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.

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.

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.

Thin Film Phonon Heat Conduction by the Dispersion Lattice Boltzmann Method

2007 ◽  
Author(s):  
Rodrigo A. Escobar ◽  
Cristina H. Amon ◽  
Amador M. Guzma´n
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Heat Conduction ◽  
Lattice Boltzmann Method ◽  
Thermal Energy ◽  
Lattice Boltzmann ◽  
Energy Transport ◽  
Time Dependent ◽  
Boltzmann Method ◽  
Thermal Energy Transport

Numerical simulations of time-dependent thermal energy transport in semiconductor thin films are performed using the Lattice Boltzmann Method applied to phonon transport. The discrete Lattice Boltzmann Method is derived from the continuous Boltzmann transport equation assuming nonlinear, frequency-dependent phonon dispersion for acoustic and optical phonons. Results indicate that the heat conduction in silicon thin films displays a transition from diffusive to ballistic energy transport as the characteristic length of the system becomes comparable to the phonon mean free path, and that the thermal energy transport process is characterized by the propagation of multiple, superimposed phonon waves. The methodology is used to characterize the time-dependent temperature profiles inside films of decreasing thickness. Thickness-dependent thermal conductivity values are computed based on steady-state temperature distributions obtained from the numerical models. It is found that reducing feature size into the subcontinuum regime decreases the thermal conductivity when compared to bulk values, at a higher rate than what was displayed by the Debye-based gray Lattice Boltzmann Method.

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.

Thin Film Phonon Heat Conduction by the Dispersion Lattice Boltzmann Method

2008 ◽  
Vol 130 (9) ◽  
Author(s):  
Rodrigo A. Escobar ◽  
Cristina H. Amon
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Heat Conduction ◽  
Lattice Boltzmann Method ◽  
Thermal Energy ◽  
Lattice Boltzmann ◽  
Energy Transport ◽  
Time Dependent ◽  
Boltzmann Method ◽  
Thermal Energy Transport

Numerical simulations of time-dependent thermal energy transport in semiconductor thin films are performed using the lattice Boltzmann method applied to phonon transport. The discrete lattice Boltzmann Method is derived from the continuous Boltzmann transport equation assuming nonlinear, frequency-dependent phonon dispersion for acoustic and optical phonons. Results indicate that the heat conduction in silicon thin films displays a transition from diffusive to ballistic energy transport as the characteristic length of the system becomes comparable to the phonon mean free path and that the thermal energy transport process is characterized by the propagation of multiple superimposed phonon waves. The methodology is used to characterize the time-dependent temperature profiles inside films of decreasing thickness. Thickness-dependent thermal conductivity values are computed based on steady-state temperature distributions obtained from the numerical models. It is found that reducing feature size into the subcontinuum regime decreases thermal conductivity when compared to bulk values, at a higher rate than what was displayed by the Debye-based gray lattice Boltzmann method.

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