Estimation Of Effective Thermal Conductivity Research Articles

Numerical estimation of effective thermal conductivity of reconstructed 2D structures of cement-based building materials

Cement-based building materials are fundamental for constructing modern buildings, and accurate determination of their thermal conductivity is crucial for calculating building energy consumption. In this study, random growth theory is used to reconstruct the two-dimensional pore structures of cement-based building materials in different forms. Furthermore, heat transfer simulations and calculations of effective thermal conductivity based on the finite element method are conducted for these pore structures. The effect of pore structure parameters on the effective thermal conductivity of cement-based building materials is investigated by this method. The results indicate that porosity, pore size, and the degree of pore regularity can all influence the effective thermal conductivity of cement-based building materials. At a porosity of 0.3, the fluctuations in the effective thermal conductivity caused by variations in pore sizes and degrees of pore regularity are most drastic.

Estimation of Effective Thermal Conductivity of Spherical and Ellipsoidal Shaped Randomly Packed Mono-Sized, Binary-Sized, and Poly-Dispersed Ceramic Pebble Beds

Estimation of Effective Thermal Conductivity of Spherical and Ellipsoidal Shaped Randomly Packed Mono-Sized, Binary-Sized, and Poly-Dispersed Ceramic Pebble Beds

Modeling on effective thermal conductivity of hydrate-bearing sediments considering the shape of sediment particle

The estimation of effective thermal conductivity (ETC) of hydrate-bearing sediment is of great importance for the exploitation of natural gas hydrate. At present, existing ETC models have been lack of consideration of the influences of sediment particle shape and stacking patterns. Thus, in this work, new models considering the shape (octahedral, plate-shaped, spindle-shaped and elongated) of sediment particles and stacking patterns were established and verified by a series of existed laboratory data. The verification results indicate that the octahedral model, plate-shape model and the average values of the four models have high accuracy in predicting ETC of hydrate-bearing sediments. The ETC of hydrate-bearing sediment under water-saturated state were calculated by the models in this work. The average ETC predicted by four models decreased from 2.87 W⋅m-1⋅K-1 to 1.47 W⋅m-1⋅K-1 with porosity increasing from 0.22 to 0.47 and decreased from 1.61 W⋅m-1⋅K-1 to 1.58 W⋅m-1⋅K-1 with hydrate saturation increasing from 0 to 1. Finally, the effects of porosity, hydrate saturation and intrinsic thermal conductivity of sediment particles on the ETC were discussed and analyzed. This modeling work could contribute to the understanding and prediction of the ETC of hydrate-bearing sediment with different shapes of sediment particles in the complex porous system.

Estimation of Effective Thermal Conductivity of Copper-Plated Carbon Fibers Reinforced Iron-Based Composites by 2D Image Analysis

Dies with high thermal conductivity (TC) can not only speed up heat transfer but also improve the production efficiency of parts and extend the life of the dies. Taking advantage of the high axial TC of carbon fibers (Cf), thermal channels are established in the composite. To protect Cf from being destroyed, Cf was electroless plated with Cu to form copper-plated Cf (Cf-Cu). Pores impede heat conduction, and the TC of the matrix is corrected by Bruggeman’s equation. Cf-Cu has high anisotropic, and its orientation can significantly affect the TC of iron-based composites. The mathematical equation between the orientation of Cf-Cu in the 3D model, the orientation of Cf-Cu on 2D cross-section, and the aspect ratio of an ellipse were obtained by Cf-Cu intersects with cross-section was determined by establishing a model of the orientation of Cf-Cu in 3D space. The simulated TC of the composite was calculated by 2D image analysis (finite element method). The effect of the orientation of Cf-Cu on the TC of composites with different Cf-Cu contents was investigated. When the volume fraction of Cf-Cu was 20%, the measured and simulated TC reached the maximum of 68.89 W m−1 K−1 and 71.02 W m−1 K−1, respectively. Before rolling, there is a significant difference between the simulated and measured TC. After rolling on the side surface of the rolling plane of the composite, both the simulated and measured TC on the rolling plane and its side surface show the same trend with the increasing of Cf-Cu content.

