Sub-Continuum Heat Conduction in Electronics Using the Lattice Boltzmann Method

2003 ◽  
Author(s):  
Sartaj S. Ghai ◽  
Rodrigo A. Escobar ◽  
Myung S. Jhon ◽  
Cristina H. Amon
Keyword(s):  
Heat Conduction ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Internal Heat ◽  
Numerical Data ◽  
Computational Effort ◽  
Silicon On Insulator ◽  
Boltzmann Transport ◽  
Boltzmann Method

The lattice Boltzmann method (LBM) is used to examine multi-length scale, confined heat conduction problems in one dimension for which sub-continuum effects are important. This paper describes the implementation of the method and its application to electronic devices. A silicon-on-insulator device with internal heat generation is used as a case study to illustrate the advantages of the LBM. We compare our results with various hierarchical equations of heat transfer such as Fourier, Cattaneo, and Boltzmann transport equations, as well as with experimental and numerical data from the literature. Our results provide excellent agreement with other methodologies, at a far less computational effort.

Nanoscale Heat Transfer Modeling in Solids: Data Storage and Electronic Devices

2003 ◽  
Author(s):  
Sartaj S. Ghai ◽  
Myung S. Jhon ◽  
Cristina H. Amon ◽  
Yiao-Tee Hsia
Keyword(s):  
Heat Transfer ◽  
Data Storage ◽  
Electronic Devices ◽  
Internal Heat ◽  
Numerical Data ◽  
Computational Effort ◽  
Two Dimensions ◽  
Boltzmann Transport ◽  
Boltzmann Method ◽  
Good Agreement

Lattice Boltzmann method (LBM), is used to examine multi-length scale, confined heat conduction phenomena in solids for which sub-continuum regime is important. This paper describes the implementation of the method and its application to cases pertinent to data storage and electronic devices. Thin solid films with internal heat generation and with temperature difference across the boundaries are used as case studies to illustrate the benefits of the LBM. We compare our results with various hierarchical equations of heat transfer such as Fourier, Cattaneo, and Boltzmann transport equations, as well as with experimental and numerical data from the literature. Our results exhibit a good agreement with other methodologies in one and two dimensions, at a much lower computational effort.

Estimation of an Appropriate Lattice Structure for Phonon Transport Using Lattice Boltzmann Method

2013 ◽  
Author(s):  
Ankur Chattopadhyay ◽  
Arvind Pattamatta
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Energy Transport ◽  
Lattice Structure ◽  
Detailed Comparison ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Boltzmann Method

Heat transport at nanoscales departs substantially from the well established classical laws governing the physical processes at continuum level. The Fourier Law of heat conduction cannot be applied at sub-continuum level due to its inability in modeling non-equilibrium energy transport. Therefore one must resort to a rigorous solution to the Boltzmann Transport Equation (BTE) in the realm of nanoscale transport regime. Some recent studies show that a relatively inexpensive and accurate way to predict the behavior of sub continuum energy transport in solids is via the discrete representation of the BTE referred to as the Lattice Boltzmann method (LBM). Although quite a few numerical simulations involving LBM have been exercised in the literature, there has been no clear demonstration of the accuracy of LBM over BTE; also there exists an ambiguity over employing the right lattice configurations describing phonon transport. In the present study, the Lattice Boltzmann Method has been implemented to study phonon transport in miniaturized devices. The initial part of the study focuses upon a detailed comparison of the LBM model with that of BTE for one dimensional heat transfer involving multiple length and time scales. The second objective of the present investigation is to evaluate different lattice structures such as D1Q2, D1Q3, D2Q5, D2Q8, D2Q9 etc. for 1-D and 2-D heat conduction. In order to reduce the modeling complexity, gray model assumption based on Debye approximation is adopted throughout the analysis. Results unveil that the accuracy of solution increases as the number of lattice directions taken into account are incremented from D2Q5 to D2Q9. A substantial increase in solution time with finer directional resolutions necessitates an optimum lattice. A novel lattice dimension ‘Mod D2Q5’ has been suggested and its performance is also compared with its compatriots. It is also demonstrated that the inclusion of the center point within a particular lattice structure can play a significant role in the prediction of thermal conductivity in the continuum level. However, as the size of the device comes down to allow high Knudsen numbers, in the limiting case of ballistic phonon transport, the choice of lattice seems to have negligible effect on thermal conductivity.

