# Interdisciplinary Applied Mathematics

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profile and mass flowrate for pipe and duct flows.

In Chapter 5 we consider heat transfer in gas microflows. In the first section we concentrate on the thermal creep (transpiration) effects that may be important in channels with tangential temperature gradients on their surfaces. We also study other temperature-induced flows and investigate the validity of the heat conduction equation in the limit of zero Knudsen number. In the second and third sections we investigate the combined effects of thermal creep, heat conduction, and convection in pressure-, force-, and shear-driven channel flows.

In Chapter 6 we consider rarefied gas flows encountered in applications other than simple microchannels. In the first section, we present the lubrication theory and its application to the slider bearing and squeezed film problems. In the second and third sections, we consider separated flows in internal and external geometries in the slip flow regime in order to investigate the validity of continuum-based slip models under flow separation. In the fourth section, we present theoretical and numerical results for Stokes flow past a sphere including rarefaction effects. In the fifth section we summarize important results on gas flows through microfilters used for capturing and detecting airborne biological and chemical particles. In the last section, we consider high-speed rarefied flows in micronozzles, which are used for controlling the motion of microsatellites.

In Chapter 7 we present basic concepts and a mathematical formulation of microflow control and pumping using electrokinetic effects, which do not require any moving components. We cover electroosmotic and electrophoretic transport in detail both for steady and time-periodic flows, and we discuss simple models for the near-wall flow. We also present dielectrophoresis, which enables separation and detection of similar size particles based on their polarizability.

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