Estimation of effective thermal conductivity and heat transfer coefficient of lithium orthosilicate pebble bed in carbon dioxide–air medium

ABSTRACT Lithium orthosilicate has the highest absorption capacity among other materials used to capture carbon dioxide (CO2) at a higher temperature. To design a CO2 adsorption system consisting of lithium orthosilicate pebble bed, effective thermal conductivity and heat transfer coefficient data are necessary, and till date, these are not reported in the literature. In the present study, experiments were conducted to estimate the effective thermal conductivity and heat transfer coefficient of lithium orthosilicate pebble bed in CO2–air medium. Effects of CO2 concentration in air, bed temperature, and gas flowrate on the hydrodynamic as well as heat transfer properties of the pebble bed of lithium orthosilicate pebbles were also studied. The effective thermal conductivity and heat transfer coefficients were found in the range of 0.2–0.75 Wm−1K−1 and 14–63 Wm−2K−1, respectively.

Estimation of effective thermal conductivity in open-cell foam with hierarchical pore structure using lattice Boltzmann method

• Hierarchical pore structure is built in open-cell foam by an artificial algorithm. • Effective thermal conductivity (ETC) was calculated by lattice Boltzmann method. • Effects of hierarchical pore structure on ETC were investigated. • ETC correlation for open-cell foam with hierarchical pore structure is derived. Effective thermal conductivity in open-cell foam with hierarchical pore structure was estimated using lattice Boltzmann method. A new structure algorithm was proposed to reconstruct hierarchical pore structure in open-cell foam. In order to elucidate the heat transfer characteristics in hierarchical pore structure, the effect of structure parameters, namely the hierarchical pore size ratio ( d 2 / d 1 ), the hierarchical pore volume ratio ( V 2 / V 1 ), and temperature on the effective thermal conductivity was investigated. These results indicated that hierarchical pore structure is unfavorable to the effective thermal conductivity in open-cell foam for the heat conduction process. At high temperatures ( T ave =450-1650 K ), however, the effective thermal conductivity in hierarchical pore structure is higher than that in uniform pore structure considering heat radiation. Furthermore, for the heat conduction process, a correlation of the effective thermal conductivity related to open-cell foam with hierarchical pore structure was proposed and validated by available experimental data.

Estimation of thermal conductivity of short fiber composites

The present study deals with estimation of effective thermal conductivity of short fibers with polymer composites. This work proves enhancing the thermal conductivity property of composites can be achieved with the addition of short fibers (glass) whose thermal conductivity is more than the matrix material. In this work short glass fibers of 3 mm in length used and added in a proportions ranging of 0%, 2%, 4%, 6% by volume fraction and polyester resin as matrix material and have been prepared by simple hand Lay-up technique. The apparatus is used to find thermal conductivity is Lee’s Disc apparatus. And to validate the apparatus, experiment has been carried out to determine the thermal conductivity of existing material (glass) whose thermal conductivity is known. Thus experimentally determined values of the composite are then compared with the analytical models such as Rule of mixture (ROM), Maxwell model and Bruggeman model. Further finite element analysis (FEA) is used to determine effective thermal conductivity of the composite materials using commercially available software ABAQUS. From the obtained experimental results, numerical results and FEA results, it can be observed that there is a gradual increase in effective thermal conductivity of the composites with the addition of glass fiber content. This study also proves that FEA is a best method to validate and to compare with experimental results of the investigation. And with this unique increased thermal conductivity property and light weight composites can be used in many sophisticated applications.

Processing and characterization of TiO2 filled polymer composites

This paper reports on the research dealing with the processing and characterization of TiO 2 filled polymer composites. It also presents the test results in regard to the physical, mechanical and micro-structural characteristics of the epoxy and polypropylene composites filled with micro-sized TiO 2 particles. The effective thermal conductivity of polymer composites with uniformly distributed micro-sized particulates are estimated using a theoretical heat conduction model proposed previously by the authors and the correlation is validated for TiO 2 filled polymers through numerical analysis and experimentation. Some other important thermal characteristics, such as glass transition temperature (T g ) and coefficient of thermal expansion (CTE) of epoxy and polypropylene composites are also estimated. The effects of TiO 2 content on these properties of epoxy and polypropylene have been studied experimentally. The estimation of effective thermal conductivity of the composites using finite element method (FEM) and the proposed theoretical model is done and the results are validated by corresponding experimental results. The findings of this research suggest that incorporation of TiO 2 into epoxy and polypropylene leads to substantial improvement in thermal conductivity and glass transition temperature of the resins. At the same time, TiO 2 helps in lowering the coefficient of thermal expansion of such composites. This work further shows that the FEM serves as a good predictive tool for assessment of thermal conductivity of these composites. The theoretical correlation proposed in this work can serve as a very good empirical model for spherical inclusions to estimate the effective thermal conductivity of the composites within the percolation limit. With light weight and improved heat conduction capability, the TiO 2 filled polymer composites can be used for applications such as electronic packaging, encapsulations, communication devices, thermal interface material, printed circuit board substrates etc.

