Effective Thermal Conductivity in Multidimensional Bodies

1994 ◽  
Vol 116 (1) ◽  
pp. 17-27 ◽  
Author(s):  
Y.-M. Lee ◽  
A. Haji-Sheikh ◽  
L. S. Fletcher ◽  
G. P. Peterson
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Spherical Inclusion ◽  
Applied Pressure ◽  
Three Dimensional ◽  
Thermal Conductance ◽  
Surface Conductance ◽  
Three Dimensional Model ◽  
Elliptical Inclusion ◽  
Aspect Ratios

The effective thermal conductivity in three-dimensional bodies is studied analytically. The three-dimensional model considers a spherical inclusion centrally located in a cubical body. Later, the spherical inclusion is replaced by an elliptical inclusion to study the biased effect or directionality of heat flux. Two different aspect ratios for the elliptical inclusion are considered. It is shown that the effective thermal conductivity is influenced by surface conductance in addition to geometric factors. Also, the effective thermal conductivity is measured for different samples. Spherical inclusions are placed inside cylindrical bodies for convenience of the experiments. The data show that cracks induced by applied pressure and thermal stress during the experiment reduce the thermal conductance. Using the measured effective thermal conductivity data, an analytical procedure is used to calculate the average values of the apparent contact conductance.

scholarly journals A Multiscale Investigation on the Thermal Transport in Polydimethylsiloxane Nanocomposites: Graphene vs Borophene

2021 ◽  
Author(s):  
Alessandro Di Pierro ◽  
Bohayra Mortazavi ◽  
Hamidreza Noori ◽  
Timon Rabczuk ◽  
Alberto Fina
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Effective Thermal Conductivity ◽  
Volume Content ◽  
Thermal Conductance ◽  
Single Layer ◽  
Interfacial Thermal Conductance ◽  
Aspect Ratios ◽  
The Matrix ◽  
Dynamics Simulations

Graphene and borophene are highly attractive two-dimensional materials with outstanding physical properties. In this study we employed a combined atomistic continuum multiscale modeling to explore the effective thermal conductivity of polymers nanocomposites made of PDMS polymer as the matrix and graphene and borophene as nanofillers. We first conduct classical molecular dynamics simulations to investigate the interfacial thermal conductance between graphene/PDMS and borophene/PDMS interfaces. Acquired results confirm that the interfacial thermal conductance between nanosheets and polymer increases from the single-layer to multilayered nanosheets and finally converges. The data provided by the atomistic simulations were then used in the finite element method simulations to evaluate the effective thermal conductivity of polymer nanocomposites at continuum level. We explore the effects of nanofillers type, their volume content, geometry aspect ratio and thickness on the nanocomposites effective thermal conductivity. As a very interesting finding, we show that borophene nanosheets, despite almost two orders of magnitude lower thermal conductivity than graphene, can yield very close enhancement in the effective thermal conductivity in comparison with graphene, particularly for low volume content and small aspect ratios and thicknesses. We conclude that for the polymer-based nanocomposites, significant improvement in the thermal conductivity can be reached by improving the bonding between the fillers and polymer or in another word enhancing the thermal conductance at the interface. By taking into account the high electrical conductivity of borophene, our results suggest borophene nanosheets as promising nanofillers to simultaneously enhance the polymers thermal and electrical conductivity.

scholarly journals A Multiscale Investigation on the Thermal Transport in Polydimethylsiloxane Nanocomposites: Graphene vs. Borophene

Nanomaterials ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1252
Author(s):  
Alessandro Di Pierro ◽  
Bohayra Mortazavi ◽  
Hamidreza Noori ◽  
Timon Rabczuk ◽  
Alberto Fina
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Effective Thermal Conductivity ◽  
Polymer Nanocomposites ◽  
Volume Content ◽  
Thermal Conductance ◽  
Single Layer ◽  
Md Simulations ◽  
Aspect Ratios ◽  
Wide Range

