Interdisciplinary Applied Mathematics

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The heat flux necessary to maintain this condition is



(l + 2Kn)2

The temperature variation for a microchannel without thermal creep effects is    also    given    in    Figure    5.14    (bottom).    This result    suggests    that    the

temperature of the insulated surface will be smaller than its counterpart modeled by the continuum theory.

Remark: The results presented in this section assume small temperature and pressure fluctuations compared to the reference pressure and temperature. However, planar shear-driven channels have zero pressure gradient. Thus, the only limitation on the incompressibility assumption is small temperature fluctuations, which is satisfied, since AT « O(1) in this study.


Prototype Applications of Gas Flows

In this chapter we consider rarefied gas flows encountered in applications other than simple microchannels. In the first section, we consider the lubrication theory, focusing mainly on the slider bearing and squeezed film problems. The slider bearing problem is relevant for magnetic storage units, where the head levitates about 50 nm above the media, corresponding to transition flow regime. The squeezed film flows are important for design of micromechanical accelerometers, where the gas is used as the damping medium, and the desired frequency response is obtained by controlling carefully the gas pressure.

In the second and third sections, we consider separated flows in internal and external geometries in the slip flow regime. To this end, we employ continuum modeling in conjunction with slip effects. The objective of this study is to investigate the validity of continuum-based slip models under flow separation. Such conditions are encountered in typical components of microsystems such as microchannels and microprobes, as well as in low-pressure applications, e. g., flow inside instruments operating at high altitude.

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