Study of Microstructure-Based Effective Thermal Conductivity of Graphite Foam

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Y. Chai ◽  
X. H. Yang ◽  
M. Zhao ◽  
Z. Y. Chen ◽  
X. Z. Meng ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Effective Thermal Conductivity ◽  
Thermophysical Properties ◽  
Heat Exchangers ◽  
Geometric Model ◽  
Three Dimensional ◽  
High Specific Surface Area ◽  
Simplified Model ◽  
Graphite Foam

As a relatively new type of functional material, porous graphite foam exhibits unique thermophysical properties. It possesses the advantages of low density, high specific surface area, and high bulk thermal conductivity and could be used as the core component of compact, lightweight, and efficient heat exchangers. Effective thermal conductivity serves one of the key thermophysical properties of foam-based heat exchangers. The complex three-dimensional topology and interstitial fluids significantly affect the heat conduction in the porous structure, reflecting a topologically based effective thermal conductivity. This paper presents a novel geometric model for representing the microstructure of graphite foams with simplifications and modifications made on the realistic pore structure, where the complex surfaces and tortuous ligaments were converted into a simplified geometry with cylindrical ligaments connected between cuboid nodes. The multiple-layer method was used to divide the proposed geometry into solvable areas, and the series–parallel relation was used to derive the analytical model for the effective thermal conductivity. To explore heat conduction mechanisms at the pore scale, direct numerical simulation was also conducted on the realistic geometric model. Achieving good agreement with experimental data, the simplified geometric model was validated. The numerically simulated conductivity followed the simplified model prediction that the two geometries are equivalent from thermal aspect. It validates further that the simplified model is capable of reflecting the internal microstructure of graphite foam, which would benefit the understandings of the thermophysical mechanisms of pore-scaled heat conduction and microstructures of graphite foam.

Study of Micro-Structure Based Effective Thermal Conductivity of Graphite Foam

2016 ◽  
Author(s):  
Yue Chai ◽  
Xiaohu Yang ◽  
Xiangzhao Meng ◽  
Qunli Zhang ◽  
Liwen Jin
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Effective Thermal Conductivity ◽  
Analytical Model ◽  
Geometric Model ◽  
Three Dimensional ◽  
Heat Sinks ◽  
High Porosity ◽  
Geometry Model ◽  
Graphite Foam

As a new type of functional material, porous graphite foam exhibits unique thermal physical properties and geometric characteristics in heat transfer applications. It has the advantages of low density, high specific surface area, high porosity and high bulk thermal conductivity, which can be used as the core component of small, lightweight, compact and efficient heat sinks. Effective thermal conductivity serves one of the key thermophysical properties for foam-cored heat sinks. The complex three-dimensional topology and interstitial fluids significantly affect the heat conduction through such kind of porous structures, reflecting a topologically based effective thermal conductivity. This paper presents a novel geometric model for representing the microstructure of graphite foams, with simplifications and modifications made on the actual pore structure of graphite foam. For calculation simplicity, we convert the realized geometry consisting of complex surfaces and tortuous ligaments into a simplified geometry with circular ligaments joined at cuboid nodes, on the basis of the volume equivalency rule. The multiple-layer method is used to divide the proposed geometry into solvable areas and the series-parallel relations are used to derive the analytical model for effective thermal conductivity. To physically explore the heat conduction mechanisms at pore scale, direction numerical simulations were conducted on the reconstructed geometric model. Achieving good agreement with experimental data, the present analytical model (based on the simplified geometry) is validated. Further, the numerically simulated conductivities follow the model prediction, favoring thermally that the two geometries are equal. The present geometry model is more realized and capable of reflecting the internal microstructure of graphite foam, which will benefit the understandings for the thermo-physical mechanisms of pore-scaled heat conduction and micro structures of graphite foam.