Graphene and borophene are highly attractive two-dimensional materials with outstanding physical properties. In this study we employed combined atomistic continuum multi-scale modeling to explore the effective thermal conductivity of polymer nanocomposites made of polydimethylsiloxane (PDMS) polymer as the matrix and graphene and borophene as nanofillers. PDMS is a versatile polymer due to its chemical inertia, flexibility and a wide range of properties that can be tuned during synthesis. We first conducted classical Molecular Dynamics (MD) simulations to calculate the thermal conductance at the interfaces between graphene and PDMS and between borophene and PDMS. Acquired results confirm that the interfacial thermal conductance between nanosheets and polymer increases from the single-layer to multilayered nanosheets and finally converges, in the case of graphene, to about 30 MWm−2 K−1 and, for borophene, up to 33 MWm−2 K−1. The data provided by the atomistic simulations were then used in the Finite Element Method (FEM) simulations to evaluate the effective thermal conductivity of polymer nanocomposites at the continuum level. We explored the effects of nanofiller type, volume content, geometry aspect ratio and thickness on the nanocomposite effective thermal conductivity. As a very interesting finding, we found that borophene nanosheets, despite having almost two orders of magnitude lower thermal conductivity than graphene, can yield very close enhancement in the effective thermal conductivity in comparison with graphene, particularly for low volume content and small aspect ratios and thicknesses. We conclude that, for the polymer-based nanocomposites, significant improvement in the thermal conductivity can be reached by improving the bonding between the fillers and polymer, or in other words, by enhancing the thermal conductance at the interface. By taking into account the high electrical conductivity of borophene, our results suggest borophene nanosheets as promising nanofillers to simultaneously enhance the polymers’ thermal and electrical conductivity.

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.

Qualitative Equivalence Between Electrical Percolation Threshold and Effective Thermal Conductivity in Polymer/Carbon Nanocomposites

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Majid Baniassadi ◽  
Akbar Ghazavizadeh ◽  
Yves Rémond ◽  
Said Ahzi ◽  
David Ruch ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Percolation Threshold ◽  
Effective Thermal Conductivity ◽  
Electrical Percolation ◽  
Aspect Ratios ◽  
Wide Range ◽  
Statistical Continuum ◽  
Electrical Percolation Threshold

In this study, a qualitative equivalence between the electrical percolation threshold and the effective thermal conductivity of composites filled with cylindrical nanofillers has been recognized. The two properties are qualitatively compared on a wide range of aspect ratios, from thin nanoplatelets to long nanotubes. Statistical continuum theory of strong-contrast is utilized to estimate the thermal conductivity of this type of heterogeneous medium, while the percolation threshold is simultaneously evaluated using the Monte Carlo simulations. Statistical two-point probability distribution functions are used as microstructure descriptors for implementing the statistical continuum approach. Monte Carlo simulations are carried out for calculating the two-point correlation functions of computer generated microstructures. Finally, the similarities between the effective conductivity properties and percolation threshold are discussed.

Evaporation, Condensation, and Flow in an Idealized Micro Heat Pipe

2002 ◽  
Author(s):  
Jin Zhang ◽  
Harris Wong
Keyword(s):  
Thermal Conductivity ◽  
Heat Pipe ◽  
Effective Thermal Conductivity ◽  
Three Dimensional ◽  
Heat Pipes ◽  
Rigorous Analysis ◽  
Evaporation And Condensation ◽  
Micro Heat Pipe ◽  
Complicated Geometry ◽  
Micro Heat Pipes

Micro heat pipes have been used in cooling micro electronic components. However their effective thermal conductivity is low compared with that of conventional heat pipes. Due to the complexity of the coupled heat and mass transport, and to the complicated three-dimensional bubble geometry inside micro heat pipes, there is a lack of rigorous analysis. As a result, the relatively low effective thermal conductivity remains unexplained. We have conceptualized an idealized micro heat pipe that eliminates the complicated geometry, but retains the essential physics. Given the simplified geometry, many effects can be studied, such as thermocapillary flow, and evaporation and condensation physics. In this talk, we will present the flow field induced by evaporation.

