measured. Eight soil thermal conductivity models (including two semi-empirical models and six empirical models) were compared and evaluated. By analyzing the inadequacies of the existing models and microscopic mechanism of soil, a grain size distribution parameter was defined, and an improved model was proposed. The results showed that four empirical models from published literature provided relatively satisfactory performance but still required improvement. The improved model can accurately predict the thermal conductivity of different types of soils as the root mean square error for the three soils were 0.072, 0.073, and 0.056 W·m−1· k−1, respectively. Moreover, compared with the existing models, the improved model provided more scientific explanations for the limiting cases of porosity and saturation. In addition, this model revealed a close linear relationship between the thermal conductivity of soil and solid particles. The prominent nonlinear relationships between thermal conductivity and porosity or saturation were also depicted. Furthermore, the content of fine particles has a remarkable impact on the thermal conductivity of dry soil. It is suggested that the improved model can be used for predicting the complete thermal conductivity of soil in case there is no available field test data.

Insights and theoretical model of thermal conductivity of thermally damaged hybrid steel-fine polypropylene fiber-reinforced concrete

The use of hybrid steel-fine polypropylene fiber-reinforced concrete (HFRC) may be an effective strategy for avoiding concrete thermal spalling under fire loading. The thermal conductivity of HFRC is one key parameter for the fire resistance assessing. In this research, the thermal conduction behavior of HFRC is experimentally and numerically studied to obtain a thorough understanding on its thermal degradations and their mechanisms after high-temperature exposure. New mechanisms are discovered to explain the remarkable reduction of thermal conductivity. In addition to the effect of moisture loss and porosity increase, the combined effect of heat bridge and interfacial thermal resistance (ITR) is found to be the dominant mechanisms. Moreover, the evaporation of polypropylene fibers adhering to the coarse aggregates enhances the ITR effect. Based on these mechanisms, a multi-scale homogenization method is also proposed to evaluate the thermal conductivity of thermally damaged HFRC, whose accuracy are demonstrated by the excellent agreements between the experimental data and the numerical results.

Influencing factors of rock thermal conductivity and applicability evaluation of its mixing law predictive models

The thermal conductivity (TC) of rocks is a very important parameter in geothermal theory and applied research, its value is related to rock composition, mineral grains characteristics, rock porosity, and pore fluid etc., and simultaneously is affected by formation thermodynamic environment (temperature, pressure,etc.). Statistical analysis results of the thermophysical property parameters of borehole samples from Jizhong Depression indicated that the TC is mainly controlled macroscopically by lithology, compared with sandstone, mudstone, conglomerate, and gneiss, dolomite has a greater TC. In the dry state, the TC of dolomite samples showed a decrease with increasing temperature, the values of TC decreased by 12.3–27.5% in the temperature interval of 30–130 °C. Moreover, under the same temperature conditions, excluding the effects of water content and mineral fraction, the TC of medium–coarse crystalline dolomite, medium–fine crystalline dolomite, microcrystalline dolomite, and mud-powder crystalline dolomite decreased successively, reflecting the influence of the mineral grain size on TC. The validity and applicability of six commonly used mixing law predictive models for TC were evaluated based on X-ray diffraction (XRD) data from 70 borehole samples. The results showed that Geometric mean model displayed the best fit (goodness of fit, R2 = 0.878) for rocks, and Voigt-Ruess-Hill average also showed a good fit, with an R2 of 0.868, and had the best prediction for mudstone (AME = 10.16, RMSE = 0.25). In cases where the calculated values deviate significantly from the measured values, it may reflect the limitation that the mixing models consider only the composition of minerals but ignores the structural characteristics of rocks.

Fractal model of thermal contact conductance of rough surfaces based on cone asperity

Purpose The purpose of this paper is to propose a fractal model of thermal contact conductance (TCC) of rough surfaces based on cone asperity. Design/methodology/approach A detailed numerical study is conducted to examine the effects of contact load, fractal dimensional, fractal roughness and material properties on the TCC of rough surfaces. Findings The results indicate that when the fractal dimension D is less than 2.5, the TCC of rough surfaces increases nonlinearly with the increase of the contact load. However, when the fractal dimension D is greater than or equal to 2.5, the TCC of rough surfaces increases linearly with the increase of the contact load; the TCC of the rough surfaces increases with the increase of the fractal dimension D and the decrease of the fractal roughness G; the material parameters also have an influence on the TCC of the rough surfaces, and the extent of the effect on the TCC is related to the fractal dimension D. Originality/value A fractal model of TCC of rough surfaces based on cone asperity is established in this paper. Some new results and conclusions are obtained from this work, which provides important theoretical guidance for further study of TCC of rough surfaces.

