Efficient numerical model for effective thermal conductivity of concrete with aggregates of different morphologies and imperfect interfaces

2022 ◽  
Vol 185 ◽  
pp. 122358
Author(s):  
Weiwen Quan ◽  
Xianyong Ma ◽  
Xinkai Li ◽  
Zejiao Dong
Keyword(s):  
Thermal Conductivity ◽  
Numerical Model ◽  
Effective Thermal Conductivity ◽  
Imperfect Interfaces

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.

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.

Numerical determination of pressure-dependent effective thermal conductivity in Berea sandstone

2021 ◽  
Author(s):  
Mirko Siegert ◽  
Marcel Gurris ◽  
Erik Hans Saenger
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Numerical Model ◽  
Effective Thermal Conductivity ◽  
Rock Sample ◽  
Rock Physics ◽  
Contact Phase ◽  
Data Set ◽  
Computed Tomography Images ◽  
Thermal Conductivities

<p>Within the scope of the present work, the pressure-dependent effective thermal conductivity of rock samples is simulated. Our workflow can be assigned to the field of digital rock physics. In a first step, a 3D micro-CT scan of a rock sample is taken. Subsequently, the resulting greyscale images are analysed and segmented depending on the occurring phases. Based on this data set, a computational mesh is created and the corresponding thermal conductivities are assigned to each phase. Finally the numerical simulations can be carried out.<br>For the representation of the pressure dependency we use the approach proposed by Saenger [1]. By making use of the watershed algorithm, boundaries between the individual grains of the rock sample are detected and assigned to an artificial contact phase. In the course of several simulations, the thermal conductivity of the contact phase is continuously increased. Starting with the thermal conductivity of the pore phase and ending with the thermal conductivity of the grain phase. A linear correlation is used to match the thermal conductivity of the contact phase with the pressure of a given experimental data set. This enables a direct comparison between simulation and measurement.<br>In a further step, the numerical model is calibrated to optimise the agreement between experimental data and simulation results. In particular, starting from two calibration points of the experimental data set, an adjustment of the thermal conductivities in the numerical model is carried out. While the thermal conductivity of the pore phase is held constant during the whole calibration process, thermal conductivities of the grain and contact phase are adjusted.</p><p>References<br>[1] Saenger et al. 2016. Analysis of high-resolution X-ray computed tomography images of Bentheim sandstone under elevated confining pressures. Geophysical Prospecting, 64(4), 848–859.</p><p> </p>

scholarly journals Temperature and Pressure Dependence of the Effective Thermal Conductivity of Geomaterials: Numerical Investigation by the Immersed Interface Method

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Duc Phi Do ◽  
Dashnor Hoxha
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Numerical Procedure ◽  
Numerical Approach ◽  
Diffusion Problem ◽  
Immersed Interface Method ◽  
Immersed Interface ◽  
Imperfect Interfaces ◽  
Linear Behavior ◽  
Temperature And Pressure

The present work aims to study the nonlinear effective thermal conductivity of heterogeneous composite-like geomaterials by using a numerical approach based on the immersed interface method (IIM). This method is particularly efficient at solving the diffusion problem in domains containing inner boundaries in the form of perfect or imperfect interfaces between constituents. In this paper, this numerical procedure is extended in the framework of non linear behavior of constituents and interfaces. The performance of the developed tool is then demonstrated through the studies of temperature- and pressure-dependent effective thermal conductivity of geomaterials with imperfect interfaces.

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