The Fractal Model of Heat Conduction of Graphite Foam

2006 ◽  
Author(s):  
Xinming Zhang ◽  
Qinghua Chen ◽  
Danling Zeng
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Porous Material ◽  
Effective Thermal Conductivity ◽  
Geometric Model ◽  
Influence Factors ◽  
Computational Procedure ◽  
Fractal Model ◽  
Geometric Transformation ◽  
Graphite Foam

Graphite foam is a new material for effective heat conduction, which possesses exceedingly good thermal physical properties, thus the investigation on it has absorbed wide attention of scientists and engineers. By using experimental method such a material was obtained in our lab, and the factors which influence the micro-structure of the material was preliminary discussed based on our experiments. However, the main focus of the present paper is placed on the determination of the effective thermal conductivity of the material. Firstly, in accordance with the microscopic structure of the material, a simplified geometric model was constructed. Based on it a heat conduction unit cell was proposed to calculate the effective thermal conductivity of the porous material. Then, a geometric transformation was carried out to transit the original simple model to the real fractal one. The effective thermal conductivity λ' and its averaged value λ'm for the bulk porous material were derived. Examples were provided to show the computational procedure and to confirm the availability of the method proposed. The influence factors on λm. in the fractal model were also discussed in detail.

Figure of Merit-Based Optimization Approach of Phase Change Material-based Composites for Portable Electronics Using Simplified Model

2021 ◽  
Author(s):  
Ayushman Singh ◽  
Srikanth Rangarajan ◽  
Leila Choobineh ◽  
Bahgat Sammakia
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Phase Change ◽  
Effective Thermal Conductivity ◽  
Phase Change Material ◽  
Figure Of Merit ◽  
Volume Fraction ◽  
Simplified Model ◽  
Transient Temperature ◽  
Change Material

Abstract This work presents an approach to optimally designing a composite with thermal conductivity enhancers (TCEs) infiltrated with phase change material (PCM) based on figure of merit (FOM) for thermal management of portable electronic devices. The FOM defines the balance between effective thermal conductivity and energy storage capacity. In present study, TCEs are in the form of a honeycomb structure. TCEs are often used in conjunction with PCM to enhance the conductivity of the composite medium. Under constrained composite volume, the higher volume fraction of TCEs improves the effective thermal conductivity of the composite, while it reduces the amount of latent heat storage simultaneously. The present work arrives at the optimal design of composite for electronic cooling by maximizing the FOM to resolve the stated trade-off. In this study, the total volume of the composite and the interfacial heat transfer area between the PCM and TCE are constrained for all design points. A benchmarked two-dimensional direct CFD model was employed to investigate the thermal performance of the PCM and TCE composite. Furthermore, assuming conduction-dominated heat transfer in the composite, a simplified effective numerical model that solves the single energy equation with the effective properties of the PCM and TCE has been developed. The effective thermal conductivity of the composite is obtained by minimizing the error between the transient temperature gradient of direct and simplified model by iteratively varying the effective thermal conductivity. The FOM is maximized to find the optimal volume fraction for the present design.

Comparison of effective thermal conductivity in closed-loop vertical ground heat exchangers

2011 ◽  
Vol 31 (17-18) ◽  
pp. 3669-3676 ◽  
Author(s):  
Chulho Lee ◽  
Moonseo Park ◽  
Sunhong Min ◽  
Shin-Hyung Kang ◽  
Byonghu Sohn ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Heat Exchangers ◽  
Closed Loop ◽  
Ground Heat Exchangers ◽  
Vertical Ground

Modeling Heat Conduction Across Thermal Interface Materials With Micro-Particles

2008 ◽  
Author(s):  
C. Channy Wong
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Composite Materials ◽  
Effective Thermal Conductivity ◽  
Thermal Interface Materials ◽  
Conduction Path ◽  
Micro Particles ◽  
Mechanical And Electrical Properties ◽  
Interface Materials ◽  
Composite Polymeric Material

Different types of fillers with high electrical and thermal conductivities, e.g. graphite and alumina, have been added to adhesive polymers to create composite materials with improved mechanical and electrical properties. Previous modeling efforts have found that it is relatively difficult to predict the effective thermal conductivity of a composite polymeric material when incorporated with large volume content of fillers. We have performed comprehensive computational analysis that models the thermal contacts between fillers. This unique setup can capture the critical heat conduction path to obtain the effective thermal conductivity of the composite materials. Results of these predictions and its comparison with experimental data will be presented in this paper.

scholarly journals Method of Averaging the Effective Thermal Conductivity Based on Thermal Response Tests of Borehole Heat Exchangers

