# 臺灣博碩士論文加值系統

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 本文研究的目的在於利用數值方法模擬在三維封閉矩形內的自然對流與熱傳導，數值方法是以上風的有限體積法來求解三維Navier-Stokes equation，在連續方程式中加入人工壓縮因子（artificial compressibility）及壓力對時間的微分項，其中對流項採用高階的上風有限體積法，進而利用DDADI數值法對時間積分，並加入隱式殘值平滑性（implicit residual smoothing）加速穩態計算的收斂性。 在物理模型方面應用於一導熱基板上鑲有三塊通有一均勻熱通量並充滿工作流體為空氣的三維封閉矩形，晶片用不同的排列方式鑲於傳導基板上(垂直、水平與平躺)。主要模擬雷利數、基板與晶片的熱傳導係數對三維封閉矩形內的自然對流與晶片和基板間熱效應的影響。
 A numerical method is developed to investigate the three-dimensional conjugate heat transfer of natural convection and conduction problems in a cubic enclosure. The Rayleigh number is selected between 10 to10 . The numerical method applied a finite-volume technique to solve the three -dimensional steady Navier-Stokes equations. The artificial compressible method, a third-order upwind finite volume method, DDADI time integration and an implicit residual smoothing were applied in the numerical method to achieve a higher-order accurate method. In this article, we are concerned with the three-dimensional iterative- coupled heat conduction-convection problem for three heated chips mounted on a conductive substrate in a cubic enclosure filled with air. The chips are assumed to have uniform properties, with internal heat generation rate of Q [W], are mounted by different arrangements (Vertical, Horizontal, and Bottom). The main objective of the present work is to simulate the effect of Rayleigh number and substrate thermal conductivity on the three-dimensional natural convection flow within the cubic and on the heat transfer from the chips.
 目 錄中文摘要…………………………………………………Ⅰ英文摘要…………………………………………………………Ⅱ致 謝…………………………………………………………Ⅲ目 錄…………………………………………………………Ⅳ圖表目錄…………………………………………………Ⅶ符號說明………………………………………………ⅩⅡ第一章 緒 論…………………………………………1第二章 數值方法…………………………………………52.1 統御方程式……………………………………………52.2空間差分………………………………………………62.3時間積分………………………………………………112.4 DDADI數………………………………………………112.5邊界條件………………………………………………142.5.1固體邊界條件………………………………………142.5.2流入及流出的邊界條件……………………………142.6數值方法加速收斂……………………………………152.7熱傳導方程式…………………………………………152.7.1熱傳方程式…………………………………………152.7.2熱邊界條件…………………………………………162.8收斂標準………………………………………………172.9格點系統………………………………………………18第三章 程式驗證………………………………………193.1三維封閉立方體內的自然對流………………………193.1.1絕熱壁………………………………………………193.1.2線性壁………………………………………………233.2封閉矩形內自然對流與熱傳…………………………253.3封閉閉矩形內自然對流與熱傳結……………………28第四章 結果與討論………………………………………304.1三維立方體內基板上晶片組的熱傳與自然對流……304.1.1垂直排列……………………………………………314.1.2水平排列……………………………………………334.1.3平面排列……………………………………………354.2 不同排列晶片組的比較與分析……………………374.3雷利數之影響分析……………………………………394.4 熱傳導係數之影響分析……………………………40第五章 結論………………………………………………41參考文獻…………………………………………………42圖…………………………………………………………46表…………………………………………………………95自述………………………………………………………97著作權聲明………………………………………………98
 1. Davis V., 1983, “Natural Convection of Air in a square Cavity: A Bench mark Numerical Solution,” International Journal Numerical Methods Fluids, Vol. 3, pp. 249-264.2. Markatos, N. C. and Pericleous, K.A., 1984, “Laminar and Turbulent Natural Convection in an Enclosed Cavity,” International Journal of Heat and Mass Transfer, Vol. 27, pp. 755-772.3. Keyhani, M., and Chen, L., 1994, ”The Aspect Ratio Effect on Natural Convection in an Enclosure with Protruding Heat Sources,” Transactions of the ASME, Vol. 113, pp. 883-891.4. Ho, C.J., and Chang, J. Y., 1994, ”A study of Natural Convection Heat Transfer in A Vertical Rectangular Enclosure with Two-Dimensional Discrete Heating: Effect of Aspect Ratio,” International Journal of Heat and Mass Transfer, Vol. 37, pp. 917-925.5. House, J. M., and Christoph Beckermann, 1990, ”Effect of A Centered Conducting Body on Natural Convection Heat Transfer in an Enclosure,” Numerical Heat Transfer, Part A, Vol. 18.6. 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