Stepwise DE/FE combined approach for estimating effective thermal conductivity of frozen spherical particulate media

A stepwise discrete element-finite element (DE/FE) combined numerical framework was proposed for efficiently estimating the effective thermal conductivity of spherical particulate media, which considers the thermal interaction of particle-to-particle and particle-to-pore filling material. The particulate composition was numerically modeled by the discrete element method (DEM), which was followed by a series of heat-transfer analyses formulated in the finite element method (FEM). In order to overcome difficulty of generating meshes in the FE modeling, a novel particle-size-reduction method was developed in the course of the mesh generation. The effective thermal conductivity of glass-bead specimens was measured at the porosity of 0.32, 0.35 and 0.38 under saturated and saturated-frozen conditions. The numerical framework resulted in the accurate estimation of effective thermal conductivity of glass-bead specimens in comparison with the laboratory measurements with the errors less than 5%. In addition, to verify the applicability of the proposed numerical framework to actual geologic materials, the effective thermal conductivity of Jumunjin standard sand specimens was considered at the porosity of 0.41, 0.43 and 0.45 under saturated and saturated-frozen conditions. The estimation errors in the numerical framework for the Jumunjin standard sand were less than 3%, which reveals the applicability of the proposed method.

Estimation of effective thermal conductivity of packed bed with internal heat generation

Test Blanket Module (TBM) of the fusion reactor has the vital role of removing heat generated from the fusion reactor along with the heat generated internally due to tritium breeding reaction. In the initial startup phase of fusion reactor, neutron flux has a climbing ramp nature and heat gets generated in discrete locations of TBM due to non-uniform nature of neutron irradiation. Thus, there is need to establish mathematical method to estimate Effective Thermal Conductivity (ETC) of packed bed with randomly scattered internal heat sources. Novel Induction Heating technique was used to simulate above mentioned conditions in packed bed of Li2TiO3 pebbles. An input-output FDM (Finite Difference Method) based model has been developed to estimate ETC of packed beds with non-uniform and discrete Internal Heat Generation (IHG). The inputs to the FDM based model are experimental results along with various operating and process parameters of the packed bed system under consideration. Also, an empirical correlation has been proposed to yield ETC of above mentioned packed bed systems valid for bed voidage of 0.44-0.47. The experimental and analytical methods used for this study are detailed in this paper.

Effect of convective heat transfer coefficient on estimation of effective thermal conductivity of two-phase material

Two-phase materials are involved in applications of day to day life, the reason being it is having discrete properties like firmness, required thermal conductivity, durability as well as good impact properties, etc. Thermal conductivity of two-phase material is a basic property to envision its evaluation in engineering. Distinct geometry for example cylinder, spherical, random size particles are being proposed by researchers for computation of effective thermal conductivity (ETC) of material like two-phase. This paper includes a two-dimensional two-phase system with hollow square geometry which is being considered for mathematically deriving an algebraic equation for computing ETC with the inclusion of the convective heat transfer coefficient. A unit cell approach is considered for deriving the equations. The obtained results are validated with the basic available models for distinctive types of two-phase materials. Hollow square model with Ψ = 0.3 gives approximate reasonable agreement for predicting ETC having a mean percentage error of 5.73% which is acceptable.

Analytical estimation of the effective thermal conductivity of a granular bed in a stagnant gas including the Smoluchowski effect

An analytical model including the Smoluchowski effect to estimate the effective thermal conductivity of a monosized granular assembly with interstitial stagnant gas from the microstructural parameters of the assembly, as well as the bulk properties of the granules and the gas is proposed in this paper. The discrete element method (DEM) is used for the generation and compaction of the granular assemblies. In the granular systems with interstitial gas, heat transfer occurs through the conduction between particles by solid overlap contacts and through the surrounding stagnant gas. Thermal radiation is included in the analytical model to study the influence of radiation on the thermal behavior of the assembly. The effective thermal conductivity is strongly influenced by the pressure of the gas as the conductivity of the gas decreases with decreasing pressure when confined in small gaps. This influence of the gas pressure is implemented in the analytical model. The effect of cyclic loading on the microstructural parameters is investigated through DEM simulations. Parametric correlations are developed to predict the values of microstructural parameters from experimentally measurable parameters so as to bypass any simulations for the estimation of effective thermal conductivity. A good agreement is observed between the analytical model and the experimental results for different assembly parameters and materials. The proposed analytical model can be used to get a first hand estimate of the effective thermal conductivity of a granular assembly to aid in the design process of such systems.

