臺灣博碩士論文加值系統

本研究旨在探討具有高壁面電位的微渠道中，電滲和壓力共同驅動的流體流動中的熱傳遞現象。本文採用非傳統使用的方法，即通過求解完整的Poisson-Boltzmann方程來準確地決定電雙層中的電位分佈，而非使用常見的線性Debye-Hückel近似方法。在動量方程中考慮了電雙層效應產生的電動力和外部施加的壓力梯度，並求解出速度分佈的表達式。同時在能量方程式的求解中考慮了焦耳熱和粘性耗散的影響。一旦獲得速度和溫度的分佈情況，便可以利用這些結果計算微渠道中全展流之紐塞爾數。本文將詳細探究長度尺度比和高壁面電位強度對紐塞爾數的影響。

This study aims to investigate the heat transfer phenomena in fluid flow driven by combined electro-osmotic and pressure force in a microchannel with walls charged with a high zeta potential. A non-conventional approach is employed, which accurately determines the potential distribution in the electrical double layer by solving the complete Poisson-Boltzmann equation instead of using the common linear Debye-Hückel approximation. The momentum equation considers the electrodynamic force generated by the electrical double layer and the externally applied pressure gradient, resulting in the expression for the velocity distribution. The energy equation takes into account the effects of Joule heating and viscous dissipation. Once the velocity and temperature distributions are obtained, the Nusselt number for fully developed flow in microchannels can be calculated using these results. Effects of the length scale ratio and the strength of the zeta-potential on the Nusselt number was investigated in depth.

摘要..........i
Abstract..........ii
目錄..........iii
圖次..........vi
符號說明..........viii
第一章 緒論..........1
1.1 前言..........1
1.2 研究動機與背景..........1
1.2.1微渠道流中電雙層與電滲流之形成與效應..........1
1.3 文獻回顧..........3
1.4 論文架構..........4
第二章 理論分析..........5
2.1 物理模型..........5
2.2 基本假設..........5
2.3 統御方程式與邊界條件..........5
2.3.1 波松-波茲曼方程式（Poisson-Boltzmann equation）..........5
2.3.2 柯西動量方程式（Cauchy momentum equation）..........6
2.3.3 能量方程式（Energy equation）..........6
第三章 分析方法..........8
3.1 電位場..........8
3.2 速度場..........8
3.3 溫度場..........9
第四章 結果與討論..........11
4.1 各參數對速度場之影響..........11
4.1.1 壁面電位之效應..........11
4.1.2 微渠道半高與德拜長度比值之效應..........11
4.1.3 壓力梯度之效應..........11
4.2 各參數對溫度場之影響..........12
4.2.1 壁面電位之效應..........12
4.2.2 微渠道半高與德拜長度比值之效應..........12
4.2.3 壓力梯度之效應..........12
4.2.4 焦耳熱之效應..........13
4.2.5 黏性耗散之效應..........13
4.3 各參數對紐賽爾數之影響..........13
4.3.1 壁面電位之效應..........13
4.3.2 微渠道半高與德拜長度比值之效應..........13
4.3.3 焦耳熱之效應..........14
4.3.4 黏性耗散之效應..........14
第五章 結論與未來展望..........15
5.1 結論..........15
5.1.1速度分佈..........15
5.1.2溫度分佈..........16
5.1.3紐賽爾數..........17
5.2 未來展望..........18
附錄..........19
參考文獻..........40
EXTENDED ABSTRACT..........44

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