... that the exact normal solution of Boltzmann equation gives uniform pressure with no stresses in the flow domain. In the case of hard-sphere molecules, direct simulation Monte Carlo (DSMC) results predict nonuniform pressure field giving rise to stresses in the flow domain. The simplistic nature of the problem...

..., and petascale capacity is expected over the next decade. Multiprocess multicore environments are the norm for commodity clusters. Boltzmann equation computational fluid dynamics finite volume methods flow simulation heat transfer reviews turbulence finite volume multiscale sensitivity...

... in interpreting results. Boltzmann equation elemental semiconductors finite volume methods germanium heat conduction phonon dispersion relations semiconductor superlattices silicon thermal conductivity Three types of nanoscale physical phenomena may manifest themselves when considering...

... – 328 . 10.1115/1.1447938 26 Yang , R. , Chen , G. , Laroche , M. , and Taur , Y. , 2005 , “ Simulation of Nanoscale Multidimensional Transient Heat Conduction Problems Using Ballistic-Diffusive Equations and Phonon Boltzmann Equation ,” J. Heat Transfer , 127 , pp. 298 – 306...

... to reasonable accuracy even with this approximation ( 40 41 ). For detailed modeling results of thermal transport employing a simultaneous solution of the gas phase and phonon Boltzmann equation, the reader is referred to Ref. 42 . Typical accommodation coefficients for air on oxide-terminated surfaces...

...Toshiyuki Doi Periodic time-dependent behavior of a rarefied gas between two parallel planes caused by an oscillatory heating of one plane is numerically studied based on the linearized Boltzmann equation. Detailed numerical data of the energy transfer from the heated plane to the unheated plane...

... is applicable. 21 01 2009 12 04 2010 13 08 2010 13 08 2010 Boltzmann equation flow simulation heat transfer Particle-mediated energy transport in the transition regime between the ballistic and diffusive limits has recently received significant attention in connection...

...-1481 , 86 , pp. 240 – 246 . 05 06 2009 05 04 2010 27 07 2010 27 07 2010 Boltzmann equation entropy heat transfer phonons radiative transfer conduction entropy phonon radiative transfer thermodynamics thin film As electronic and thermal devices...

... J. Heat Transfer 0022-1481 , 130 ( 9 ), p. 092402 . 10.1115/1.2944249 Succi , S. , 2001 , The Lattice Boltzmann Equation for Fluid Mechanics and Beyond , Clarendon , Oxford, UK . Qian , Y. H. , d’Humieres , D. , and Lallemand , P. , 1992 , “ Lattice BGK...

... energy transport ultrashort-pulsed laser RKDG Auger effect Boltzmann equation carrier mean free path electron-hole recombination elemental semiconductors finite element analysis Galerkin method high-speed optical techniques laser beam effects phonons Runge-Kutta methods semiconductor...

... domain (two-dimensional versus three-dimensional), and the lateral (in-plane) dimension of the film on the statistical accuracy and computational efficiency is systematically studied and elucidated for all temperatures. 24 03 2009 23 09 2009 08 03 2010 08 03 2010 Boltzmann...

.... The left part of Eq. 1 represents the BTE equation for a mode m under a temperature gradient. Boltzmann equation elemental semiconductors lattice constants molecular dynamics method phonon dispersion relations potential energy functions silicon thermal analysis thermal conductivity...

... 2008 25 02 2009 05 06 2009 Boltzmann equation carrier mean free path carrier relaxation time electron-phonon interactions finite element analysis Galerkin method gold laser beam effects melting metallic thin films Runge-Kutta methods specific heat The physics...

.... Heat Transfer 0022-1481 10.1115/1.2911377 , 115 , pp. 835 – 841 . Yang , R. , Chen , G. , Laroche , M. , and Taur , Y. , 2005 , “ Simulation of Nanoscale Multidimensional Transient Heat Conduction Problems Using Ballistic-Diffusive Equations and Phonon Boltzmann Equation...

... the regularized 13-moment equations (R13 equations), which are of high approximation order. In addition, a complete set of boundary conditions can be derived from the boundary conditions of the Boltzmann equation. The R13 equations are linearly stable, and their results for moderate Knudsen numbers stand...

... flow simulation Boltzmann equation laminar flow convection boundary layers lattice Boltzmann method backward-facing step heat transfer field synergy principle In recent years, the lattice Boltzmann method (LBM) has emerged as a promising numerical scheme for simulating fluid flows...

... phonon mean free paths based on a solution of the Boltzmann transport equation along a layer agrees well with the experimental results. 06 03 2004 24 06 2005 silicon elemental semiconductors thermal conductivity heat conduction phonons Boltzmann equation phonon rransport...

... time of heat carriers. The transient ballistic-diffusive heat conduction equations (BDE) were developed as an approximation to the phonon Boltzmann equation (BTE) for nanoscale heat conduction problems. In this paper, we further develop BDE for multidimensional heat conduction, including nanoscale heat...

... . 11 08 2003 01 03 2005 heat conduction silicon-on-insulator transistors Boltzmann equation phonon dispersion relations finite volume methods thermal conductivity Computations BTE Finite Volume Method SOI Transistors Phonons Phonon Dispersion Phonon Polarization Micro...

... for silicon thin films over a wide range of temperatures are also matched satisfactorily. silicon elemental semiconductors microfluidics heat transfer phonon dispersion relations Boltzmann equation thermal conductivity perturbation theory finite volume methods parabolic equations diffusion...