Energies ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3737
Author(s):  
Aneta Sapińska-Śliwa ◽  
Tomasz Sliwa ◽  
Kazimierz Twardowski ◽  
Krzysztof Szymski ◽  
Andrzej Gonet ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Heat Exchanger ◽  
Effective Thermal Conductivity ◽  
Heat Exchangers ◽  
Thermal Response ◽  
Method Of Averaging ◽  
Thermal Response Test ◽  
Borehole Heat Exchanger ◽  
Measurement Results ◽  
Borehole Heat Exchangers

This work concerns borehole heat exchangers and their testing using apparatus for thermal response tests. In the theoretical part of the article, an equation was derived from the known equation of heat flow, on which the interpretation of the thermal response test was based. The practical part presents the results of several measurements taken in the AGH Laboratory of Geoenergetics. They were aimed at examining the potential heat exchange capacity between the heat carrier and rock mass. Measurement results in the form of graphs are shown in relation to the examined, briefly described wells. Result analysis made it possible to draw conclusions regarding the interpretation of the thermal response test. The method of averaging the measurement results was subjected to further study. The measuring apparatus recorded data at a frequency of one second, however such accuracy was too large to be analyzed efficiently. Therefore, an average of every 1 min, every 10 min, and every 60 min was proposed. The conclusions stemming from the differences in the values of effective thermal conductivity in the borehole heat exchanger, resulting from different data averaging, were described. In the case of three borehole heat exchangers, ground properties were identical. The effective thermal conductivity λeff was shown to depend on various borehole heat exchanger (BHE) designs, heat carrier flow geometry, and grout parameters. It is important to consider the position of the pipes relative to each other. As shown in the charts, the best (the highest) effective thermal conductivity λeff occurred in BHE-1 with a coaxial construction. At the same time, this value was closest to the theoretical value of thermal conductivity of rocks λ, determined on the basis of literature. The standard deviation and the coefficient of variation confirmed that the effective thermal conductivity λeff, calculated for different time intervals, showed little variation in value. The values of effective thermal conductivity λeff for each time interval for the same borehole exchanger were similar in value. The lowest values of effective thermal conductivity λeff most often appeared for analysis with averaging every 60 min, and the highest—for analysis with averaging every 1 min. For safety reasons, when designing (number of BHEs), safer values should be taken for analysis, i.e., lower, averaging every 60 min.

Effect of radial heat conduction on effective thermal conductivity of carbon nanotube bundles

2018 ◽  
Vol 61 (12) ◽  
pp. 1959-1966 ◽  
Author(s):  
JianLi Wang ◽  
YaMei Song ◽  
YuFeng Zhang ◽  
YuHan Hu ◽  
Hang Yin ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Carbon Nanotube ◽  
Effective Thermal Conductivity ◽  
Nanotube Bundles ◽  
Radial Heat

Numerical Simulation of Heat and Mass Transfer in Metal Hydride Hydrogen Accumulators of Different Complex Designs

2010 ◽  
Author(s):  
Dmitriy Lazarev ◽  
Valeriy Artemov ◽  
Georgiy Yankov ◽  
Konstantin Minko
Keyword(s):  
Thermal Conductivity ◽  
Mass Transfer ◽  
Effective Thermal Conductivity ◽  
Heat And Mass Transfer ◽  
Metal Hydride ◽  
Solid Phase ◽  
Three Dimensional ◽  
Calculated Data ◽  
Sorption Rate ◽  
Gas Admixtures

A three-dimensional mathematical model of unsteady heat and mass transfer in porous hydrogen-absorbing media, accounting for presence of “passive” gas admixtures, is developed. New technique for evaluation of effective thermal conductivity of porous medium, which consists of microparticles, is suggested. Effect of “passive” gas admixtures on heat and mass transfer and sorption rate in metal hydride reactor is analyzed. It is shown that decrease of effective thermal conductivity and partial hydrogen pressure under decrease of hydrogen concentration effect on the hydrogen sorption rate considerably. It is disclosed that an intensive 3D natural convection takes place in a gas volume of reactor under certain conditions. Numerical analysis of heat and mass transfer in metal-hydride reactor of hydrogen accumulation systems was done. Sorption of hydrogen in cylindrical reactors with external cooling and central supply of hydrogen are analyzed including reactors with finned active volume and tube-shell reactor with external and internal cooling cartridge matrix. Unsteady three dimensional temperature and concentration fields in solid phase are presented. Integral curves representing the dynamic of sorption and desorption are calculated. Data on efficiency of considered reactors are presented and compared.

