本論文中，我們針對平行平板微渠道內穩態氣體傳輸現象提出一合理可行的分析方法，所探討的傳輸驅動機構包含了壓力驅動流與浮力驅動流。應用Navier-Stokes方程式、能量方程式、滑動速度與不連續溫度牆表面條件及動壓力入口條件，我們完成了發展流與完全發展流之流場型態的模式建立。其中牆表面速度與溫度條件係經由Maxwell-Smoluchowski一階關係式與線性化Burnett本構方程式推導獲得，入口壓力條件係經由流線動量方程式推導獲得；完全發展近似解係利用解析法或半解析法推導獲得，發展解係利用前進隱含法(marching implicit method, MI)模擬獲得。本論文發展的數學模式與數值程序，在與可利用的實驗結果比較後，其合理性獲得驗證。
我們求解不同微渠道長度下，速度滑動、溫度不連續、速度、壓力、溫度、質流率、流阻及熱傳率。分析結果發現，微渠道長度對熱流場具顯著效應。此長度效應對壓力驅動流而言，質流率及平均流阻減少；對浮力驅動流而言，質流率及平均流阻則增加，而平均熱傳率減少。所有的熱流場特性皆隨長度增加而接近完全發展近似解。在長度達一充分大的值時，熱流場可處在完全發展條件，結果顯示此現象可藉由工作環境的調整使其效應更顯著。對壓力驅動流而言，例如升高Knudsen數(分子平均自由路徑與渠道特徵長度的比)或工作溫度，或降低開口端壓力降參數(為一描述入口至出口壓力降的無因次數)；對浮力驅動流而言，例如降低Knudsen數或Eckert數(為一描述牆溫度或熱潛的無因次數)。
我們亦詳細討論微流體系統中氣體傳輸時的稀薄化(rarefaction)、可壓縮性(compressibility)及熱潛(thermal creep)等現象。分析結果發現，這些傳輸現象對流場或熱場具顯著效應。稀薄化及熱潛效應使得質流率增加，並且獲得有價值的流阻降低及熱傳放大。當可壓縮性被考慮時，體積流率及局部流阻隨著流線位置的增加而增加。

In this study, we present a realistic analysis methodology for simulating steady gas transport in parallel-plate microchannels. Both of the pressure and the buoyancy driving mechanisms are considered. The flow patterns with respect to developing and fully developed flows are modeled by the Navier-Stokes equations and energy equation combined with the boundary conditions with respect to slip velocity and jump temperature along the wall surfaces as well as dynamic pressure at the entrance. The wall-surface conditions are obtained from the Maxwell-Smoluchowski first-order relations and the linearized Burnett constitutive equations, and the pressure condition is derived by the stream-wise momentum equation. The fully developed asymptote model is analytically or semi-analytically obtained, and the developing-flow simulation is implemented by using a marching implicit (MI) procedure. The mathematical model and the numerical code are validated through available experimental work.
Solutions of the slip, the jump, the velocity, the pressure, the temperature, the mass flow rate, the flow drag, and the heat transfer rate for different channel lengths are presented. Results reveal that channel length has significant effect on the flow and thermal fields. The length effect is to decrease the mass flow rate and the average flow drag for pressure-driven flow and to increase the mass flow rate and the average flow drag and decrease the average heat transfer rate for buoyancy-driven flow. Moreover, all of the characteristic values approach their fully developed asymptotic solutions. Fully developed conditions can be achieved for a sufficiently long channel. Such phenomenon could be enhanced by increasing the value of the Knudsen number (the ratio of the molecular mean free path to the characteristic length) or the working temperature or decreasing the value of an end-pressure-drop parameter (a dimensionless number characterizing the pressure drop from the entrance to the exit) for pressure-driven flow and by decreasing the value of the Knudsen number or the Eckert number (a dimensionless number characterizing the wall temperature or the thermal creep) for buoyancy-driven flow.
The phenomena of rarefaction, compressibility, and thermal creep in gas transport are discussed in detail. It is found that these phenomena have significant effects on the flow or thermal fields. The effects of rarefaction and creep are to increase the mass flow rate; moreover, valuable reduced flow drag and enhanced heat transfer are obtained. As the effect of compressibility is considered, we obtain increasing volume flow rate and local flow drag along the stream-wise location.

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