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.

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.

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 Fully dissipative relativistic lattice Boltzmann method in two dimensions

2018 ◽  
Vol 172 ◽  
pp. 318-331 ◽  
Author(s):  
Rodrigo C.V. Coelho ◽  
Miller Mendoza ◽  
Mauro M. Doria ◽  
Hans J. Herrmann
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Two Dimensions ◽  
Boltzmann Method

A phase-field-based lattice Boltzmann method for moving contact line problems on curved stationary boundaries in two dimensions

2019 ◽  
Vol 30 (06) ◽  
pp. 1950044
Author(s):  
Weifeng Zhao
Keyword(s):  
Boundary Conditions ◽  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Two Dimensions ◽  
Curved Boundaries ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Boltzmann Method

In this work, we propose a phase-field-based lattice Boltzmann method to simulate moving contact line (MCL) problems on curved boundaries. The key point of this method is to implement the boundary conditions on curved solid boundaries. Specifically, we use our recently proposed single-node scheme for the no-slip boundary condition and a new scheme is constructed to deal with the wetting boundary conditions (WBCs). In particular, three kinds of WBCs are implemented: two wetting conditions derived from the wall free energy and a characteristic MCL model based on geometry considerations. The method is validated with several MCL problems and numerical results show that the proposed method has utility for all the three WBCs on both straight and curved boundaries.

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