The subcontinuum energy transport mechanism in solids can be explained by the Lattice Boltzmann Method (LBM), a discrete representation of the Boltzmann Transport Equation (BTE). The present study focuses on a detailed comparison of the LBM and BTE. Results reveal that at continuum scale, the LBM follows the BTE almost precisely. However, as the device dimensions are reduced, approaching the ballistic limit, the LBM deviates from the BTE results in terms of thermal property estimation. The inherent nonisotropic lattice configuration has a dominant contribution to the performance of the LBM. A threshold length scale is also proposed for successful implementation of the LBM solver. © 2014 Taylor & Francis Group, LLC.

Arvind Pattamatta

Department of Mechanical Engineering

Periodic structures

Boltzmann transport equation

Comparative studies

Dominant contributions

ENERGY TRANSPORT MECHANISMS

Lattice Boltzmann method

Lattice boltzmann methods (LBM)

LATTICE CONFIGURATION

Property estimation

Computational fluid dynamics

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

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IIT Madras

A Comparative Study of Submicron Phonon Transport Using the Boltzmann Transport Equation and the Lattice Boltzmann Method

Numerical Heat Transfer, Part B: Fundamentals

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 Copyright © 2013 by ASME.

ASME 2013 Heat Transfer Summer Conf. Collocated with the ASME 2013 7th Int. Conf. on Energy Sustainability and the ASME 2013 11th Int. Conf. on Fuel Cell Science, Engineering and Technology, HT 2013

Estimation of an appropriate lattice structure for phonon transport using lattice boltzmann method

Numerical Heat Transfer, Part A: Applications

High Knudsen Number Thermal Flows with the D2Q13 Lattice Boltzmann Model

Journal of Computational Physics

On the lattice Boltzmann method for phonon transport

Microfluidics and Nanofluidics

Lattice Boltzmann method for microfluidics: models and applications

Lattice Boltzmann Method

The Boltzmann Equation

A comparative study of submicron phonon transport using the Boltzmann transport equation and the lattice Boltzmann Method

Journal	Data powered by TypesetNumerical Heat Transfer, Part B: Fundamentals
Publisher	Data powered by TypesetTaylor and Francis Ltd.
ISSN	10407790
Open Access	No