臺灣博碩士論文加值系統

現今，微流道在許多領域上都有所應用，因此微流道之特性值得深入研究。本論文主要是研究滑移邊界條件對微管內冪次律流體之電滲流的影響，透過電位場、動量方程式、能量方程式求得速度分布、溫度分布、紐塞爾數和摩擦係數等數值。其中的統御參數包括流動行為指數（n）、無因次化滑移長度（）、無因次化焦耳熱參數（S）及流道半徑與德拜長度之比值（Z）。
結果表示當流動行為指數(n)減少時，無因次化速度隨之增加。探討剪切稀化流體之情況，流道半徑與德拜長度比值（Z）值較小時，無因次化速度隨Z值增加而增加；當Z值較大時無因次化速度隨Z值增加而減少。當無因次滑移長度（）降低時，無因次化速度隨之減少。流道半徑與德拜長度比值（Z）值影響無因次化溫度之增加或減少取決於表面加熱或冷卻，且當Z值較大時，無因次化溫度便不因Z值而產生變化。
紐塞爾數在表面冷卻且流道半徑與德拜長度比值（Z）值足夠大時會產生奇異點。摩擦係數隨著Z值的增加而增加，而當Z值較大時摩擦係數隨著Z值的增加而減少，且無因次化滑移長度（）能夠有效降低摩擦係數。

Nowadays, Microfluidic channels have applications in a wide range of fields, therefore the momentum and thermal transport characteristics of microflows. This work mainly studies the influence of the slip boundary conditions on the electro-osmotic flow of power-law fluids in a microtube. The numerical results for velocity and temperature distributions, Nusselt number and friction coefficient are obtained by solving the potential field, momentum equation and energy equation. The governing parameters include the flow behavior index（n）,dimensionless slip length（）,dimensionless Joule heating parameter（S）and ratio of tube radius to Debye length（Z）.
The results show that when the flow behavior index（n）decreases, the dimensionless velocity profile increases. For shear thinning fluids, the dimensionless velocity profile increases with increasing the ratio of tube radius to Debye length（Z）when is Z small, while the opposite trend is observed when Z is sufficiently large. When the dimensionless slip length（）decreases, the dimensionless velocity profile decreases. An increase in the value of Z may increase or decrease the dimensionless temperature, depending on the thermal boundary conditions, i.e. surface heating or cooling. When Z is sufficiently large, the effect of Z on the dimensionless temperature becomes insignificant.
Also, singularities occur in the Nusselt number variations for surface cooling as Z value is sufficiently large. The friction coefficient increases with the increase of Z for small and moderate values of Z, but the friction coefficient decreases with increasing Z when it is large enough. Moreover, increasing the dimensionless slip length（）can effectively reduce the friction coefficient.

摘要.............i
Abstract.........ii
誌謝.............iv
目錄.............v
圖目錄...........viii
符號說明.........x
第一章 緒論.......1
1.1 前言..........1
1.2 研究動機與背景.........1
1.2.1 電雙層的形成與結構....1
1.3 文獻回顧...............2
1.4 論文架構...............4
第二章 理論分析.............5
2.1 物理模型...............5
2.2 冪律流體...............5
2.3 基本假設...............5
2.4 統御方程式與邊界條件....5
2.4.1 波松-波茲曼方程式（Poisson-Boltzmann equation）....6
2.4.2 柯西動量方程式（Cauchy momentum equation）.........6
2.4.3 能量方程式（Energy equation）......................6
第三章 分析方法.........7
3.1 電位場.............7
3.2 速度場.............8
3.3 溫度場.............10
3.3.1 壁面熱通量為定值....10
3.3.2 能量方程式的解法....10
第四章 結果與討論.........12
4.1 各參數對無因次化速度分布之影響.........12
4.1.1 流動行為指數對速度之效應.............12
4.1.2 流道半徑與德拜長度比值對速度之效應...12
4.1.3 無因次滑移長度對速度之效應..........13
4.2 各參數對無因次化溫度分布之影響.........13
4.2.1 流動行為指數對溫度之效應............13
4.2.2 流道半徑與德拜長度比值對溫度之效應....13
4.2.3 無因次化焦耳熱參數對溫度之效應........13
4.3 各參數對紐塞爾數之影響.................14
4.3.1 流道半徑與德拜長度比值對紐塞爾數之效應....14
4.3.2 無因次滑移長度對紐塞爾數之效應...........14
4.3.3 無因次化焦耳熱參數對紐塞爾數之效應........14
4.4 各參數對摩擦係數之影響.....................15
4.4.1 流道半徑與德拜長度比值對摩擦係數之效應.....15
4.4.2 無因次滑移長度對摩擦係數之效應............15
第五章 結論與未來展望...........16
5.1 結論...........16
5.1.1 速度分布.....16
5.1.2 溫度分布.....16
5.1.3 紐塞爾數.....17
5.1.4 摩擦係數.....17
5.2 未來展望.......18
參考文獻...........19
附錄...............23
Extended Abstract..40

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