一些研究者比較了已發表的有關微流道摩擦及熱傳的實驗數據後，發現實驗數據與傳統大管道理論所預測的有相當差距，不同的實驗所得的結果差異很大，實驗結果的趨勢也不盡相同。有些研究者認為實驗數據與傳統大管道理論的差異可能是由下列的微尺寸效應所造成：溫度效應、壓縮效應、稀薄效應、黏滯消散、電滲效應、壁面粗糙度及實驗誤差等因素。此外，有些學者為了簡化分析與計算，皆假設熱導係數與黏滯係數為常數，而忽略了溫度變化對這些參數的影響，這也是造成差異的原因。
    本研究主要是針對三維不可壓縮層流長微流道中，溫度效應對液態流體流力與熱傳現象影響的探討，因此將研究重心放在摩擦與熱傳特性上。本研究發現受到溫度效應的影響，使得 較不考慮溫度效應時小，且黏滯係數改變進而造成雷諾數的變化較傳統大尺寸流道來得大，因此過渡區提早發生於雷諾數1200~1500之間，而增加管壁溫度或熱通量的輸入皆會使得磨擦因子降低。在熱傳方面，同樣受到溫度效應的影響，其熱傳效果較不考慮溫度效應時好，而深寬比越大，熱傳效果也越好。此外在溫度效應影響下，等溫壁面條件的Nusselt number會隨著雷諾數的加大而跟著增加，但固定熱通量條件的Nusselt number卻不會改變。
    而本研究利用簡化的Navier-Stokes方程式，來計算長微流道裡的摩擦與熱傳特性。本數值計算的優點，在於它的統御方程式是一個具有拋物線型特性的方程式，在求解速度上至少比完全 Navier-Stokes 方程式快上百倍到千倍。而此一快速及準確的研究工具將可幫助我們詳細的研究微流道中，因溫度效應造成流體性質變化所引起的種種現象。此外也可讓我們了解更多微流道中的現象及解釋實驗數據與傳統大管道理論的差異。

Several researchers have conducted careful reviews on the published experimental friction and heat transfer data in microchannels. They found that in many cases the experimental data of the friction factor and of the Nusselt number in Microchannels disagree with the conventional theories but they also appear to be inconsistent with one another. Also, the information in the literature does not point to unequivocal trends of variation or reasons of such trends. Some researchers proposed that the deviations between measured data and conventional predictions may be explained by the micro-scale effects. The following scaling effects in micro-flow devices can be identified: temperature effects, compressibility effects, rarefaction effects, viscous dissipation effects, electro-osmotic effects（EDL）, channel surface conditions and experimental errors.
  The objective of this research is to investigate numerically the effect of temperature on friction and heat transfer characteristics of incompressible flow in microchannels. It was found that the temperature effect reduces  . The reduction in viscosity due to rising temperature increases Reynolds number, so that transition was initiated at Re=1200~1500. Increasing wall temperature or heat flux reduces friction factor. In the heat transfer characteristics, the Nusselt number is increased by taking the temperature effect into account. Nusselt number also increases with increasing channel aspect ratio.
  The major advantage of the present numerical procedure is its fast speed due to the parabolic character of the governing equations. It is at least two to three orders of magnitude faster than the full Navier-Stokes simulation. The present numerical procedure can be a fast and accurate tool in studying long microchannels flows. It also provides some useful explanations on the differences between published experimental data and conventional theories and among experimental data themselves.

目錄 ..................................................... I
表目錄 ................................................. III
圖目錄 .................................................. IV
符號說明 ................................................. X

第一章  序論
1.1	研究背景與動機 ................................. 1
1.2	文獻回顧 ....................................... 3
1.3	研究目的 ....................................... 9

第二章  數值計算方法
2.1	水的物理性質 .................................. 11
2.2	統御方程式 .................................... 12
2.3	動量與能量方程式之計算方法 .................... 17
2.4	邊界條件及初始條件之定義 ...................... 26
2.5	數值計算流程 .................................. 28

第三章  數值模擬程式驗證
3.1   之數值驗證 ....................................... 31
3.2  Nusselt numbers（Nu）之數值驗證 ................... 33

第四章	結果與討論
4.1  溫度效應影響 ...................................... 40
4.2  摩擦特性 .......................................... 43
4.3  熱傳特性 .......................................... 47
   4.3.1  等溫壁面（Isothermal wall temperature）....... 47
   4.3.2  固定熱通量（Uniform heat flux）............... 50

