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研究生:蔡佳儒
研究生(外文):Chia-Ju Tsa
論文名稱:在微面板加熱的熱剪應力感測器的熱傳數值模擬
論文名稱(外文):Numerical Simulation of Heat Transfer on Micro-Plate Thermal Shear Stress Sensor
指導教授:林三益林三益引用關係
指導教授(外文):San-Yih Lin
學位類別:碩士
校院名稱:國立成功大學
系所名稱:航空太空工程學系碩博士班
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:2008
畢業學年度:96
語文別:中文
論文頁數:97
中文關鍵詞:邊界層熱剪應力
外文關鍵詞:boundary layerThermal Shear Stress Sensor
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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 I
Abstract II
致 謝 III
目錄 IV
圖目錄 VI
符號說明 IX
第一章 緒論 1
1.1 前言 1
1.2 內容大綱 3
第二章 數值方法 6
2.1 統御方程式 6
2.2 壓力場和速度場之數值方法 7
2.2.1 流場之有限體積法 8
2.2.2 擴散項(Diffusive Terms) 11
2.2.3 時間積分 12
2.2.3.1 穩態公式(Steady-State Formulation) 12
2.2.3.2 非穩態公式(UnSteady-State Formulation) 14
2.3 溫度場之有限差分法 14
2.4 邊界條件 15
2.4.1 固體邊界條件: 15
2.4.2 流入及流出的邊界條件: 15
2.5 收斂標準 16
第三章 程式驗證 18
3.1 平板層流: 18
3.2 溫度邊界層: 20
第四章 結果與討論 22
4.1 穩態流場 23
4.2 非穩態流場 26
第五章 結論 36
參考文獻 38
自述 97
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