Extending the diffusion approximation to the boundary using an integrated diffusion model

Extending the diffusion approximation to the boundary using an integrated diffusion model

The widely used diffusion approximation is inaccurate to describe the transport behaviors near surfaces and interfaces. To solve such stochastic processes, an integro-differential equation, such as the Boltzmann transport equation (BTE), is typically required. In this work, we show that it is possib...

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Main Authors: Chen Chen, Zhidong Du, Liang Pan
Format: Article
Language:English
Published: AIP Publishing LLC 2015-06-01
Series:AIP Advances
Online Access:http://dx.doi.org/10.1063/1.4922269
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spelling doaj-bdedcb0412d943deb3045d0da42396b82020-11-25T00:20:21ZengAIP Publishing LLCAIP Advances2158-32262015-06-0156067115067115-710.1063/1.4922269014506ADVExtending the diffusion approximation to the boundary using an integrated diffusion modelChen Chen0Zhidong Du1Liang Pan2School of Mechanical Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USASchool of Mechanical Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USASchool of Mechanical Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USAThe widely used diffusion approximation is inaccurate to describe the transport behaviors near surfaces and interfaces. To solve such stochastic processes, an integro-differential equation, such as the Boltzmann transport equation (BTE), is typically required. In this work, we show that it is possible to keep the simplicity of the diffusion approximation by introducing a nonlocal source term and a spatially varying diffusion coefficient. We apply the proposed integrated diffusion model (IDM) to a benchmark problem of heat conduction across a thin film to demonstrate its feasibility. We also validate the model when boundary reflections and uniform internal heat generation are present.http://dx.doi.org/10.1063/1.4922269
collection DOAJ
language English
format Article
sources DOAJ
author Chen Chen
Zhidong Du
Liang Pan
spellingShingle Chen Chen
Zhidong Du
Liang Pan
Extending the diffusion approximation to the boundary using an integrated diffusion model
AIP Advances
author_facet Chen Chen
Zhidong Du
Liang Pan
author_sort Chen Chen
title Extending the diffusion approximation to the boundary using an integrated diffusion model
title_short Extending the diffusion approximation to the boundary using an integrated diffusion model
title_full Extending the diffusion approximation to the boundary using an integrated diffusion model
title_fullStr Extending the diffusion approximation to the boundary using an integrated diffusion model
title_full_unstemmed Extending the diffusion approximation to the boundary using an integrated diffusion model
title_sort extending the diffusion approximation to the boundary using an integrated diffusion model
publisher AIP Publishing LLC
series AIP Advances
issn 2158-3226
publishDate 2015-06-01
description The widely used diffusion approximation is inaccurate to describe the transport behaviors near surfaces and interfaces. To solve such stochastic processes, an integro-differential equation, such as the Boltzmann transport equation (BTE), is typically required. In this work, we show that it is possible to keep the simplicity of the diffusion approximation by introducing a nonlocal source term and a spatially varying diffusion coefficient. We apply the proposed integrated diffusion model (IDM) to a benchmark problem of heat conduction across a thin film to demonstrate its feasibility. We also validate the model when boundary reflections and uniform internal heat generation are present.
url http://dx.doi.org/10.1063/1.4922269
work_keys_str_mv AT chenchen extendingthediffusionapproximationtotheboundaryusinganintegrateddiffusionmodel
AT zhidongdu extendingthediffusionapproximationtotheboundaryusinganintegrateddiffusionmodel
AT liangpan extendingthediffusionapproximationtotheboundaryusinganintegrateddiffusionmodel
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