第五章	結論與建議
5.1  結論 .............................................. 92
   5.1.1  基本參數 ..................................... 92
   5.1.2  摩擦特性 ..................................... 93
   5.1.3  熱傳特性 ..................................... 94
5.2  建議 .............................................. 95

參考文獻 ............................................... 96

表2-1：溫度關係式之各個常數 ............................ 11
表2-2：進口、出口與邊界條件的因次化設定 ................ 26
表3-1：f*Re之數值驗證的各參數設定 ...................... 37
表3-2：固定截面積為 ，壓差為1.001，不同深寬比（AR）條件下之 與數值解[27]驗證之比較 ................................. 37
表3-3：均勻熱通量（Uniform heat flux）條件下，Nusselt numbers（Nu）之數值驗證的各參數設定 .................... 38
表3-4：固定截面積為 ，壓差為1.0025，均勻熱通量（Uniform heat flux）條件下，不同深寬比（AR）之Nusselt number（Nu）與數值解[27]驗證之比較 ................................... 38
表3-5：等溫壁面（Isothermal wall temperature）條件下，Nusselt numbers（Nu）之數值驗證的各參數設定 ............ 39
表3-6：固定截面積為 ，壓差為1.00275，等溫壁面（Isothermal   wall temperature）條件下，不同深寬比（AR）之Nusselt number（Nu）與數值解[27]驗證之比較 ........................... 39
表4-1：溫度效應對微流道內速度、溫度及壓力等基本參數影響之邊界條件設定 ............................................. 53
表4-2：考慮與不考慮溫度效應時， 沿著流道管軸（x/L）比較之邊界條件設定 ............................................. 53
表4-3：等溫壁面（Isothermal wall temperature）、固定熱通量（Uniform heat flux）條件下，不同深寬比（AR）的摩擦因子（f）比較之邊界條件設定...................................... 54
表4-4：等溫壁面條件下，不同深寬比（AR）對Nusselt number（Nu）的影響之邊界條件設定 ............................. 54
表4-5：等溫壁面條件下，不同雷諾數（Re）對Nusselt number（Nu）的影響之邊界條件設定 ............................. 55
表4-6：固定熱通量條件下，不同深寬比（AR）對Nusselt number（Nu）的影響之邊界條件設定 ............................. 55
表4-7：固定熱通量條件下，不同雷諾數（Re）對Nusselt number（Nu）的影響之邊界條件設定 ............................. 56