Performance evaluation of thermal conductivity models for fission gases with application to [formula omitted]-zirconium dispersion fuel

In this paper, the modeling of fission gases, particularly xenon and krypton, and their effects on the thermal performance with application to UO2-zirconium dispersion fuel is investigated.To investigate the consequence of fission gas behavior in nuclear dispersion fuel, in the first step, our obtained single atom diffusion coefficient, Ds, of xenon in UO2 by implementing molecular dynamics is used and open source code SCIANTIX is improved and employed to obtain the density of bubbles through the fuel. A microstructure model of dispersed fuel has been used to treat fuel meat thermal conductivity by taking into account fission gas bubbles density. Furthermore, the results of other models are given to evaluate fission bubbles' evolution.To explore thermal conductivity models of dispersion fuel, a code called Kowsar-1 is developed by including fission gases generation.

New recommendation for the thermal conductivity of irradiated (U, Pu)O2 fuels under fast reactor conditions. Comparison with recent experimental data

New experimental results obtained at the Joint Research Centre in Karlsruhe (JRC-Karlsruhe) within the European Sustainable Nuclear Industrial Initiative Plus project (ESNII+) were used to develop an updated recommendation for the thermal conductivity of (U, Pu)O2 fuels irradiated in fast reactor (FR) conditions. Fresh and irradiated FR fuels were characterised, and their thermal diffusivity and heat capacity were measured by the laser flash technique. The thermal conductivity of those fuels was calculated, using hydrostatic density measurements when available or using calculated density.The thermal conductivity model, developed in this work, describes different effects induced by irradiation on the degradation of thermal conductivity: soluble fission products (FPs), precipitated FPs, radiation damage, and porosity. Those effects are considered in separate corrective factors, which depend on the chemical composition of the irradiated fuel, its microstructure, and the temperature. To estimate these parameters, thermomechanical calculations (PLEIADES-GERMINAL V2) and thermochemical calculations (Thermo-Calc V4.1 with the TAF-ID V11 database) were carried out in conjunction. The data provided for each fuel sample consisted of fuel temperature, burn-up, end-of-life (EOL) isotopic composition, molar fraction of the dissolved FPs in the matrix, molar fraction of the oxide, and the metallic precipitated phases, density, produced and released fission gases.In this work, we showed a clear discrepancy between the experimental data and the most widely used thermal conductivity model for irradiated fuels (Lucuta et al., 1996). Lucuta's model was then modified and a new recommendation for FR (U, Pu)O2 fuels was provided. This work demonstrates that by introducing the neodymium content as the parameter driving the thermal conductivity of the matrix, a better agreement between the model and the experimental data can be achieved. This paper discusses the uncertainties related to the irradiation conditions and the data provided by the GERMINAL-Thermo-Calc calculation.

Effects of stretching velocity on double fractional Jeffreys fluids with rheological synergistic heat conductivity

Abstract Double fractional Jeffreys fluids are widely used in production and life. In this paper, the effects of stretching velocity on the flow and heat transfer of double fractional Jeffreys fluid are studied. Three types of stretching velocity are considered, i.e., (i) uniform velocity; (ii) acceleration; and (iii) deceleration. The rheological synergistic thermal conductivity model introduced to the energy equation is formulated based on experiments. The governing equations are solved by using a combination of the finite difference technique and the L1 algorithm. Results show that there is an inflection point on each velocity profile which divides the velocity field into two sections, convex (the elasticity plays a primary effect) and concave (the viscosity plays a primary effect). As the stretching velocity parameter increases, the thickness of the region where the elasticity plays a major role does not change in case (i), however, it reduces in case (ii) and grows in case (iii). We also found that, compared with uniform stretching, accelerated stretching can lead to higher heat transfer, while decelerated stretching causes less heat transfer. And for uniform velocity stretching, the stretching velocity parameter has little effect on the temperature field. In the case of accelerated stretching, increasing the stretching velocity parameter enhances heat transfer, however, for decelerated stretching, it weakens heat transfer. These results are instructive for industrial design.

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.

