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研究生:侯奕丞
研究生(外文):Yi-Cheng Hou
論文名稱:多孔性奈米谷碲化鉍材料熱傳導性質研究
論文名稱(外文):Numerical and Model Predictions of the Thermal Conductivity of Porous Bismuth Telluride Nanocanyons
指導教授:黃美嬌黃美嬌引用關係
口試委員:陳軍華周雅文
口試日期:2014-06-26
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:中文
論文頁數:82
中文關鍵詞:多孔性碲化鉍奈米谷蒙地卡羅晶格熱傳導等效介質近似
外文關鍵詞:Porous bismuth telluridenanoCanyonsMonte – CarloLattice thermal conductivityEffective medium approximation
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本論文主要的研究目的為預測多孔性碲化鉍材料之晶格熱傳導係數,並觀察在多孔性材料中之熱傳導情形,為達成此一目的,我們先利用數值模擬進行研究,再檢驗既有理論模型的可用性及準確性。
所模擬之碲化鉍多孔性材料具有奈米谷(nano Canyons)結構,研究包括其平行及垂直軸向之熱傳現象。因奈米谷結構及孔隙皆為不規則分布,我們乃開發運用非結構性網格的蒙地卡羅模擬工具(Monte-Carlo, MC),使之能夠模擬聲子在具複雜結構之多孔性材料內的傳輸現象,進而計算出該材料結構之等效熱傳導係數。在求解聲子波茲曼方程式的過程中,本質散射部分採用單一鬆弛時間近似法,而聲子性質則使用灰介質假設。
在理論模型方面,我們首先透過實際模擬取得多孔性材料之平均自由路徑,以此作為顆粒尺寸的特徵值,再利用Chunag &; Huang的等效介質近似(EMA)模型及三鍵結滲透理論,得以預測多孔性奈米結構材料垂直軸向之熱傳導係數。至於平行軸向之熱傳導係數,則採塊材觀點,取顆粒並聯後之等效熱傳導係數為理論預測值。
研究發現晶粒與晶粒及晶粒與孔隙間之介面散射為降低熱傳的主因,其中當熱傳主要方向垂直奈米谷軸向時,孔隙影響甚巨,晶粒內靠近孔隙處明顯有較為顯著的溫度梯度;垂直方向之等效熱傳導係數因此較平行軸方向之等效熱傳導係數更低,約只有塊材的一半。另一方面理論模型因未考慮孔隙的分佈方向,故僅能提供孔隙隨機均勻分佈的材料預測,對於本研究之三維奈米谷材料之垂直軸向熱傳能力偏向高估。


目錄
口試委員會審定書 i
致謝 ii
摘要 iii
Abstract iv
目錄 vi
表目錄 ix
圖目錄 x
第一章 緒論 1
1-1 文獻回顧 1
1-2 研究動機及目的 7
1-3 論文架構 8
第二章 非結構性網格聲子蒙地卡羅法 9
2-1 基本理論 9
2-1-1 聲子波茲曼傳輸方程式 9
2-1-2 灰介質假設 10
2-1-3 介面穿透模型 12
2-1-4 結構均質性 14
2-2 聲子性質初始化 14
2-3 主程式 16
2-3-1 聲子位移與本質散射 16
2-3-2 介面散射 17
2-3-3 邊界條件與邊界熱流控制 18
2-3-4 能量守恆及網格性質資料更新 22
2-3-5 主程式流程與平行化 24
2-4 後處理 25
2-5 程式及網格驗證 25
第三章 多孔性奈米谷材料熱傳導係數理論預測模型 28
3-1 稀薄EMA模型 28
3-2 高濃度EMA模型 30
3-3 BDEMA模型 32
3-4 三鍵結滲透系統的EMA模型 34
3-5 塊材熱阻分析 36
第四章 多孔性奈米谷材料晶格熱傳導係數模擬 38
4-1 數值模型建立與網格劃分 38
4-1-1 多孔性奈米谷材料結構 38
4-1-2 多孔性奈米谷模型及網格劃分 39
4-2 多孔性奈米谷材料垂直軸向之熱傳性質 40
4-2-1 熱通量及溫度分布 41
4-2-2 等效熱傳導係數 42
4-2-2a 不同介面光滑係數下之等效熱傳導係數 42
4-2-2b 理論模型與蒙地卡羅法模擬值之比較 42
4-3 多孔性奈米谷材料平行軸向之熱傳性質 45
4-3-1 熱通量及溫度分布 46
4-3-2 等效熱傳導係數 48
4-3-2a 不同介面光滑係數下之等效熱傳導係數 48
4-3-2b 理論模型與蒙地卡羅法模擬值之比較 48
第五章 結論與未來展望 49
5-1 結論 49
5-1-1 多孔性奈米谷材料理論預測模型 49
5-1-2 多孔性奈米谷材料熱傳導係數 50
5-2 未來展望 50
參考文獻 52


