Interdisciplinary Applied Mathematics

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4.1 Slip Flow Regime


In this section, we present pressure-driven isothermal adiabatic flows. While the adiabatic flows are treated using Fanno flow theory, the isothermal flows are studied using compressible Navier-Stokes equations subject to the slip models presented in Chapter 2. We give comparisons of the numerical results with    the    available    experimental    data.    Due    to    some scatter    in    exper


imental measurements, we further validate the continuum-based slip flow results, using the DSMC method and solutions of the linearized Boltzmann equation (see Chapter 15). This approach enables pointwise comparisons between the fundamentally different atomistic and continuum simulation models. Finally, we discuss the surface roughness effects and present results of inlet flow simulations.

4.1.1 Isothermal Compressible Flows


We consider two-dimensional isothermal flow between two parallel plates of length L, separated a distance h apart, where L/h ^ 1. The flow is sustained by    a pressure    drop    from    inlet    (i)    to outlet    (o)    of    the channel


(ДР = Pi — Po). Since the channel thickness h is fixed, the equation of conservation of mass can be simplified as


piui — pouo?


where p and u denote the channel averaged density and velocity, respectively. The momentum equation in the streamwise direction results in


(Pi — Po)h — 2Lt — M(uo — ui).    (4.1)


The pressure, density, and velocity are averaged across the channel at respective streamwise locations. The shear stress (denoted by t) is also averaged, but along the streamwise direction. The mass flowrate (per unit channel width) is denoted by M.


If we divide the momentum equation by (hPo), we obtain


(Pi — Po) _ AP _    I M(uo — ui)

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