Application of the Lattice-Boltzmann Method to Sub-Continuum Heat Conduction

2002 ◽  
Author(s):  
Wei Zhang ◽  
T. S. Fisher
Keyword(s):  
Heat Conduction ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Close Agreement ◽  
Computational Effort ◽  
Two Dimensions ◽  
Analysis Tool ◽  
Two Dimensional ◽  
One Dimensional ◽  
Boltzmann Method

The Lattice Boltzmann Method (LBM) is introduced in this paper as a method to simulate heat conduction across broad length scales in which continuum and sub-continuum effects exist. The paper describes the implementation of the method in both one and two dimensions. Results are presented for cases involving problems with existing solutions and show close agreement with both continuum and subcontinuum solutions of one-dimensional heat transfer through thin films. Results for a two-dimensional continuum problem agree with a known solution to within one percent. These results, combined with relative small computational effort, indicate that the LBM is a useful analysis tool for simulation of multiscale heat conduction.

A Finite Difference Lattice Boltzmann Method to Simulate Multidimensional Subcontinuum Heat Conduction

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Cheng Chen ◽  
James Geer ◽  
Bahgat Sammakia
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Boltzmann Transport ◽  
Conduction Model ◽  
Total Energy Density ◽  
Diffusion Term ◽  
Boltzmann Method ◽  
The Impact

In this paper, a lattice Boltzmann method (LBM)-based model is developed to simulate the subcontinuum behavior of multidimensional heat conduction in solids. Based on a previous study (Chen et al., 2014, “Sub-Continuum Thermal Modeling Using Diffusion in the Lattice Boltzmann Transport Equation,” Int. J. Heat Mass Transfer, 79, pp. 666–675), phonon energy transport is separated to a ballistic part and a diffusive part, with phonon equilibrium assumed at boundaries. Steady-state temperature/total energy density solutions from continuum scales to ballistic scales are considered. A refined LBM-based numerical approach is applied to a two-dimensional simplified transistor model proposed by (Sinha et al. 2006, “Non-Equilibrium Phonon Distributions in Sub-100 nm Silicon Transistors,” ASME J. Heat Transfer, 128(7), pp. 638–647), and the results are compared with the Fourier-based heat conduction model. The three-dimensional (3D) LBM model is also developed and verified at both the ballistic and continuous limits. The impact of film thickness on the cross-plane and in-plane thermal conductivities is analyzed, and a new model of the supplementary diffusion term is proposed. Predictions based on the finalized model are compared with the existing in-plane thermal conductivity measurements and cross-plane thermal conductivity molecular dynamics (MD) results.

scholarly journals Lattice Boltzmann method simulation of the gas heat conduction of nanoporous material

2020 ◽  
Vol 24 (6 Part A) ◽  
pp. 3749-3756
Author(s):  
Ya Han ◽  
Shuai Li ◽  
Hai-Dong Liu ◽  
Weipeng Cui
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Lattice Boltzmann Method ◽  
Knudsen Number ◽  
Lattice Boltzmann ◽  
Size Effects ◽  
Temperature Jump ◽  
Boundary Scattering ◽  
Nanoporous Material ◽  
Boltzmann Method

In order to deeply investigate the gas heat conduction of nanoporous aerogel, a model of gas heat conduction was established based on microstructure of aerogel. Lattice Boltzmann method was used to simulate the temperature distribution and gas thermal conductivity at different size, and the size effects of gas heat conduction have had been obtained under micro-scale conditions. It can be concluded that the temperature jump on the boundary was not obvious and the thermal conductivity remained basically constant when the value of Knudsen number was less than 0.01; as the value of Knudsen number increased from 0.01 to 0.1, there was a clear temperature jump on the boundary and the thermal conductivity tended to decrease and the effect of boundary scattering increased drastically, as the value of Knudsen number was more than 0.1, the temperature jump increased significantly on the boundary, furtherly, the thermal conductivity decreased dramatically, and the size effects were significantly.

scholarly journals Modelling of transient heat transport in metal films using the interval lattice Boltzmann method

2016 ◽  
Vol 64 (3) ◽  
pp. 599-606 ◽  
Author(s):  
A. Piasecka Belkhayat ◽  
A. Korczak
Keyword(s):  
Lattice Boltzmann Method ◽  
Heat Transport ◽  
Lattice Boltzmann ◽  
Relaxation Times ◽  
Metal Films ◽  
Thin Metal ◽  
Heating Process ◽  
Boltzmann Transport ◽  
Thin Metal Films ◽  
Boltzmann Method

Abstract In the paper a description of heat transfer in one-dimensional crystalline solids is presented. The lattice Boltzmann method based on Boltzmann transport equation is used to simulate the nanoscale heat transport in thin metal films. The coupled lattice Boltzmann equations for electrons and phonons are applied to analyze the heating process of thin metal films via laser pulse. Such approach in which the parameters appearing in the problem analyzed are treated as constant values is widely used, but in the paper the interval values of relaxation times and electron-phonon coupling factor are taken into account. The problem formulated has been solved by means of the interval lattice Boltzmann method using the rules of directed interval arithmetic. In the final part of the paper the results of numerical computations are shown.

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