Monte Carlo Simulation of Steady-State Microscale Phonon Heat Transport

2008 ◽  
Vol 130 (7) ◽  
Author(s):  
Jaona Randrianalisoa ◽  
Dominique Baillis
Keyword(s):  
Heat Transfer ◽  
Thin Films ◽  
Monte Carlo ◽  
Heat Conduction ◽  
Steady State ◽  
Monte Carlo Method ◽  
Silicon Nanowires ◽  
Silicon Film ◽  
Relaxation Times ◽  
Phonon Transport

Heat conduction in submicron crystalline materials can be well modeled by the Boltzmann transport equation (BTE). The Monte Carlo method is effective in computing the solution of the BTE. These past years, transient Monte Carlo simulations have been developed, but they are generally memory demanding. This paper presents an alternative Monte Carlo method for analyzing heat conduction in such materials. The numerical scheme is derived from past Monte Carlo algorithms for steady-state radiative heat transfer and enables us to understand well the steady-state nature of phonon transport. Moreover, this algorithm is not memory demanding and uses very few iteration to achieve convergence. It could be computationally more advantageous than transient Monte Carlo approaches in certain cases. Similar to the famous Mazumder and Majumdar’s transient algorithm (2001, “Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization,” ASME J. Heat Transfer, 123, pp. 749–759), the dual polarizations of phonon propagation, the nonlinear dispersion relationships, the transition between the two polarization branches, and the nongray treatment of phonon relaxation times are accounted for. Scatterings by different mechanisms are treated individually, and the creation and/or destruction of phonons due to scattering is implicitly taken into account. The proposed method successfully predicts exact solutions of phonon transport across a gallium arsenide film in the ballistic regime and that across a silicon film in the diffusion regime. Its capability to model the phonon scattering by boundaries and impurities on the phonon transport has been verified. The current simulations agree well with the previous predictions and the measurement of thermal conductivity along silicon thin films and along silicon nanowires of widths greater than 22nm. This study confirms that the dispersion curves and relaxation times of bulk silicon are not appropriate to model phonon propagation along silicon nanowires of 22nm width.

A Modified Monte Carlo Method for Phonon Radiative Transfer in Nanoscale Materials

2013 ◽  
Vol 652-654 ◽  
pp. 188-191
Author(s):  
Ya Fen Han ◽  
Xin Lin Xia ◽  
Hai Dong Liu
Keyword(s):  
Heat Transfer ◽  
Thin Films ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Transfer ◽  
Good Accuracy ◽  
Nanoscale Materials ◽  
Numerical Accuracy ◽  
Silicon Thin Films ◽  
Temperature Distributions

A Modified Monte-Carlo Method (MMCM) in which phonon bundles take non-energy is developed to model the steady state phonon radiative transfer in nanoscale materials. Heat transfer in silicon thin films is analyzed to examine the validity of the developed method. The temperature distributions and cross-plane thermal conductivity are determined by using the developed method for the silicon thin films and compared with the results in reference. The results indicate that the developed method has a good accuracy in solving the phonon radiative transfer in nanoscale materials. In addition, numerical accuracy can be improved by the increase of the number of samples in the simulations.

An overview of phonon-based heat conduction models and their solution

2016 ◽  
Vol 26 (3/4) ◽  
pp. 916-949 ◽  
Author(s):  
V.M Wheeler ◽  
K K Tamma
Keyword(s):  
Heat Transfer ◽  
Thin Films ◽  
Heat Conduction ◽  
Thermal Transport ◽  
Phonon Transport ◽  
Random Motion ◽  
Comprehensive Overview ◽  
Content Type ◽  
The Subject ◽  
Numerical Discretization

