Formula For Thermal Conductivity Research Articles

Study on thermal conductivity of improved soil under different freezing temperatures.

Based on the influence of moisture content, dry density and temperature (≦ 0°C) on the thermal conductivity of lime-modified red clay, the thermal conductivity was measured by transient hot wire method. A total of 125 data were obtained and the evolution law of thermal conductivity with influencing factors was analyzed. The fitting formula of thermal conductivity of lime-modified red clay and a variety of intelligent prediction models were established and compared with previous empirical formulas. The results show that the thermal conductivity of lime-modified red clay increases linearly with water content and dry density. The change of thermal conductivity with temperature is divided into three stages. In the first stage, the thermal conductivity increases slowly with the decrease of temperature in the temperature range of-2°Cto 0°C. In the second stage, in the temperature range of-5°Cto (-2)°C, the thermal conductivity increases rapidly with the decrease of temperature. In the third stage, in the range of-10°Cto (-5)°C, the thermal conductivity changes little with the decrease of temperature, and the fitting curve tends to be stable. The fitting formula model and various intelligent prediction models can realize the accurate prediction of the thermal conductivity of lime-improved soil. Using RMSE (Root Mean Square Error) and MAPE (Mean Absolute Percentage Error) to evaluate the model, it is found that the GBDT decision tree model has the best prediction effect, the RMSE value of the predicted value is 0.084, and the MAPE value is 4.1%. The previous empirical models have poor prediction effect on the thermal conductivity of improved red clay. The intelligent prediction models such as GBDT decision tree with strong universality and high prediction accuracy are recommended to predict the thermal conductivity of soil.

Linking Thermal Conductivity and Self-Diffusion Coefficient with a Simple Dimensionless Calorimetric Parameter for Saturated Liquids

Thermal conductivity and self-diffusion coefficients for saturated liquids were linked with a simple dimensionless calorimetric parameter (DCP) in this work. Similar to the DCP approach with the viscosity proposed in our previous research study, it was found that by scaling the thermal conductivity and self-diffusion coefficient, linear relations of these two transport properties with the DCP could be exhibited. On this basis, two-parameter formulas for calculating the thermal conductivity and self-diffusion coefficient through the DCP were put forward. Meanwhile, the slope and intercept of the linear formula for thermal conductivity were found to be one-dimensionally related, while the slopes of the self-diffusion coefficient equations fell in the narrow interval of −1.64 ± 0.21, revealing a quasi-universality for various nonassociation fluids. The new DCP-based model for calculating thermal conductivity was evaluated and validated with the experimental data of 21 pure fluids representing different molecular structures. The average absolute deviation and the maximum absolute deviation between the linked thermal conductivities and the literature data were within 5.04 and 8.30%, respectively. This work provided novel methods for calculating the thermal conductivity and self-diffusion coefficient of saturated liquids.

Flexural Toughness Test and Inversion Research on a Thermal Conductivity Formula on Steel Fiber-Reinforced Concrete Components Post-Fire.

Steel fibers are widely used because they can effectively improve the tensile, compressive and flexural properties of concrete structures. The selection of steel fiber dosage and aspect ratio at high temperature has an important impact on the flexural toughness of concrete components post-fire. In this paper, discussions are made on the simulated fire test in compliance with the ISO 834 standard to study the steel fiber-reinforced concrete (SFRC) components post-fire. The research reveals the influence of two commonly used steel fiber aspect ratios (50, 70) and steel fiber dosages (30 kg/m3, 40 kg/m3, 45 kg/m3) on the changes of the internal temperature field, the initial crack flexural strength and the flexural toughness of the SFRC components under a single-side fire. Moreover, combined with the four-point flexural test of the SFRC components post fire, the research also describes the damage of high temperatures to the flexural toughness of SFRC components, and suggests a calculation formula for SFRC thermal conductivity by way of the numerical inversion method. The results of this study have verified that the incorporation of steel fiber into concrete helps to reduce its internal thermal stress difference and improve the crack resistance and fire resistance of the concrete. Moreover, under high temperature conditions, the concrete component added with the steel fiber in an aspect ratio of 70 and a dosage of 45 kg/m3 increased their initial crack flexural strength by 56.8%, higher than that of plain concrete components, and the loss of equivalent flexural strength and flexural toughness of SFRC post fire was only 45.2% and 13.6%, respectively. The proposed calculation formula of thermal conductivity can provide a reference for a numerical simulation study of the temperature field of SFRC components in a high temperature environment.

