利用聲子波茲曼方程式模擬非均質奈米多孔材料之熱傳性質

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葉崇宇(Yeh, Chung-Yu) 查詢紙本館藏

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能源工程研究所

論文名稱

利用聲子波茲曼方程式模擬非均質奈米多孔材料之熱傳性質

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摘要(中)

在微觀尺度下，當系統的特徵尺寸與熱載子的平均自由路徑相近或小於時，熱的傳輸不是擴散傳輸而是彈道傳輸，使用巨觀傅立葉定律分析會高估其熱傳導係數，這時需使用聲子的輻射傳輸方程式來描述微尺度下的熱傳現象。
本文利用聲子波茲曼方程式(Boltzmann transport equation,BTE)來模擬奈米尺度非均質多孔矽薄膜之熱傳性質，內容探討不同孔隙率、孔洞大小、非均質孔洞排列方式與薄膜厚度對熱傳導係數的影響。數值模擬使用COMSOL Multiphysics多重物理量耦合模擬軟體。利用有限元素法並結合分離座標法(discrete ordinate method,DOM)求解波茲曼傳輸方程式。模擬結果發現，在高孔隙率與小孔徑孔洞下，表面積與體積比(surface to volume ratio)高，增加聲子與孔洞界面散射的比例能有效降地熱傳導係數。薄膜在相同厚度與孔洞數時，總溫降是相同的，但薄膜內孔徑的大小與擺放位置會影響其中的溫度分佈，不同孔徑孔洞的排列順序會改變熱通量大小與限制其傳輸路徑而造成熱傳導係數的改變，本文透由計算不同孔徑孔洞間的界面熱阻並利用熱組串聯方式來預測其熱阻值。

摘要(英)

As the characteristic length of a system become comparable to or smaller than the mean free path of heat carriers, the energy transport behaviors become ballistic rather than diffusive. In this case, it will overestimate the thermal conductivity of the matter by using Fourier law. The phonon radiative transfer equation can be a better way to describe the microscale heat transfer.
In this study, the thermal property of inhomogeneous porous thin films are considered. The effects of porosity, pore size, thickness of the thin film, and inhomogeneous arrangements on the thermal conductivity are discussed by Boltzmann transport equation (BTE).We use the COMSOL Multiphysics software as the numerical tool to solve the BTE combined with angular discretization by the discrete ordinate method. The results shows that at high porosity and small pore size, increasing the phonon-pore’s interface scatterings can effectively decrease the thermal conductivity due to the high surface-to-volume ratio. In the case of the same film thickness and same pore number, the total temperature drops of diffenrent samples are the same, however, the temperature distribution are different for different the pore arrangements. The higher temperature gradient happens at the vicinities of the smaller pores. It is the reason for the changes of apparent thermal conductivity. The equivalent themal resistance model is also used to interpret the thermal resistance change at different inhomogeneous cases.

關鍵字(中)

★ 波茲曼方程式
★ 奈米多孔材料
★ 熱傳導係數

關鍵字(英)

★ Boltzmann transport equation
★ Nanoporous materials
★ Thermal conductivity

論文目次

摘要 i
Abstract ii
目錄 iii
圖目錄 v
表目錄 ix
符號對照表 xi
第一章緒論1
1-1 引言 1
1-2 聲子 1
1-3 微觀熱傳導 2
1-4 文獻回顧與研究動機 6
1-5 研究內容 9
第二章聲子傳輸理論 11
2-1 波茲曼傳輸方程式 11
2-2 聲子輻射熱傳方程式(EPRT) 12
2-3 一維薄膜熱傳分析 15
2-4 二維薄膜熱傳分析 16
2-5 邊界條件 17
2-6 二維多孔薄膜熱傳分析 20
2-7 等效介質模型(Effective Medium Model) 21
第三章數值方法 23
3-1 有限元素分析法 23
3-1-1 邊界值問題 23
3-1-2 有限元素法 24
3-1-3 葛樂金法 26
3-1-4 COMSOL Multiphysics 27
3-1-5 統御方程式與邊界條件 27
3-2 離散座標法 29
3-2-1 方向角離散 29
3-2-2 射線效應(Ray effect) 34
3-3 網格測詴 39
3-4 模擬參數 40
3-4-1 灰質模型(Gray Model ) 40
3-4-2 材料參數 41
3-4-3 非均質孔洞設計 42
3-4-4 數值求解流程圖 44
第四章結果與討論 45
4-1 一維薄膜等溫邊界聲子傳輸 45
4-2 二維薄膜等溫邊界聲子傳輸 46
4-2-1 一維與二維之對稱邊界模型比較 46
4-2-2 二維薄膜反射邊界模型 47
4-3 均值(homogeneous)孔洞薄膜 50
4-3-1 薄膜厚度與熱傳導係數 50
4-3-2 孔隙率與熱傳導係數 53
4-3-3 孔徑大小與熱傳導係數 53
4-4 非均質孔洞薄膜 56
4-4-1 非均質孔洞模型建立 56
4-4-2 孔洞串聯分析 59
4-4-3 孔洞排列順序與熱阻 63
4-4-4 界面熱阻與等效串聯熱組模型 73
4-4-5 非均質孔洞串聯與並聯模型 83
第五章結論與未來展望 90
參考文獻 92

參考文獻

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指導教授

洪銘聰(Hung, Ming-Tsung)

審核日期

2013-8-27

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