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標題: | 應用高解析算則及修正分離座標法之微觀薄膜熱傳分析 High Resolution Schemes and Modified Discrete Ordinate Method for Microscale Heat Transfer in Thin Film |
作者: | Yi-Chieh Lin 林義傑 |
指導教授: | 楊照彥(Jaw-Yen Yang) |
關鍵字: | 微觀熱傳,聲子輻射傳輸方程式,高解析算則,修正分離座標法, Microscale Heat Transfer,Equation of Phonon Radiative Transport,High Resolution Scheme,Modified Discrete Ordinate Method, |
出版年 : | 2007 |
學位: | 碩士 |
摘要: | 熱在巨觀尺度下,遵從傅立葉熱傳方程式。當尺度縮小到微奈米等級的時候,利用傅立葉熱傳方程式分析模擬會跟實際上的物理量產生很大的出入。這代表了傅立葉熱傳方程式不再能適用於微尺度下探討分析真實熱傳導現象。一般在半導體或絕緣體材料中,熱是由熱載子(電子、聲子和光子)來傳遞的。其中最主要是由聲子來傳遞,本文主要利用聲子輻射熱傳方程式模擬在微尺度下薄膜內之暫態熱傳現象。
聲子輻射熱傳方程式為一多變數且非線性的積分微分方程式,在數學上極難求解,故其碰撞項常用一碰撞模式取代(採用鬆弛時間近似為一線性關係),可使得在數學處理上較容易。本文數值模擬方面,對於方向空間上應用分離座標法將方向餘弦離散化,對於位置空間上則應用高解析算則(WENO3和Min-Mod)於離散的位置格點上來分析。 利用加權型基本不振盪算則(WENO3算則)配合分離座標法,以求解聲子輻射熱傳方程式,可以測試其準確性,並與其它高解析算則比較之。在分離座標法上,立體角方向數上的離散化會產生射線效應現象,使得模擬出來的暫態情形會出現如波浪分佈的現象,此時套用修正分離座標法來做分析,可以減少射線效應的影響而消除波浪狀的溫度分佈情形。 本文利用聲子波茲曼方程式分析一維單層和雙層薄膜的問題,尺度介於奈米到微米之間,主要分析在暫態下之熱傳問題,並討論其穩態時的熱通量。 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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/29025 |
全文授權: | 有償授權 |
顯示於系所單位: | 應用力學研究所 |
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