Experimental Study on Thermal Conductivity of Organic-Rich Soils under Thawed and Frozen States

Thermal properties are important for featuring the water-heat transfer capacity of soil. They are also key to many processes in earth sciences, such as the land surface processes and ecological and geoenvironmental dynamics and their changes in permafrost regions. With loose and porous structures, the organic matter layer in soil strata substantially influences soil thermal conductivity. So far, thermal conductivity of mineral soils has been explored extensively and in depth, but there are only limited studies on that of organic soils. In this study, influences of soil temperature, soil moisture saturation (SMS), and soil organic matter (SOM) content on soil thermal conductivity were analyzed on the basis of laboratory experiments on the silt-organic soil mixtures of varied mixing ratios. Results show that soil thermal conductivity declines slowly with the lowering temperatures from 10 to 0°C; however, it increases and finally stabilizes when temperature further lowers from 0 to -10°C. It is important to note that thermal conductivity peaks in the temperature range of -2~0°C (silty and organic-poor soil) and -5~0°C (organic-rich soil), possibly due to phase changes of ice/water in warm permafrost. Under both thawed and frozen states, soil thermal conductivity is positively related with SMS. However, with rising SOM content, the growth rate of soil thermal conductivity with SMS slows gradually. Given the same SMS, soil thermal conductivity declines exponentially with increasing SOM content. Based on the experimental and theoretical analyses, a new empirical computational formula of soil thermal conductivity is established by taking into account of the SOM content, SMS, and soil temperature. The results may help better parameterize in simulating and predicting land surface processes and for optimizing frozen soil engineering designs and provide theoretical bases for exploring the dynamic mechanisms of environmental changes in cold regions under a changing climate.

Influence of Lubricant Physical Property Models on Thermal Elastohydrodynamic Lubrication Solutions

The influence of changes in the physical properties of lubricants on thermal elastohydrodynamic lubrication solutions is examined numerically at the nominal line contact for both Newtonian and non-Newtonian fluids. Specific heat, thermal conductivity, density, and viscosity were considered as functions of temperature and pressure for polyalphaolefin, polyglycol, and mineral oils. It was found that, when considering the physical and rheological properties of lubricants individually, the solutions were over- or under-estimated. The thermal conductivity formula mostly corresponds to solutions for both fluids. The effects of changes in the physical properties of non-Newtonian lubricants were shown to be less than those of Newtonian lubricants. Near-identical qualitative behaviors occurred regardless of oil type under these lubricant models.

Finite-size effects on thermal property predictions of molten salts

It is of great importance to obtain the accurate thermal properties of molten salts over the entire operating temperature for system design in concentrated solar power or other thermal storage systems. In this work, we explore size effects on density, viscosity and thermal conductivity predictions of molten nitrate and chloride salts by molecular dynamics. Equilibrium molecular dynamics and reverse nonequilibrium molecular dynamics methods are applied to calculate thermal conductivities of NaNO3 and NaCl regarding different simulation cell sizes at the specific temperatures to study size effects on thermal conductivity predictions of melts. The results show that the size effects are neglected on density and viscosity predictions while a linear positive relationship between 1/λ and 1/Lz is found in the reverse nonequilibrium molecular dynamics method. Through analyzing the phenomenon from a view of microstructure, phonon-phonon-scattering rates are found to be the key factors. The influences of temperature and particle species on size effects are further discussed. Subsequently, appropriate simulation cell sizes are selected for NaNO3, KNO3 and Hitec salt, and the calculated thermal properties are in good agreement with the experimental values. The mean relative errors and fitting formula for density, thermal conductivity, and viscosity for the three salts are also obtained.

