Abstract
The behaviour of monatomic and dilute gas is studied in the slip and early transition regimes using the extended macroscopic theory. The gas is confined within a two-dimensional microcavity where the longitudinal sides are in the opposite motion with constant velocity ±Uw. The microcavity walls are kept at the uniform and reference temperature T0. Thus, the gas flow is transported only by the shear stress induced by the motion of upper and lower walls. From the macroscopic point of view, the regularized 13-moment equations of Grad, R13, are solved numerically. The macroscopic gas proprieties are studied for different values of the so-called Knudsen number (Kn), which gives the gas-rarefaction degree. The results are compared with those obtained using the classical continuum theory of Navier-Stokes and Fourier (NSF).
Highlights
The technology of the Microelectromechanical Systems (MEMS) has greatly developed and they have wide areas of application [1,2,3]
The Knudsen number, in MEMS, is not sufficiently small to guarantee the validity of the Navier-Stokes and Fourier (NSF) equations and the processes in MEMS need to be modelled with more accurate transport models
The main goal of this paper is to investigate the behaviour of a dilute gas flow inducing only the longitudinal shear stress using the classical theory of NSF, with slip and jump boundary conditions, and the regularized 13-moment equations of Grad approaches
Summary
The technology of the Microelectromechanical Systems (MEMS) has greatly developed and they have wide areas of application [1,2,3] This fast growth of MEMS use is not followed enough by the physical understanding of rarefied gas flows in these microdevices. The so-called Knudsen number Kn ∼ λ/L of gas flow is in the slip-transition regimes range; that is, 0.001 < Kn ≤ 10 In this case, the conventional computational fluid dynamics (CFD) scheme, based on the classical Navier-Stokes and Fourier (NSF) equations, becomes inappropriate to describe the gas flow behaviour in MEMS devices. The direct simulation Monte Carlo (DSMC) is the largely kinetic method used to simulate a rarefied gas flow where the behaviour is mainly described by the Boltzmann equation [16] The accuracy of this method is proved by many previous studies especially with the actual computers capabilities. The Grad 13-moment equations are hyperbolic in nature, yielding finite
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