scholarly journals Heat conduction in multifunctional nanotrusses studied using Boltzmann transport equation

2016 ◽  
Vol 108 (1) ◽  
pp. 011902 ◽  
Author(s):  
Nicholas G. Dou ◽  
Austin J. Minnich
Keyword(s):  
Heat Conduction ◽  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport

Thermal Conductivity and Phonon Engineering in Low-Dimensional Structures

1998 ◽  
Vol 545 ◽  
Author(s):  
G. Chen ◽  
S. G. Volz ◽  
T. Borca-Tasciuc ◽  
T. Zeng ◽  
D. Song ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Dynamics Simulation ◽  
Boltzmann Transport ◽  
Model Based ◽  
Conduction Mechanisms ◽  
Interface Scattering ◽  
Low Dimensional

AbstractUnderstanding phonon heat conduction mechanisms in low-dimensional structures is of critical importance for low-dimensional thermoelectricity. In this paper, we discuss heat conduction mechanisms in two-dimensional (2D) and one-dimensional (1D) structures. Models based on both the phonon wave picture and particle picture are developed for heat conduction in 2D superlattices. The phonon wave model, based on the acoustic wave equations, includes the effects of phonon interference and tunneling, while the particle model, based on the Boltzmann transport equation, treats the internal as well interface scattering of phonons. For 1D systems, both the Boltzmann transport equation and molecular dynamics simulation approaches are employed. Comparing the modeling results with experimental data suggest that the interface scattering of phonons plays a crucial role in the thermal conductivity of low-dimensional structures. We also discuss the minimum thermal conductivity of low-dimensional structures based on a generalized thermal conductivity integral, and suggest that the minimum thermal conductivities of low-dimensional systems may differ from those of their corresponding bulk materials. The discussion leads to alternative ways to reduce thermal conductivity based on the propagating phonon modes.

Prediction of Non-Equilibrium Heat Conduction Using Parallel Computation of the Phonon Boltzmann Transport Equation

2014 ◽  
Author(s):  
Syed A. Ali ◽  
Gautham Kollu ◽  
Sandip Mazumder ◽  
P. Sadayappan
Keyword(s):  
Heat Conduction ◽  
Transport Equation ◽  
Parallel Computation ◽  
Large Scale ◽  
Phonon Scattering ◽  
Boltzmann Transport Equation ◽  
Computational Time ◽  
Spectral Space ◽  
Boltzmann Transport ◽  
Non Equilibrium

Non-equilibrium heat conduction, as occurring in modern-day sub-micron semiconductor devices, can be predicted effectively using the Boltzmann Transport Equation (BTE) for phonons. In this article, strategies and algorithms for large-scale parallel computation of the phonon BTE are presented. An unstructured finite volume method for spatial discretization is coupled with the control angle discrete ordinates method for angular discretization. The single-time relaxation approximation is used to treat phonon-phonon scattering. Both dispersion and polarization of the phonons are accounted for. Three different parallelization strategies are explored: (a) band-based, (b) direction-based, and (c) hybrid band/cell-based. Subsequent to validation studies in which silicon thin-film thermal conductivity was successfully predicted, transient simulations of non-equilibrium thermal transport were conducted in a three-dimensional device-like silicon structure, discretized using 604,054 tetrahedral cells. The angular space was discretized using 400 angles, and the spectral space was discretized into 40 spectral intervals (bands). This resulted in ∼9.7×109 unknowns, which are approximately 3 orders of magnitude larger than previously reported computations in this area. Studies showed that direction-based and hybrid band/cell-based parallelization strategies resulted in similar total computational time. However, the parallel efficiency of the hybrid band/cell-based strategy — about 88% — was found to be superior to that of the direction-based strategy, and is recommended as the preferred strategy for even larger scale computations.

scholarly journals A ballistic-diffusive heat conduction model extracted from Boltzmann transport equation

2011 ◽  
Vol 467 (2131) ◽  
pp. 1851-1864 ◽  
Author(s):  
Mingtian Xu ◽  
Haiyan Hu
Keyword(s):  
Heat Conduction ◽  
Transport Equation ◽  
Heat Conductivity ◽  
Boltzmann Transport Equation ◽  
Propagation Speed ◽  
Coarse Graining ◽  
Heat Propagation ◽  
Boltzmann Transport ◽  
Conduction Model ◽  
Heat Conduction Model

A ballistic-diffusive heat conduction model is derived from the Boltzmann transport equation by a coarse-graining approach developed in the present study. By taking into account of the lagging effect, this model avoids the infinite heat propagation speed implied by the classical Fourier law. By expressing the heat conductivity as a function of the Knudsen number, it accounts for the size effect of the nanoscale heat conduction. The variation of the obtained effective heat conductivity with respect to the characteristic length shows an agreement with the experimental results for thin silicon films and nanowires in the nanoscale regime.

Generalized Ballistic-Diffusive Formulation and Hybrid SN-PN Solution of the Boltzmann Transport Equation for Phonons for Nonequilibrium Heat Conduction

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Arpit Mittal ◽  
Sandip Mazumder
Keyword(s):  
Heat Conduction ◽  
Transport Equation ◽  
Large Scale ◽  
A Priori ◽  
Boltzmann Transport Equation ◽  
Transient Heat Conduction ◽  
Discrete Ordinates ◽  
Boltzmann Transport ◽  
Discrete Ordinates Method ◽  
Diffusive Component

A generalized form of the ballistic-diffusive equations (BDEs) for approximate solution of the Boltzmann Transport equation (BTE) for phonons is formulated. The formulation presented here is new and general in the sense that, unlike previously published formulations of the BDE, it does not require a priori knowledge of the specific heat capacity of the material. Furthermore, it does not introduce artifacts such as media and ballistic temperatures. As a consequence, the boundary conditions have clear physical meaning. In formulating the BDE, the phonon intensity is split into two components: ballistic and diffusive. The ballistic component is traditionally determined using a viewfactor formulation, while the diffusive component is solved by invoking spherical harmonics expansions. Use of the viewfactor approach for the ballistic component is prohibitive for complex large-scale geometries. Instead, in this work, the ballistic equation is solved using two different established methods that are appropriate for use in complex geometries, namely the discrete ordinates method (DOM) and the control angle discrete ordinates method (CADOM). Results of each method for solving the BDE are compared against benchmark Monte Carlo results, as well as solutions of the BTE using standalone DOM and CADOM for two different two-dimensional transient heat conduction problems at various Knudsen numbers. It is found that standalone CADOM (for BTE) and hybrid CADOM-P1 (for BDE) yield the best accuracy. The hybrid CADOM-P1 is found to be the best method in terms of computational efficiency.

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