表目錄
表3-1幾何圖形與孔隙函式 57
表3-2幾何圖形與View Factor 57
表4-1 二維結構模型幾何相關數據 58
表4-2不同介面光滑係數之垂直軸向熱傳導係數 58
表4-3 Model-2D之介面平均自由路徑計算 59
表4-4 Model-2D-Modified之介面平均自由路徑計算 60
表4-5 Model-2D-Modified之平均水力直徑 61
表4-6 理論模型與蒙地卡羅模擬值之比較 61
表4-7非完全粗糙介面的三鍵結滲透系統EMA模型預測值 62
表4-8新舊網格之統計資料 62
表4-9不同介面光滑係數之平行軸向熱傳導係數 63



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圖目錄
圖2.1 Bi_2 Te_3 之晶格結構 64
圖2.2實驗量測之碲化鉍[112]及[111]方向色散關係曲線圖 64
圖2.3實驗量測之碲化鉍的塊材熱傳導係數圖 65
圖2.4碲化鉍材料所算出來的平均聲子性質對溫度的函數圖 65
圖2.5碲化鉍奈米谷垂直軸方向截面圖。 65
圖2.6 (a) 三角形網格 (b)四面體網格示意圖。 66
圖2.7聲子位移追蹤示意圖。 66
圖2.8 (a) 鏡穿射 (b) 鏡反射 示意圖。 66
圖2.9主程式流程圖。 67
圖2.10結構與網格示意圖。 68
圖2.11塊材熱傳導係數模擬結果之各截面熱通量及各種穩態溫度分布圖 68
圖3.1第一類複合物示意圖 70
圖3.2第二類複合物示意圖 70
圖3.3熱流穿過一個厚度為L的薄膜示意圖 70
圖3.4 Matrix結構及孔隙結構示意圖 70
圖3.5 2D/3D無限延伸熱阻網路示意圖 71
圖3.6多孔性奈米谷結構示意圖 72
圖3.7並聯熱阻圖 72
圖4.1奈米谷結構之SEM圖 73
圖4.2二維數值模型Model-2D 73
圖4.3 Model-2D的二維網格 73
圖4.4二維模型Model-2D-Modifed 74
圖4.5 Model-2D-Modifed 的二維網格 74
圖4.6 Model-2D-Modifed的三維結構及三維網格 74
圖4.7 P=0時Model-2D模擬結果之各截面熱通量及穩態溫度分布圖 75
圖4.8 P=0時Model-2D網格溫度分布圖 75
圖4.9 P=0時Model-2D的二維溫度分布圖 76
圖4.10 P=0.5時奈米谷平行軸向熱傳模擬結果之各截面熱通量及穩態溫度分布圖 77
圖4.11 P=0.5時奈米谷平行軸向熱傳之瞬時熱通量與FFT結果圖 77
圖4.12 P=0.5時奈米谷平行軸向熱傳之四面體網格溫度分布圖 78
圖4.13 P=1-奈米谷平行軸向熱傳之四面體網格溫度分布圖及網格分布圖 79
圖4.14新舊網格的性質比較圖 80
圖4.15 P=1時新網格-奈米谷平行軸向熱傳之四面體網格溫度分布圖 81
圖4.16奈米谷結構之三維溫度分布圖 81
圖4.17單獨一根晶粒柱表面之溫度分布圖 82


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