Thermodynamic and acoustic behaviors of prefabricated composite wall panel

The thermodynamic and acoustic behaviors of prefabricated composite wall panel were investigated based on the heat transmission and acoustic principles. Moreover, the thermal conductivity formula of the prefabricated composite wall panel based on thermal conductivity equivalence method was proposed by deducing the solving process of thermodynamic parameters. Changes of sound reduction index and sound pressure level (SPL) of the prefabricated composite wall panel with sound frequency range were analyzed by experimental test and numerical simulation. The research results demonstrate that the thermal conductivity of wall panel can be calculated accurately by the thermal conductivity equivalence method. The calculation model of sound reduction index can be used to determine the sound reduction index in the middle and low frequency ranges. The designed wall panel has satisfying heat insulation and sound insulation with a heat transfer coefficient of 0.55 W/m2·K and about the weighted standard acoustic pressure difference (DnT,w) of 42 dB.

A Ubiquitous Thermal Conductivity Formula for Liquids, Polymer Glass, and Amorphous Solids*This work is supported by the National Key R&D Program of China (Grant No. 2017YFB0406004), the National Natural Science Foundation of China (Grant No. 11890703). JH and JL are supported by the National Science Foundation of USA (Award No. CBET-1943813) and the Faculty Research and Professional Development Fund at

The microscopic mechanism of thermal transport in liquids and amorphous solids has been an outstanding problem for a long time. There have been several approaches to explain the thermal conductivities in these systems, for example, Bridgman’s formula for simple liquids, the concept of the minimum thermal conductivity for amorphous solids, and the thermal resistance network model for amorphous polymers. Here, we present a ubiquitous formula to calculate the thermal conductivities of liquids and amorphous solids in a unified way, and compare it with previous ones. The calculated thermal conductivities using this formula without fitting parameters are in excellent agreement with the experimental data. Our formula not only provides a detailed microscopic mechanism of heat transfer in these systems, but also resolves the discrepancies between existing formulae and experimental data.

Influence of wavy enclosure and nanoparticles on heat release rate of PCM considering numerical study

The main goal of this attempt is achieving higher rate of solidification with employing two passive techniques. Mixing the based PCM with nanoparticles and considering the wavy shape for walls were two techniques were incorporated. Copper oxide nanomaterial was dispersed in to water with concentration of 0.04 which let us employing homogeneous model. Based on this fact, empirical formulations were utilized for predicting features of NEPCM and various shapes of nano sized particles were considered in thermal conductivity formula. Due to inherent of solidification phenomena, buoyancy can be ignored and pure conduction mechanism with involving the transient source term of solid faction was solved by means of FEM. During the process, the configurations of grids change and the regions around the solid front have finer grid. This opportunity offers outputs with greater accuracy. As shape factor rises, the greater conduction mode can be obtained and similar behavior can be achieved with considering greater amplitude of wavy walls. The best case in term of discharging time is that of m = 5.7 and A = 0.5 in which 156.17 s required to finish the process. Greater amount of shape factor can decrease the time about 5.91% and 5.89% when A = 0.5 and 0.1, respectively. Also, with growth of A, time reduces about 22.66% which indicate better solidification rate. Inclusion of nanoparticles can improve the discharging rate about 17.9%.

Effect of gradation on the thermal conductivities of backfill materials of ground source heat pump based on loess and iron tailings

The addition of iron tailings to backfill soil of ground source heat pump (GSHP) systems can efficiently improve backfill thermal conductivity. The engineering properties of iron tailings and soil are significantly affected by particle gradation. Therefore, the effect of gradation on the thermal conductivity of backfill material composed of iron tailing and loess was investigated. The thermal conductivities of natural (bad) gradation and manmade (good) gradation materials with different iron tailings content, water content, and dry density were tested and analyzed. Results showed that the thermal conductivity of manmade gradation materials was usually higher than that of natural gradation materials. For the same water content and dry density, the influence of gradation on thermal conductivity decreased with increasing water content. For saturated material, the maximum difference in thermal conductivity caused by gradation ranged from 39.1% to 8.6% compared to dry material. The maximum increases in thermal conductivity caused by gradation were approximately 0.12–0.24 W/(m·K). The maximum increase percentage of thermal conductivity increases with decreasing water content, and the value range is 28.4–60.5%. The empirical formula for thermal conductivity was established based on the water saturation. The influence of gradation on formula parameters is analyzed. Finally, suggestions for gradation selection in practical applications of GSHP backfill materials are given.

