High Resolution Schemes and Modified Discrete Ordinate Method for Microscale Heat Transfer in Thin Film
Date Issued
2007
Date
2007
Author(s)
Lin, Yi-Chieh
DOI
zh-TW
Abstract
The Phonon Boltzmann equation is a nonlinear, integral, differential equation with many variables. It is difficult to be solved mathematically, so the collision term is usually replaced with a collision model. This will make it easier to deal with. In this work, the direction space will be discretized by applying discrete ordinate method. After applying the discrete ordinate method, it becomes a set of differential equations. With this treatment, the difficulties of numerical calculation will be greatly reduced.
Heat transport in semiconductor and dielectric materials is mainly by phonon. The transient heat conduction in microscale semiconductor thin films is investigated by using the equation of phonon radiative transfer (EPRT). The accuracy of using the simplified condition of equilibrium on the heat transfer characteristics is studied.
Accurate numerical methods for transient heat conduction problems using EPRT are presented and compared with various known methods. The present method is a deterministic and direct solver in phase space where the discrete ordinate method is used for angular discretization and high resolution schemes are used for spatial discretization. Nanoscale heat conduction covering wide range of Knudsen numbers are computed.
In this study, the Weighted Essentially Non-Oscillatory (WENO3) scheme in conjunction with discrete ordinate method was applied to solve the EPRT, and the explicit scheme for the EPRT was developed to solve the transient steady solutions.
To mitigating ray effect, we introduce Modified Discrete Ordinate Method to solve EPRT. We can find that ray effect would be reduced and the solutions become more accurate.
Subjects
微觀熱傳
聲子輻射傳輸方程式
修正分離座標法
Microscale Heat Transfer
Equation of Phonon Radiative Transport
High Resolution Scheme
Modified Discrete Ordinate Method
Type
thesis
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