Purpose – The purpose of this paper is to provide an overview and some recent advances in the models, analysis and simulation of thermal transport of phonons as related to the field of microscale/macroscale heat conduction in solids. The efforts focus upon a fairly comprehensive overview of the subject matter from a unified standpoint highlighting the various approximations inherent in the thermal models. Subsequently, the numerical formulations and illustrations using the current state-of-the-art are provided. Design/methodology/approach – This paper is dedicated to the approximate solution to the relaxation time phonon Boltzmann equation (BE). While original contributions are pointed out and addressed appropriately, the efforts and contributions will be focussed on a relatively complete overview highlighting the field from one unified standpoint and clearly stating all assumptions that go into the approximations inherent to existing models. The contents will be divided as follows: In the first section the authors will give an overview of semi-classical phonon transport physics. Then the authors will discuss the equation of phonon radiative transport (EPRT) and its approximations—the ballistic-diffusive approximation (BDA) and the new heat equation (NHE). Next the authors derive and discuss the C-F model. A numerical discretization method valid for all models is then presented followed by results to numerical simulations and discussion. Findings – From a unified treatment based on the introduction of an energy distribution function, the authors have derived the EPRT and its two well-known approximations: BDA and NHE. For completeness and to provide a vehicle for a general numerical discretization approach, the authors have also included analysis of the C-F model and the parabolic and hyperbolic descriptions of heat transfer along with it. The approximation of angular dependence of phonons in radiation-like descriptions of transport has been given special attention. The assumption of isotropy was found to be of paramount importance in the formulation of position space models for phononic thermal transport. For the thin film problem considered here, the NHE along with the proper boundary condition appears to be the best choice to approximate the phonon BE. Not only does it provide predictions that are in excellent agreement with EPRT, it does not require the discretization of phase space making it far more computationally efficient. Originality/value – The authors hope this work will help dispel the idea that since Fourier’s law describes diffusion (under limiting assumptions) and it has shown to be ineffective in describing heat transfer for very thin films, that diffusion cannot describe heat transfer in thin films and one should look to a radiative description instead. If one considers diffusion in the sense of random motion, as invisaged by the original builders of the subject (Smoluchowski, Einstein, Ornstein et al.), instead of a temperature gradient, the idea that diffusion can govern thermal transport at this scale is not surprising. Indeed, the NHE is essentially a diffusion equation that describes the motion of particles up to the point of true randomness (isotropy) as well as thereafter.

scholarly journals A Monte Carlo Method of Solving Heat Conduction Problems

1980 ◽  
Vol 102 (1) ◽  
pp. 121-125 ◽  
Author(s):  
S. K. Fraley ◽  
T. J. Hoffman ◽  
P. N. Stevens
Keyword(s):  
Monte Carlo ◽  
Heat Conduction ◽  
Monte Carlo Method ◽  
Transport Equation ◽  
Heat Conduction Equation ◽  
Analytical Techniques ◽  
Conduction Equation ◽  
Geometric Complexity ◽  
New Approach ◽  
Temperature Distributions

A new approach in the use of Monte Carlo to solve heat conduction problems is developed using a transport equation approximation to the heat conduction equation. A variety of problems is analyzed with this method and their solutions are compared to those obtained with analytical techniques. This Monte Carlo approach appears to be limited to the calculation of temperatures at specific points rather than temperature distributions. The method is applicable to the solution of multimedia problems with no inherent limitations as to the geometric complexity of the problem.

Multidimensional numerical simulation of heat radiation in direct injection diesel engines

2000 ◽  
Vol 214 (4) ◽  
pp. 453-466 ◽  
Author(s):  
S Chen ◽  
T. L. Chan ◽  
C. W. Leung ◽  
M. A. Liu ◽  
K. Y. Pan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Soot Formation ◽  
Direct Injection ◽  
Complex Structure ◽  
Heat Radiation ◽  
Radiant Heat Transfer ◽  
The Monte Carlo Method ◽  
Total Exchange

A multidimensional theoretical model of radiation heat transfer in the cylinder of a direct injection (DI) diesel engine has been developed, which includes submodels of heat release, geometrical description, radiation temperature, soot formation and oxidation, the absorption coefficient and the Monte Carlo method for total exchange areas. In this code, the cylinder is divided into 10 surface zones and four gas zones. The Monte Carlo method integrated with a smoothing technique considering reciprocity and conservation is used to calculate the radiation total exchange areas directly for both the absorbing—emitting media and the complex structure of the cylinder. Using the multi—dimensional approach, the variation in radiant heat transfer with crank angle can be obtained across the whole combustion chamber. The computed results are analysed and discussed in the present study, and they are found to be in agreement with the experimental results.

Line-by-Line Random-Number Database for Monte Carlo Simulations of Radiation in Combustion System

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Tao Ren ◽  
Michael F. Modest
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Heat ◽  
Random Number ◽  
Test Cases ◽  
Combustion System ◽  
Absorption Coefficients ◽  
One Dimensional ◽  
The Monte Carlo Method

With today's computational capabilities, it has become possible to conduct line-by-line (LBL) accurate radiative heat transfer calculations in spectrally highly nongray combustion systems using the Monte Carlo method. In these calculations, wavenumbers carried by photon bundles must be determined in a statistically meaningful way. The wavenumbers for the emitting photons are found from a database, which tabulates wavenumber–random number relations for each species. In order to cover most conditions found in industrial practices, a database tabulating these relations for CO2, H2O, CO, CH4, C2H4, and soot is constructed to determine emission wavenumbers and absorption coefficients for mixtures at temperatures up to 3000 K and total pressures up to 80 bar. The accuracy of the database is tested by reconstructing absorption coefficient spectra from the tabulated database. One-dimensional test cases are used to validate the database against analytical LBL solutions. Sample calculations are also conducted for a luminous flame and a gas turbine combustion burner. The database is available from the author's website upon request.

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