圖2-1：三維微流道流場幾何及座標系統示意圖 .............. 12
圖2-2：速度條件示意圖 .................................. 27
圖2-3：溫度條件示意圖 .................................. 27
圖2-4：數值計算流程示意圖 .............................. 30
圖4-1：溫度效應對熱傳導係數的物理性質影響 .............. 57
圖4-2：溫度效應對黏滯係數的物理性質影響 ................ 58
圖4-3：溫度效應對流道內平均速度的影響 .................. 59
圖4-4：溫度效應對流道內平均溫度的影響 .................. 60
圖4-5：溫度效應對流道內壓力的影響 ...................... 61
圖4-6：溫度效應及不同壓力比的條件下，流道內之壓力分佈 .. 62
圖4-7：溫度效應對沿著流道軸向（x/L）之 的影響（Re=302）. 63
圖4-8：溫度效應對沿著流道軸向（x/L）之局部摩擦因子（f）的影響（Re=302）............................................ 64
圖4-9：溫度效應對沿著流道軸向（x/L）之局部雷諾數（f）的影響（Re=302）.............................................. 65
圖4-10：溫度效應對平均摩擦因子（f）與平均雷諾數（Re）之間關係的影響 ............................................... 66
圖4-11：高低兩種雷諾數（Re）沿著流道管軸（x/L）的比較 .. 67
圖4-12：等溫壁面（Isothermal wall temperature）條件下，不同深寬比（AR）與壁溫對平均摩擦因子的影響 ................. 68
圖4-13：固定熱通量（Uniform heat flux）條件下，不同深寬比（AR）與熱通量（Heat flux）對平均摩擦因子的影響 ........ 69
圖4-14：等溫壁面（Isothermal wall temperature）及有溫度效應條件下，不同深寬比（AR）對沿著流道軸向（x/L）之局部Nusselt number的影響 ........................................... 70
圖4-15：等溫壁面（Isothermal wall temperature）及有溫度效應條件下，不同深寬比（AR）對沿著流道軸向（x/L）之溫度分佈的影響 ..................................................... 71
圖4-16：等溫壁面（Isothermal wall temperature）及有溫度效應條件下，不同深寬比（AR）對沿著流道軸向（x/L）之溫差與溫度梯度的分佈 ............................................... 72
圖4-17：等溫壁面（Isothermal wall temperature）及有無溫度效應條件下，不同深寬比（AR）對沿著流道軸向（x/L）之局部Nusselt number的影響 ................................... 73
圖4-18：等溫壁面（Isothermal wall temperature）及有無溫度效應條件下，深寬比（AR）為2時，對沿著流道軸向（x/L）之溫度分佈的影響 ................................................. 74
圖4-19：等溫壁面（Isothermal wall temperature）及有無溫度效應條件下，深寬比（AR）為2時，對沿著流道軸向（x/L）之溫差與溫度梯度的分佈 ........................................... 75
圖4-20：等溫壁面（Isothermal wall temperature）及有溫度效應條件下，不同雷諾數（Re）對沿著流道軸向（x/L）之局部Nusselt number的影響（AR=1）.................................... 76
圖4-21：等溫壁面（Isothermal wall temperature）及有溫度效應條件下，不同雷諾數（Re）對沿著流道軸向（x/L）之溫度分佈的影響（AR=1）.............................................. 77
圖4-22：等溫壁面（Isothermal wall temperature）及有無溫度效應條件下，不同雷諾數（Re）對沿著流道軸向（x/L）之局部Nusselt number的影響（AR=1）............................ 78
圖4-23：等溫壁面（Isothermal wall temperature）及無溫度效應條件下，不同雷諾數（Re=403、1070）對沿著流道軸向（x/L）之溫差與溫度梯度的分佈（AR=1）.............................. 79
圖4-24：等溫壁面（Isothermal wall temperature）及有溫度效應條件下，不同雷諾數（Re=406、1069）對沿著流道軸向（x/L）之溫差與溫度梯度的分佈（AR=1）.............................. 80
圖4-25：等溫壁面（Isothermal wall temperature）及溫度效應條件下，雷諾數（Re）與局部Nusselt number之間的關係（AR=1). 81
圖4-26：固定熱通量（Uniform heat flux）及有溫度效應條件下，不同深寬比（AR）對沿著流道軸向（x/L）之局部Nusselt number的影響 ................................................... 82
圖4-27：固定熱通量（Uniform heat flux）及無溫度效應條件下，不同深寬比（AR）對沿著流道軸向（x/L）之局部Nusselt number的影響 ................................................... 83
圖4-28：固定熱通量（Uniform heat flux）及有無溫度效應條件下，深寬比（AR）為2時，對沿著流道軸向（x/L）之溫度分佈 . 84
圖4-29：固定熱通量（Uniform heat flux）及有無溫度效應條件下，深寬比（AR）為2時，對沿著流道軸向（x/L）之溫差的影響.85
圖4-30：固定熱通量（Uniform heat flux）及有溫度效應條件下，不同雷諾數（Re）對沿著流道軸向（x/L）之局部Nusselt number的影響（AR=1）............................................ 86
圖4-31：固定熱通量（Uniform heat flux）及有溫度效應條件下，不同雷諾數（Re）對沿著流道軸向（x/L）之溫度分佈的影響（AR=1）................................................ 87
圖4-32：固定熱通量（Uniform heat flux）及有溫度效應條件下，不同雷諾數（Re）對沿著流道軸向（x/L）之溫差的比較（AR=1).88
圖4-33：固定熱通量（Uniform heat flux）條件，有無溫度效應影響之局部Nusselt number的比較（Re=421、AR=1）............ 89
圖4-34：固定熱通量（Uniform heat flux）及有無溫度效應條件下，沿著流道軸向（x/L）之溫度的分佈（Re=421、AR=1）..... 90
圖4-35：固定熱通量（Uniform heat flux）及有無溫度效應條件下，沿著流道軸向（x/L）之溫差（ ）分佈的比較（Re=421、AR=1）.................................................. 91

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