Lie group method for analyzing the generalized heat transfer mathematical model for Lake Tahoe

The one-dimensional time-dependent heat transfer equation in a vertical direction is introduced in terms of a general formula of density and thermal conductivity. One-parameter Lie symmetry group transformation is applied to determine the suitable forms of water density and thermal conductivity based on experimental measurements. The general equation is investigated again using Lie group analysis after substitution by the two possible forms of water density and thermal conductivity from the first part. The obtained partial differential equation is solved numerically using explicit 4th and 5th Runge–Kutta formula or analytically if it is possible assuming the physical parameters of Lake Tahoe in the Sierra Nevada of the United States. The temperature distribution across the lake depth from each case is illustrated graphically to indicate the thermal stratification phenomenon of lakes.

Comparison and validation of the lattice thermal conductivity formulas used in equilibrium molecular dynamics simulations for binary systems

The Green-Kubo relations have been widely utilized in equilibrium molecular dynamics (MD) simulations to evaluate the lattice thermal conductivity (TC) of condensed matter. In previous studies, however, three different formulas have been used to calculate the TC. In the present study, focusing on binary systems, we investigate differences among the three TC formulas to evaluate the appropriateness of each formula and estimate possible errors. First, by using theoretical means, the differences are explicitly expressed in terms of material properties such as the Maxwell-Stefan (MS) diffusion coefficient, the partial specific enthalpy, and the reduced heat of transport. Subsequently, MD simulations are conducted to quantify the differences over wide temperature ranges in Li2O and TiO2 model systems including crystal, amorphous and liquid phases. The results show that although the three TC formulas give virtually identical results at low temperatures, one TC formula may cause significant errors at high temperatures when the MS diffusion coefficient reaches approximately 10−6–10−7 cm2/s. These large diffusion coefficients usually occur in liquid phases, often occur in amorphous and super-ionic crystal phases, and may occur in defective systems. Finally, a simple equation to roughly estimate the error in this TC formula is derived.

The physical mechanism of extremely low thermal conductivity of BiCuTeO and BiCuSeO revealed by inelastic neutron and Raman spectroscopy

Layered structure BiCuSeO-based compounds have extremely low thermal conductivity about ∼0.5–0.8 W/m·K, and the corresponding physical origin has been extensively studied by the first-principles calculations. Here we experimentally revealed the physical mechanism of extremely low thermal conductivity in BiCuSeO and BiCuTeO through inelastic neutron and Raman scattering spectroscopy. Generalized phonon density of states (PDOS) characterized by inelastic neutron scattering reveals that the average acoustic-phonon velocities of BiCuSeO and BiCuTeO are as low as 2104 and 1547 m/s, respectively, which are lower than most of normal materials (∼3000 m/s), and strong anharmonic effect in BiCuSeO and BiCuTeO. Strongly anharmonic effect is also verified by the large Grüneisen constant of specific optical-phonon mode of BiCuSeO and BiCuTeO (∼6.7 in BiCuTeO). The calculated thermal conductivities of BiCuSeO and BiCuTeO by phenomenological thermal conductivity formula, under approximation of the relaxation-time as minimum quasi-particle lifetime of optical-phonon mode, are close to experimental values. Our work sheds more light on the physical mechanism of extremely low thermal conductivity in these compounds.

单原子层薄膜热传导性质的晶格动力学研究(I)——声子线宽和热传导系数公式

单原子层薄膜热传导性质的晶格动力学研究(I)——声子线宽和热传导系数公式

Finite-size effect of the thermal conductivity in one dimensional chain

Finite-size effect of the thermal conductivity in one dimensional chain is theoretically investigated with a phenomenological model. Boundary temperature dropping and the spectrum-dependent linear temperature profile within the chain are given self-consistently at high temperatures. A general formula of thermal conductivity is presented and a good agreement with the molecular dynamics simulations is obtained. It is found that while decreases with increasing of 1/L monotonically, the well known linear dependence of thermal resistance 1/κ on the reciprocal length 1/L of systems is, however, valid only in two limit cases of and/or .

Thermal conductivity of aluminum foam based on 3‐D stochastic sphere model

AbstractTo accurately characterize the geometric structure of closed‐cell aluminum foam, a three‐dimensional stochastic sphere model with adjustable porosity and pore size was established, and its thermal conductivity was studied by numerical simulation. A closed‐cell aluminum foam heat conduction experiment was designed to verify the accuracy of the model. Using this model, the thermal conductivity of aluminum foam with different pore sizes and porosity was calculated, and the variation of thermal conductivity was studied. The results show that with the same porosity, the thermal conductivity increases linearly with the pore size. With the same pore size, the thermal conductivity decreases linearly with the porosity. The equivalent thermal conductivity decreases with the increase of porosity. According to the simulation results, the formula of equivalent thermal conductivity of aluminum foam is .