Computational Evaluation of Effective Conductivity of Particulate Composites with Imperfect Interfaces

2009 ◽  
Vol 631-632 ◽  
pp. 35-40
Author(s):  
M. Zhang ◽  
Peng Cheng Zhai ◽  
Qing Jie Zhang
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Effective Properties ◽  
Effective Conductivity ◽  
Three Dimensional ◽  
Particulate Composite ◽  
Imperfect Interface ◽  
Particulate Composites ◽  
Imperfect Interfaces ◽  
Volume Fractions

This paper is aimed to numerically evaluate the effective thermal conductivity of randomly distributed spherical particle composite with imperfect interface between the constituents. A numerical homogenization technique based on the finite element method (FEM) with representative volume element (RVE) was used to evaluate the effective properties with periodic boundary conditions. Modified random sequential adsorption algorithm (RSA) is applied to generate the three dimensional RVE models of randomly distributed spheres of identical size with the volume fractions up to 50%. Several investigations have been conducted to estimate the influence of the imperfect interfaces on the effective conductivity of particulate composite. Numerical results reveal that for the given composite, due to the existence of an interfacial thermal barrier resistance, the effective thermal conductivity depends not only on the volume fractions of the particle but on the particle size.

Effective Thermal Conductivity of Lithium Ion Battery Electrodes Employing Fully Resolved Simulations for Use in Volume Averaged Models

2013 ◽  
Author(s):  
Ajay Vadakkepatt ◽  
Bradley L. Trembacki ◽  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Volume Fraction ◽  
Effective Properties ◽  
Three Dimensional ◽  
Lithium Ion ◽  
Volume Averaging ◽  
Porous Electrodes ◽  
Multiphase Materials ◽  
Averaged Models

Simulations of lithium ion batteries on a cell level are usually performed with volume averaging methods that employ effective transport properties. Bruggeman’s model, which is widely used to determine these effective properties, is solely based on the volume fraction of these porous electrodes. However, other factors like the topology and microstructure of electrodes also play a crucial role in determining effective properties. In this paper, a general derivation of the effective thermal conductivity of multiphase materials, which can be correlated with these factors, is derived using the volume averaging technique. For demonstration, three-dimensional microstructures of various porous materials are reconstructed from scanned images. These images are used to generate fully-resolved finite volume meshes representing the various constituents. The resulting mesh is then employed for numerical analysis of thermal transport, results from which are used for correlating the effective thermal conductivity with various parameters describing the microstructure. It is shown that commonly used power law exponents in the Bruggeman model for effective thermal conductivity must be recalibrated to fit the effective thermal conductivity computed from these detailed simulations.

Laminar Natural Convection in a Discretely Heated Cavity: I—Assessment of Three-Dimensional Effects

1995 ◽  
Vol 117 (4) ◽  
pp. 902-909 ◽  
Author(s):  
T. J. Heindel ◽  
S. Ramadhyani ◽  
F. P. Incropera
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Companion Paper ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Nusselt Numbers ◽  
Aspect Ratios ◽  
Laminar Natural Convection

Two and three-dimensional calculations have been performed for laminar natural convection induced by a 3 × 3 array of discrete heat sources flush-mounted to one vertical wall of a rectangular cavity whose opposite wall was isothermally cooled. Edge effects predicted by the three-dimensional model yielded local and average Nusselt numbers that exceeded those obtained from the two-dimensional model, as well as average surface temperatures that were smaller than the two-dimensional predictions. For heater aspect ratios Ahtr ≲ 3, average Nusselt numbers increased with decreasing Ahtr. However, for Ahtr ≳ 3, the two and three-dimensional predictions were within 5 percent of each other and results were approximately independent of Ahtr. In a companion paper (Heindel et al., 1995a), predictions are compared with experimental results and heat transfer correlations are developed.

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