本文是利用FEMLAB軟體（依據有限元素法）模擬可壓縮氣體在微流道（平行板以及圓管）的熱流特性和物理效應，並與解析解、實驗數據以及他人的數值結果比對。馬赫數與雷諾數分別介於0.5×10-3<Ma<0.84以及10-3<Re<800，而克德森數之計算範圍則是包括滑動流與過渡流滑動(0.024<Kn<3.44)，管徑尺寸介於0.01μm~0.01m。
有鑒於前人（陳家勇, 2002）的數值解並未考慮邊界上不連續的滑動速度、溫度躍昇現象，使其數值解並不完備。因此，為補足前人在探討微管流物理效應之不足，除了滑動流之修正外，本文也考慮多重物理效應（稀薄效應、壓縮性、黏滯消散以及可逆功）對流場熱流特性的影響；而這些效應在傳統管多被忽略。同時利用三種滑動模式探討克德森數在落入過渡流後的速度與壓降分佈。由數值結果發現：1) 隨進口壓力的增加，非線性壓力分佈愈明顯；2) 滑動流之質量流率高於不可滑動流；3) 流體之壓縮性隨進口壓力增高而增大，加上流場並不會形成完全發展流，因此摩擦係數已不再是定值，而是局部馬赫數之函數；4) 隨管徑縮減，黏性耗散愈明顯；5) 當克德森數逐漸落入過渡流後，利用一階滑動邊條件所得之速度分佈會愈趨扁平，與兩種修正模式之差異也愈大，隨克德森數之增高此現象愈明顯，修正模式所得之速度分佈則仍是維持類似拋物線的型態。

This work studies the compressible gaseous flow in microchannels (diameter size ranging from 0.01 μm to 0.01 m) using the FEMLAB software. Simulations are performed by solving Navier-Stokes equations with modification wall boundary conditions (slip velocity and temperature jump). The flow regime simulated is from the slip flow upto the transitional flow, which consist of the following flow parameters: 0.224≦Kn≦3.44, 10-3≦Re≦800 and 0.5x10-3≦Ma≦0.84. In order to thoroughly analyze various physical effects in the microchannel flow, this work studies multiphysics effects (rarefaction, compressibility, viscous dissipation, reversible work) on the thermal-flow characteristics of the microchannel. Results reveal several interesting features: 1) as the inlet pressure increase, the streamwise nonlinear pressure distribution appears visibly; 2) the slip flow has a higher mass flowrate than that of the nonslip flow; 3) compressibility effect cause the local friction factor increases with increasing local Ma; 4) due to high velocity gradients in the microchannel flow, viscous dissipation and reversible work can not be neglected; 5) first-order slip velocity gives unrealistically over-prediction of velocity at transitional flow regime, and the new continuum based slip model is extended successfully to the transitional flow regime.

陳家勇，壓縮微管流的熱流分析，國立中央大學碩士論文，中壢市，2002。
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