Quick estimate of effective thermal conductivity for fluid-saturated metal frame and prismatic cellular structures

Metal frame and prismatic cellular structures are promising candidates for compact heat exchangers and heat sinks with capability of carrying both mechanical and thermal loads. Useful formulas and corresponding laws were analytically derived for quickly estimating the individual effective thermal conductivity components of these structures. Such effective thermal conductivity estimates were made for metal foam structures, cubic cell structures, octet-truss structures, tetrakaidecahedron structures and various architectures of prismatic cellular honeycomb. The estimated values are found to agree well with existing experimental data and those obtained from exhaustive numerical computations. These formulas and laws enable us to design the structures with directionally controlled thermal conductivity, which is quite advantageous for maintaining an optimum temperature range and a uniform temperature distribution in thermal engineering applications such as in electric vehicles, batteries and HVAC industries.

Artificial neural network-based prediction of effective thermal conductivity of a granular bed in a gaseous environment

Artificial neural network (ANN), a machine learning technique, is employed to predict the effective thermal conductivity of granular assemblies in the presence of a stagnant gas. ANN is trained with the help of estimated thermal conductivities calculated through resistor network (RN) model. RN model considers the effect of the presence of stagnant gas and the gas pressure (Smoluchowski effect) for the calculation of effective thermal conductivity. Granular assemblies are generated and compacted through discrete element method (DEM). The ANN is trained to predict the effective thermal conductivity of a granular assembly for a set of measurable experimental parameters (stress and packing fraction) without requiring the knowledge of microstructural details (coordination numbers and overlaps) of the assembly. The predicted effective thermal conductivity values through ANN are in good agreement with the experimental results. Estimation of effective thermal conductivity through the trained ANN is much faster (few seconds compared to few hours required for DEM together with RN approach) with very good accuracy.

Estimation of effective thermal conductivity of packed beds incorporating effects of primary and secondary parameters

This paper presents a detailed description and experimental validation of a modified collocated unit cell model for the estimation of effective thermal conductivity of packed beds. The effect of primary and secondary parameters influencing the effective thermal conductivity viz. conductivity ratio (α) and concentration (ν) of the spherical particles (fraction of total volume occupied by the particles) of the packed bed, inter-particle gap, thermal contact conductance between the surfaces in contact, temperature, pressure and Knudsen number respectively are investigated in detail. Analytical expressions for effective thermal conductivity are derived for spatially periodic 2D square cylinder and in-line touching geometries based on the unit cell based thermal resistance approach. Using the developed model, the effective thermal conductivity of various packed materials in the conductivity ratio (ks/kf) range between 1–1000 and concentration (ν) 0 to 1 are predicted for varied temperature and pressure regimes. Predictions obtained from the developed model are compared against existing models available in literature in the pressure range 10−2 to 103 kPa at constant temperature. Furthermore, effective thermal conductivities of packed beds comprising of glass and ceramic beads are predicted using the developed model and compared with measured values obtained using the standard square guarded hot plate (SGHP) apparatus in the temperature range of 323–673 K. Both values are found to agree within ±12.24% and ±14.54% for glass and ceramic beads respectively.

Effect of interfacial thermal resistance and nanolayer on estimates of effective thermal conductivity of nanofluids

Colloidal suspensions of nanoparticles (nanofluids) are materials of interest for thermal engineering, because their heat transfer properties are typically enhanced as compared to the base fluid one. Effective medium theory provides popular models for estimating the overall thermal conductivity of nanofluids based on their composition. In this article, the accuracy of models based on the Bruggeman approximation is assessed. The sensitivity of these models to nanoscale interfacial phenomena, such as interfacial thermal resistance (Kapitza resistance) and fluid ordering around nanoparticles (nanolayer), is considered for a case study consisting of alumina nanoparticles suspended in water. While no significant differences are noticed for various thermal conductivity profiles in the nanolayer, a good agreement with experiments is observed with Kapitza resistance ≈10−9 m2K/W and sub-nanometer nanolayer thickness. These results confirm the classical nature of thermal conduction in nanofluids and highlight that future studies should rather focus on a better quantification of Kapitza resistance at nanoparticle-fluid interfaces, in order to allow bottom up estimates of their effective thermal conductivity.