New formula for predication thermal conductivity for homologous alkanes series function of carbon number

The main aim of this paper is to establish a correlation for prediction the thermal conductivity of n-alkanes within a give temperature range for homologous n-alkanes series from CH4 to C30H62. The predicted thermal conductivity values depend on the temperature and carbon number for each alkanes component. This paper describes a method of predicting the thermal conductivity of any alkanes between the temperature range, based on a measurement of the thermal conductivity. Where prediction are based on lower temperature measurements, where the accuracy is generally better then 3.1% for 178 data points. Useful predictions can also be made from any temperature measurements for most alkanes, but with reduced accuracy. This method permits alkanes to be used in situations where the thermal conductivity is important without having to make (or find) direct measurements over the entire temperature range of interest. Recommended thermal conductivity values are presented for 30 components.

Multiscale modeling and theoretical prediction for the thermal conductivity of porous plain-woven carbonized silica/phenolic composites

As a typical phenolic resin-based ablative material, silica/phenolic composites are extensively used in the aerospace industry. However, thermodynamic properties of carbonized plain-woven composites formed during ablation process are rarely studied. Toward this end, we propose a multiscale prediction model to investigate the effective thermal conductivity of porous plain-woven carbonized silica/phenolic composites by combining finite element analysis with existing two-phase composite models. A general approach is presented to compute the effective thermal conductivity with varying structural parameters. First, to consider effect of pores in phenolic resin matrix, the porous model is established to calculate the effective thermal conductivity of matrix with different porosities and pore morphologies. Then, heat transfer simulations are conducted on the multiscale model, including the yarn scale in the axial and transverse directions and the woven composite scale in the in-plane and out-of-plane directions. Empirical formulas for effective thermal conductivity are obtained, which comprehensively considers the factors of matrix porosity, fiber volume fraction, and temperature.

Numerical simulation for thermal conductivity of nanograin within three dimensions

In order to improve the accuracy of simulation, the lattice Boltzmann method was adopted to get the thermal conductivities of 3-D nanograins. For the wide application, the length of nanograins axis is between 1 nm to 9 nm, and the diameter ratio of gap to spherical segment is 0.2 to 0.9, 30 sets of results of numerical simulation were taken. Correlations were fitted from the results of numerical simulation by multiple linear regression analysis. Then, in the range of temperature between 294 K to 700 K, the temperature value was taken every 50 K. Then final fitted formula of thermal conductivity for nanograins was got by the binomial fitting method. The results of fitted formula agree well with the numerical results. The results show that the thermal conductivities decrease with the diameter of nanograins reducing within the 3-D spherical segment when the diameter ratio, ?, of the gap to spherical segment is fixed. The effective thermal conductivities would increase with the ratio, ?, increasing when the spherical segment diameter is fixed and the ratio is lower than 0.6. The thermal conductivities would remarkably decrease when the ratio is larger 0.6.

Boiling on fins with wire screen of variable effective conductivity

The high scale of integration of modern equipment used for medical, military and other purposes puts heavy demands as regards the removal of great heat fluxes. This can be achieved only in exchangers that apply the phase change phenomena. Among many methods to improve boiling heat transfer, the wire mesh covering demonstrates some advantages due to the possibilities of designing the desired microstructure parameters, availability on the market, and low cost. The wire mesh microstucture with specified geometrical parameters produces anisotropy in conductivity. The different arrangement of the mesh layers relative to the direction of the heat flux is a cause of the change of temperature distribution within the layer. The consequence is a respective change in the discharge conditions of the gas phase and liquid feed. The experiments were conducted on fins covered with a single layer of copper mesh with lumen of 38 % and boiling FC-72 at ambient pressure. Compared with the smooth surface, the wire mesh structures yield an increase in the heat transfer rate at boiling. It is also shown that nucleate boiling is initiated at lower wall superheat. Formulas for longitudinal and perpendicular thermal conductivity are given for different mesh structure arrangements.