# Interdisciplinary Applied Mathematics

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Level T (K)

9    301.06

8    300.927

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1    300

given in Figure 3.28. The increase in temperature in the middle of the channel is due to viscous heating resulting from large shear stresses in this low Reynolds number flow. The viscous heating effect for slip flow is less than that    of no-slip    flow    due    to    the    reduction    in    the    shear    stresses.    The

temperature of the gas at the wall is different from the prescribed wall temperature. Since the temperature of the fluid is higher in the middle of the channel, the channel loses heat. Therefore, the gas temperature is higher than the surface temperature due to the temperature jump. This may create a problem for gas microflow temperature measurements. Although the change in the temperature due to the viscous heating seems to be small in magnitude, the gradients in temperature (as seen by the contour density in Figure 3.28) can be quite large due to the small length scales associated with the microflows.

## 4

### Pressure-Driven Flows

In this Chapter we present models for pressure-driven gas flows in the slip, transition, and free-molecular flow regimes. We are particularly interested in microchannel, pipe, and duct flows, since such flows have primary engineering importance, and they also allow analytical solutions due to their simple geometry.    In    the first    section,    we    present    analysis    in    the    slip flow

regime. This is followed by an analysis in the transition and free-molecular flow regimes. In particular, in Section 4.2.2 we develop a unified flow model that can accurately predict the volumetric flowrate, velocity profile, and pressure distribution in the entire Knudsen regime for pipes and ducts, as well as the Knudsen minimum.

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