Finite element analysis of the impact of particles aggregation on the thermal conductivity of nanofluid under chemical reaction

A theoretical investigation is being conducted to determine the impact of nanoparticle aggregation (NPA) and thermal radiation on the radiant heat of nanofluids along with the vertical cylinder. An efficient thermal conductivity model for nanofluids is constructed based on the fractal distributive properties of nanoparticle aggregation. In view of two alternative methods of heat conduction, comprising particle aggregation and convection, the model is represented as a function of the fractal size and concentration. The contemporary models for nanofluid thermal conductivity include a significant role in nanoparticle aggregation. The impact of particle diffusion in the temperature field on aggregation and transport has yet to be investigated. The controlling boundary value problem is transformed into a system of nonlinear ordinary differential conditions, which are then solved numerically by utilizing the finite element technique with similarity transformations. The exceptional features of nanoparticles, such as high thermal conductivity, are highly significant in advancing nanotechnology, heat exchangers, material sciences, and electronics. The temperature field is observed higher in the presence of nanoparticle aggregation. The concentration gradient decreases the viscosity of water-based nanofluids, resulting in an increasing velocity. It is observed that the effect of nanoparticles aggregation on the boundary is descending by the including parameters causing an increment in heat transfer rate. The numerical approach to optimal meshing has reached convergence, and the accuracy of the presented results is supported by the fact that they are close to the results found in the relevant research.

Nonequilibrium Ionization Modeling of Petschek-type Shocks in Reconnecting Current Sheets in Solar Eruptions

Nonequilibrium ionization (NEI) is essentially required for astrophysical plasma diagnostics once the plasma status departs from the assumption of ionization equilibrium. In this work, we perform fast NEI calculations combined with magnetohydrodynamic (MHD) simulations and analyze the ionization properties of a Petschek-type magnetic reconnection current sheet during solar eruptions. Our simulation reveals Petschek-type slow-mode shocks in the classical Spitzer thermal conduction models and conduction flux-limitation situations. The results show that under-ionized features can be commonly found in shocked reconnection outflows and thermal halo regions outside the shocks. The departure from equilibrium ionization strongly depends on plasma density. In addition, this departure is sensitive to the observable target temperature: the high-temperature iron ions are strongly affected by the effects of NEI. The under-ionization also affects the synthetic SDO/AIA intensities, which indicates that the reconstructed hot reconnection current sheet structure may be significantly underestimated either for temperature or apparent width. We also perform an MHD-NEI analysis on the reconnection current sheet in the classical solar flare geometry. Finally, we show the potential reversal between the under-ionized and over-ionized states at the lower tip of reconnection current sheets where the downward outflow collides with closed magnetic loops, which can strongly affect multiple SDO/AIA band ratios along the reconnection current sheet.

Entropy analysis in single phase nanofluid in square enclosure under effectiveness of inclined magnetic field by executing finite element simulations

One of the important phenomena concerning with dynamical and thermal attributes of heat transferring liquids is the measure of randomness generated at molecular level. This randomness in the system is generated due to presence of multiple factors which includes extensive heat transfer, strong magnetic field and viscous diffusion. To control and minimize disorder ness the concept of entropy is taken into account. Minimization in entropy is valuable in optimization of design objectivity in engineering structures. In addition, it measures and controls exergy loss to generate highly efficient systems likes heat exchangers, heat pumps, power plants, nuclear reactors, air conditioners and so many. So, the prime objective of this work is to analyze entropy in square enclosure filled with water and containing Copper (Cu) particles. Convection in the considered physical domain is generated by providing uniform temperature at upper wall while keeping rest of boundaries cold. In view of velocity field distribution is concerned all the extremities of cavity are at no slip condition. Inclined magnetic field is also employed to measure change in entropy due to magnetization. Formulation of problem expressing thermophysical relation of inducted nanoparticles in manifested in the form dimensionless representation. Patel and Brinkman models for effective thermal conductivity and viscosity are opted to visualize their effectiveness in entropy change. Finite element computations are performed to simulate results showing the impact of flow controlling parameters on associated distributions. Three different types of entropy namely, magnetic, thermal and viscous are measured against different parameters. Quantity of interest like average heat flux coefficient is also measured. It is deduced from the analysis that by increasing nanoparticle volume fraction thermal entropy increases whereas viscous and magnetic entropy uplifts. In addition, it is noticed that by increasing Hartmann number entropy and velocity of fluid decrements. Uplift in temperature magnitude is observed against elevating values of Rayleigh number. It is concluded that employment of magnetic field will assist in controlling flow, thermal and irreversibility phenomenon.