scholarly journals Third-order thermo-mechanical properties for packs of Platonic solids using statistical micromechanics

2015 ◽  
Vol 471 (2177) ◽  
pp. 20150060 ◽  
Author(s):  
A. Gillman ◽  
G. Amadio ◽  
K. Matouš ◽  
T. L. Jackson
Keyword(s):  
Mechanical Properties ◽  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Three Dimensional ◽  
Adaptive Methods ◽  
Shape Effect ◽  
Third Order ◽  
Recent Letter ◽  
Penetrable Spheres ◽  
First Time

Obtaining an accurate higher order statistical description of heterogeneous materials and using this information to predict effective material behaviour with high fidelity has remained an outstanding problem for many years. In a recent letter, Gillman & Matouš (2014 Phys. Lett. A 378, 3070–3073. ()) accurately evaluated the three-point microstructural parameter that arises in third-order theories and predicted with high accuracy the effective thermal conductivity of highly packed material systems. Expanding this work here, we predict for the first time effective thermo-mechanical properties of granular Platonic solid packs using third-order statistical micromechanics. Systems of impenetrable and penetrable spheres are considered to verify adaptive methods for computing n -point probability functions directly from three-dimensional microstructures, and excellent agreement is shown with simulation. Moreover, a significant shape effect is discovered for the effective thermal conductivity of highly packed composites, whereas a moderate shape effect is exhibited for the elastic constants.

State of the art of thermal characterization of electronic components using computational fluid dynamic tools

2017 ◽  
Vol 27 (11) ◽  
pp. 2433-2450 ◽  
Author(s):  
Eric Monier-Vinard ◽  
Brice Rogie ◽  
Valentin Bissuel ◽  
Najib Laraqi ◽  
Olivier Daniel ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Numerical Model ◽  
Effective Thermal Conductivity ◽  
Three Dimensional ◽  
Computation Time ◽  
Printed Wiring Board ◽  
Electronic Components ◽  
Content Type ◽  
Three Dimensional Representation ◽  
Wiring Board

Purpose Latest Computational Fluid Dynamics (CFDs) tools allow modeling more finely the conjugate thermo-fluidic behavior of a single electronic component mounted on a Printed Wiring Board (PWB). A realistic three-dimensional representation of a large set of electric copper traces of its composite structure is henceforth achievable. The purpose of this study is to confront the predictions of the fully detailed numerical model of an electronic board to a set of experiment results to assess their relevance. Design/methodology/approach The present study focuses on the case of a Ball Grid Array (BGA) package of 208 solder balls that connect the component electronic chip to the Printed Wiring Board. Its complete geometrical definition has to be coupled with a realistic board layers layout and a fine description of their numerous copper traces to appropriately predict the way the heat is spread throughout that multi-layer composite structure. The numerical model computations were conducted on four CFD software then compare to experiment results. The component thermal metrics for single-chip packages are based on the standard promoted by the Joint Electron Device Engineering Council (JEDEC), named JESD-51. The agreement of the numerical predictions and measurements has been done for free and forced convection. Findings The present work shows that the numerical model error is lower than 2 per cent for various convective boundary conditions. Moreover, the establishment of realistic numerical models of electronic components permits to properly apprehend multi-physics design issues, such as joule heating effect in copper traces. Moreover, the practical modeling assumptions, such as effective thermal conductivity calculation, used since decades, for characterizing the thermal performances of an electronic component were tested and appeared to be tricky. A new approach based on an effective thermal conductivity matrix is investigated to reduce computation time. The obtained numerical results highlight a good agreement with experimental data. Research limitations/implications The study highlights that the board three-dimensional modeling is mandatory to properly match the set of experiment results. The conventional approach based on a single homogenous layer using effective thermal conductivity calculation has to be banned. Practical implications The thermal design of complex electronic components is henceforth under increasing control. For instance, the impact of gold wire-bonds can now be investigated. The three-dimensional geometry of sophisticated packages, such as in BGA family, can be imported with all its internal details as well as those of its associated test board to build a realistic numerical model. The establishment of behavioral models such as DELPHI Compact Thermal Models can be performed on a consistent three-dimensional representation with the aim to minimize computation time. Originality/value The study highlights that multi-layer copper trace plane discretization could be used to strongly reduce computation time while conserving a high accuracy level.

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