Estimation of effective thermal conductivity in U-10Mo fuels with distributed xenon gas bubbles

We simulate the influence of distributed xenon gas bubbles on the effective thermal conductivity of irradiated U-10Mo fuel using a two-dimensional finite element method (FEM). The effective thermal conductivity of the inhomogeneous materials is estimated by solving the heat equation on a two-dimensional domain and estimating the mean temperature and heat flux. Bubble size distributions representative of both intra- and inter-granular fission gas bubbles are simulated. A distribution consistent with a gas bubble superlattice is compared to less-ordered bubble distributions in the intra-granular case. For inter-granular bubbles, the bubbles' spatial and size distribution was estimated from a two-dimensional scanning electron microscopy (SEM) image of fission gas bubbles that had collected on grain boundaries. The obtained results are compared with some theoretical models and experimental results. The results indicate that the pressure inside the bubbles has minimal influence on the overall thermal conductivity. The effect of krypton concentration is also negligible compared to pure xenon bubbles. Bubble arrangement is also insignificant unless a relatively wide bubble-free path through the metal exists. However, the area fraction of xenon bubbles has a significant impact on the overall thermal conductivity.

A detailed investigation on thermal and micro-structural properties of hexagonal boron nitride composites

This work reports on the processing and characterization of Boron Nitride filled polyester composites. It emphasizes the details of the test procedures and results in regard to the thermal and micro-structural characteristics of the polyester composites filled with micro-sized boron nitride (BN) with different concentrations. The estimation of effective thermal conductivity of the composites using the proposed theoretical models is done and the results are validated by corresponding experimental results. The effects of inclusion of BN on the effective thermal conductivity (keff), glass transition temperature (Tg), coefficient of thermal expansion (CTE) of composites are also studied. With the addition of BN, the thermal conductivity enhances. Again, the embedment of BN fillers results in lowering the CTE of the composites whereas the Tg of the composites is improved manifold. The other theoretical models as well as the proposed theoretical correlation can serve as very good empirical models for particulate fillers to estimate keff for composites within the percolation limit. Again, the polyester composites serve to be a better option than the epoxy composites as polyester tends to impart better mechanical and thermal properties. By enhancement of conduction capability the light weight and micro-sized BN filled polyester composites can be used for applications such as space flight and aviation industry,electronic encapsulations,engine parts etc. Similarly a hybrid composite is fabricated with another organic filler which showed even more distinctive properties suitable for particular applications

Effect of primary and secondary parameters on analytical estimation of effective thermal conductivity of two phase materials using unit cell approach

Most of the thermal design systems involve two phase materials and analysis of such systems requires detailed understanding of the thermal characteristics of the two phase material. This article aimed to develop geometry dependent unit cell approach model by considering the effects of all primary parameters (conductivity ratio and concentration) and secondary parameters (geometry, contact resistance, natural convection, Knudsen and radiation) for the estimation of effective thermal conductivity of two-phase materials. The analytical equations have been formulated based on isotherm approach for 2-D and 3-D spatially periodic medium. The developed models are validated with standard models and suited for all kind of operating conditions. The results have shown substantial improvement compared to the existing models and are in good agreement with the experimental data.

Estimation and optimisation of effective thermal conductivity for polymer matrix composites with hybrid inclusions

Composites with hybrid inclusions have shown remarkable thermal conductivity enhancement over composites with a single type of inclusion. However, to achieve maximum thermal conductivity enhancement, the optimum ratio of inclusions in the hybrid mix needs to be determined. In this communication, an effective medium theory based model for the estimation of effective thermal conductivity of composites with hybrid inclusions is presented. The proposed model accurately captures the synergic effect of hybrid inclusions within the composite and can be used to optimise the filler ratio in the hybrid mix. The model has been validated against several published experimental results and is found to be in good agreement with them. Parametric studies have also been carried out to study the effect of material and model parameters on the optimum ratio of hybrid inclusions.