Interdisciplinary Applied Mathematics

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pressure drop of the rough channels, the viscosity in the smooth channel should increase by about 18.7%; this case corresponds to Re = 0.37 and Kn = 0.2 at the exit of the channel. Continuum flows do not depend on the details of the roughness, but for rarefied flows, as the Knudsen number increases, the roughness effect becomes more significant. In other words, microflows have “memory” in that they remember their trajectory and specific path, which is geometry-dependent. With respect to the latter, the results we obtained are inconclusive, and new computations are required to support this concept.

4.1.5 Inlet Flows

We consider next the flow between stationary parallel plates at the inlet of a microchannel as a prototype developing flow. In this analysis the compressibility effects are neglected, and the effect of rarefaction on developing flows is presented. A uniform velocity profile is specified at the inlet. Gampert analyzed the inlet flows using a vorticity-streamfunction formulation and presented results for different values of the Reynolds and Knudsen

Streamwise Distance (Dimensionless)    Streamwise Distance (Dimensionless)

FIGURE 4.13. Upper: Channel with “regularized” wall roughness. Lower: Total pressure distribution    (left)    and    deviations    from    linear    pressure    drop    (right)    for

rough and smooth channels. The flowrate is constant for all cases. The case described as “smooth 1.187” corresponds to smooth channel flow with 18.7% enhanced viscosity compared to all other cases.

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