微機電系統(Micro-electromechanical Systems, MEMS)已在電子、機械、材料、光電等專業領域成功地整合。在此方面，微流體學(micro-fluidics) 扮演不可或缺的地位，因為在流場中幾何形狀的特徵長度大小經常是以微米的等級出現，造成微流道內的流體呈現相對稀薄的情況。以探討在滑移流領域之稀薄效應，本研究在流道壁面採用馬克斯威爾之滑移速度、溫度躍升和熱潛變邊界條件。為瞭解壓縮效應與稀薄效應，在四面體與稜鏡型混合網格上利用有限體積上風法求解可壓縮流三維連續拿維-史脫克方程式和能量方程式。沿著截面為圓形或梯形之微管道壁先建立稜鏡型網格，然後在流場中其他區域建構非結構四面體網格，首先探討圓形截面微管流，經由計算所得之速度分佈與相關文獻比較可確定本數值方法之準確性。對於梯形截面之微流道，在高馬赫數的稀薄流場中是無法形成完全發展流的，而且使用滑動邊界條件會使得流場的速度分佈趨向扁平，且使得流道上的切線剪應力變小，所以微管道流中的Poiseuille number會比一般流場要小。因壓縮效應使壓力分佈非線性化及稀薄效應的壓力分佈線性化可知，在稀薄流場中稀薄效應與壓縮效應是互相牽制的兩個作用。

The progression of Micro-electromechanical Systems, MEMS is successfully integrated into the professional field such as electronics, mechanics, materials, and optoelectronics, in this case, micro-fluidics plays an essential role. Due to the characteristic length of geometrical shape in flow field appear in the level of micrometer, the flow inside microchannel is relatively rarefaction. In view of traditional theory of continuum under the measurement of micronano, the theory is facing the difficulty of application. The article aims at producing a more practical three-dimension microchannel of trapezoid cross-section and analyzing how rarefaction effect and effect of compressibility interact in the spectrum of slip flow, by using Navier-Stokes Equation in relation to the boundary condition of slip flow and 3-D tetrahedral/ prismatic mesh system； Furthermore, it will establish a three-dimension numerical simulating system through which property of flow field is fast and accurately predicted. As the micro-fluidics-related statistic data is built, analysis of physic phenomenon and the characteristics of flow field is underway.

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