Comparative analysis of the hydrothermal features of TiO2 water and ethylene glycol-based nanofluid transportation over a radially stretchable disk

This study focuses on the comprehensive analysis of the thermal characterization of an electrically conducting nanofluid flow containing TiO2 nanoparticles dissolved in two different common liquids (H2O and C2H6O2) and contained within a continuously extending disk. The heat and concentration formulation are modified by incorporating the standard interpretations of the Joule heating, energy source, dissipation, and modified activation energy with binary chemical reactions. The Darcy–Forchheimer addition is used to highlight the significance of porous media. The Brownian dispersion’s effects are clearly discernible in the current investigation. Furthermore, as a novelty, special thermophysical models of viscosity and thermal conductivity are included. The obtained differential formulations are tackled through the analytical procedure HAM. The veracity of the finding is verified through a numerical scheme (ND-solve technique). Using several graphs and charts, the perception trends of model factors are evaluated. The influence of and are estimated based on flow characteristics. The curve pattern for both nanofluids is declined by the increasing magnitude of and while thermal profile. The drag force and heat transmission rate are shown to optimize with as well as in the pictorial simulations produced from the existing model. The can also be strengthened by the presence of a high degree The outcomes are validated by previous studies and a good degree of consistency is revealed.

Fractal model for the effective thermal conductivity of microporous layer

Heat transfer in the fuel cells is generally limited by the effective thermal conductivity of the microporous layer (MPL). Due to the complexity of the microstructure and the difficulty of the test conditions, studies on the key parameters that affect the thermal conductivity of MPL is lacking. In this paper, we develop an analytical fractal model for the effective thermal conductivity of the MPL based on a lumped parametric model of the cube and a fractal particle chain model, and provide the contact ratio of the agglomerates using a 3D FIB-SEM reconstruction. The results indicate that the main factors affecting the thermal conductivity of MPL include the structural parameters, fractal dimension, and the thermal conductivity of the carbon particles and pores. The fractal characteristics of the MPL inhibit heat transfer rate and the pores act as a "thermal barrier wall" on the heat transfer path in the MPL. When the volume fraction of the MPL is 40 percent, the contact area ratio and fractal factor of the agglomerates are 0.351 and 0.84, respectively. In addition, this research will help to develop novel MPL structures with high thermal conductivity and improve simulation results for fuel cell temperatures.

Elastic Moduli: a Tool for Understanding Chemical Bonding and Thermal Transport in Thermoelectric Materials

AbstractThe elastic behavior of a material can be a powerful tool to decipher thermal transport. In thermoelectrics, measuring the elastic moduli—directly tied to sound velocity—is critical to understand trends in lattice thermal conductivity, as well as study bond anharmonicity and phase transitions, given the sensitivity of elastic moduli to the chemical bonding. In this review, we introduce the basics of elasticity and explain the origin of high‐temperature lattice softening from a bonding perspective. We then review elasticity data throughout classes of thermoelectrics, and explore trends in sound velocity, anharmonicity, and thermal conductivity. We reveal how experimental sound velocities can improve the accuracy of common thermal conductivity models and present a critical discussion of Grüneisen parameter estimates from elastic moduli. Readers will be equipped with tools to leverage elasticity measurements or calculations to accurately interpret thermal transport trends.

Elastic Moduli: a Tool for Understanding Chemical Bonding and Thermal Transport in Thermoelectric Materials.

The elastic behavior of a material can be a powerful tool to decipher thermal transport. In thermoelectrics, measuring the elastic moduli-directly tied to sound velocity-is critical to understand trends in lattice thermal conductivity, as well as study bond anharmonicity and phase transitions, given the sensitivity of elastic moduli to the chemical bonding. In this review, we introduce the basics of elasticity and explain the origin of high-temperature lattice softening from a bonding perspective. We then review elasticity data throughout classes of thermoelectrics, and explore trends in sound velocity, anharmonicity, and thermal conductivity. We reveal how experimental sound velocities can improve the accuracy of common thermal conductivity models and present a critical discussion of Grüneisen parameter estimates from elastic moduli. Readers will be equipped with tools to leverage elasticity measurements or calculations to accurately interpret thermal transport trends.

Solid and gas thermal conductivity models improvement and validation in various porous insulation materials

In the past few decades, significant efforts have been made to improve the theoretical understanding of thermal transport mechanisms in thermal insulation materials and push the thermal conductivity's lower limits. However, most works focused singularly on specific types of materials, and the models used for thermal conductivity predictions are diverse - a model that fits one material might not fit others. Here, we improve and unify the gas and solid thermal conductivity models for porous materials. Through experimental characterization of several different materials as well as literature data for other materials, these models are validated. We have also found that the pressure-dependent gas thermal conductivity of most materials can be well fitted by using one or two pore sizes without using a complex pore size distribution. With the refined models, we decompose the effective thermal conductivity of several thermal insulation materials into gas, solid, and radiation contributions. For cellular (polystyrene and polyurethane) foams, the relative contributions from air, solid, and radiation are 58–75%, 3–11%, 16–38%, respectively. For granular porous materials (polyurethane and silica in this work), the contributions from air, solid, and radiation are 45–66%, 34–46%, and 0–8%, respectively. This work is expected to provide guidance on the design and optimization of the next generation of thermal insulation materials, for example, through the effort of reducing gas conduction and radiation in foams and suppressing gas and solid conduction in aerogels.

