# 臺灣博碩士論文加值系統

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 本文研究目的在於利用數值方法模擬在二維平板層流上的剪應力與熱傳率的關係式。統御方程式是採用二維不可壓縮加入熱傳效應奈威爾－史托克方程式(Navier－Stokes equations)，並使用人工壓縮因子法（Artificial Compressibility Method）來求解此方程式。在流場方面，空間部分採用三階上風有限體積法，時間部分則是採用顯性二階郎奇－庫達法（Two-step Runge-Kutta Method），並結合虛擬時間τ（pesudo time）的方式去解一非穩態問題；在溫度場部分則是使用有限差分法和隱式時間法來計算。　　在物理問題，首先選取幾個例子：平板層流和溫度邊界層，來驗證本文數值方法之正確性。最後在平板層流上加入一位置固定且均勻熱量的晶片並以一流體通過達到散熱效果。主要模擬晶片在初始速度不同下，對剪應力與熱傳率的影響和探討之間的相互關係。經過一系列的模擬與驗證，在穩態流，吾人驗證剪應力和熱傳率的三次方成正比。而在非穩態流則必須要加入適當的修正項。
 A numerical method is applied to simulate the fluid fields in the two -dimensional flat-plate to investigate the relationship between the wall shear stress and the heat transfer rate. The governing equations are incompressible Navier-Stokes equations with the energy equation. The artificial compressibility method is applied to solve the flow fields. In the numerical method, the third-order upwind finite volume method is used to solve the convection term, the second order central difference scheme is used to solve the diffusive term, and a two-step Runge-Kutta method is applied to time matching. For the temperature field, a finite difference method with implicit time marching is used.　　In physical problems, first, the viscous flow past a flat plate and the viscous flow with the temperature boundary layer are simulated and verified. Finally, the flow and temperature fields of lay up a chip of heat on a flat-plate are simulated. The relationships between wall shear stress and heat-transfer rate under different velocities are investigated. About the relationships of shear stress and heat-transfer rate, it found that the wall shear stress is ratio to the cube of the heat-transfer rate for the steady-state flow. And the unsteady flow, two extra terms need to be added to the relationship.
 中文摘要 IAbstract II致　謝 III目錄 IV圖目錄 VI符號說明 IX第一章　緒論 1１.１　前言 1１.２　內容大綱 3第二章　數值方法 6２.１　統御方程式 6２.２　壓力場和速度場之數值方法 7２.２.１　流場之有限體積法 8２.２.２　擴散項（Diffusive Terms） 11２.２.３　時間積分 12２.２.３.１　穩態公式（Steady-State Formulation） 12２.２.３.２　非穩態公式（UnSteady-State Formulation） 14２.３　溫度場之有限差分法 14２.４　邊界條件 15２.４.１　固體邊界條件： 15２.４.２　流入及流出的邊界條件： 15２.５　收斂標準 16第三章　程式驗證 18３.１　平板層流： 18３.２ 溫度邊界層： 20第四章　結果與討論 22４.１　穩態流場 23４.２　非穩態流場 26第五章　結論 36參考文獻 38自述 97
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 1 以有限體積法探討流經圓柱渦漩曳放的壓抑現象 2 次臨界雷諾數下鈍型體非定常三維特性之研究

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