Conceptualization of the micro research reactor cooled by heat pipes (MRR-HP), part-II: safety analyses

ABSTRACT The safety of the novel Micro Research Reactor cooled by Heat Pipes (MRR-HP) design is explored. This is achieved by developing a 3D thermal conduction model using STARCCM+ software, besides, coupling it with the 3D neutronics model for reactor dynamics. The MRR-HP has a unique design characteristic, which is the implementation of dual-sets of heat pipes (HPs) in the monolithic-block: Water-HPs for operation, and Potassium-HPs for accident/post-accident scenarios. Water-HPs cool the reactor effectively, allowing for maximum fuel temperature (K). However, water-HPs may suffer from: Loss-of-heat-Sink-Accident(LOSA), which may occur due to blackout, since it requires forced convective cooling in the condenser. Non-Condensable-Gases-Generation-Accident (NCGGA), due to radiolysis. These events cause significant melting in the monolithic-block and fuel rods after 3 and 6 hours, respectively. This paper proves the reliability of potassium-HPs as a passive countermeasure against LOSA and NCGGA, while natural convective cooling in the condenser is applied. Cold-state no-scram Reactivity-Insertion-Accident (RIA) scenarios with an insertion of 2.35$ are investigated, showing that no partial or significant melting occurs, due to the negative reactivity feedback of the MRR-HP. Besides, Potassium-HPs are essential in removing the decay heat, for warm-state RIA, after water-HPs dry out. This paper proves the robustness of the MRR-HP and encourages its utilization for remote operation.

Modeling of thermal conductivity for disordered carbon nanotube networks

Several theoretical models have been developed so far to predict the thermal conductivities of carbon nanotube (CNT) networks. However, these models overestimated the thermal conductivity significantly. In this paper, we claimed that a CNT network can be considered as a contact thermal resistance network. In the contact thermal resistance network, the temperature of an individual CNT is nonuniform and the intrinsic thermal resistance of CNTs can be ignored. Compared with the previous models, the model we proposed agrees well with the experimental results of single-walled CNT networks.

A thermal conductivity model for insulation materials considering the effect of moisture in cold regions

Insulation is an important material for energy conservation and frost heave reduction in cold regions. The thermal conductivity of the insulation materials is usually considered as a constant. However, their thermal performance degenerates due to the absorption of water. To describe the variations of thermal conductivities with water content, a thermal conductivity model for three-phase insulation material was proposed by considering the insulation material's porous and moisture absorption characteristics. A tortuosity correction was introduced to reflect the heat conduction path. Then, the measured results and the existed models were used to evaluate availability of the proposed model. Finally, the quantitative influence of the porosity, water content, and thermal conductivity of solid phase on the thermal conductivity of wet insulation materials was analyzed. The results show that there is close agreement between the predicted results of the new model and the measured ones, with the maximum relative error <15%. The model with tortuosity correction can effectively calculate the thermal conductivities of the insulation materials in a full range of porosity (from 0 to 1). The thermal conductivity decreases with the increase of porosity, but increases with the increase of water content. The solid phase's thermal conductivity has little influence on the thermal conductivity of the insulation materials. The study can provide an effective method to predict the thermal performance variation of the insulation material due to the effect of moisture content in cold regions.

Construction and application analysis of thermal conductivity model of deep thermal storage pore structure

In the process of geothermal energy exploitation and utilization, effective heat extraction, natural recovery and other key issues are affected and restricted by the thermal conductivity process of geothermal reservoirs, and the relevant thermal conductivity model research is not very comprehensive at present. In this paper, the deep heat storage in pore structure is divided into development zone, wave zone and original zone according to their thermal conductivity characteristics. Based on the representative elementary volume description analysis method, the thermal conductivity analysis model of pore structure of deep heat storage is established, including simplified thermal conductivity model and fine thermal conductivity model. Taking granite as an example, numerical calculation was carried out to analyze the effects of porosity, impurity content, water content and channel composition coefficient on heat storage and thermal conductivity. The model established in this paper lays a foundation for controlling thermal storage and thermal conductivity mechanism, accurately analyzing thermal conductivity characteristics, reserve estimation and mining dynamic changes.