Couette flow with slip and jump boundary conditions

Marques, Wilson; Kremer, Gilberto M.; Sharipov, Felix

doi:10.1007/s001610050143

Cited by 67 publications

(26 citation statements)

References 4 publications

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“…The kinetic theory of gases [5,29,32,37,38] relates the tangential velocity slip at the wall u slip " Du| wall to the local shear through a series expansion in the mean free path k, or, equivalently, in the Knudsen number e = k/ L, where L is the reference length (i.e., the channel width). The general second-order slip condition is [5] …”

Section: Slip Velocitymentioning

confidence: 99%

Boundary conditions for the upwind finite difference Lattice Boltzmann model: Evidence of slip velocity in micro-channel flow

Sofonea

Sekerka

2005

Journal of Computational Physics

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Section: Slip Velocitymentioning

confidence: 99%

Boundary conditions for the upwind finite difference Lattice Boltzmann model: Evidence of slip velocity in micro-channel flow

Sofonea

Sekerka

2005

Journal of Computational Physics

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“…Equations (7)-(9) are the conservation laws for mass, momentum, and energy, where the values of s ij and q i are determined from their governing Eqs. (10) and (11). However, m ijk , R ij , and Á, appearing in Eqs.…”

Section: Governing Equations Of 13 Momentsmentioning

confidence: 95%

How Far Can 13 Moments Go in Modeling Microscale Gas Phenomena?

Barber

Emerson

2007

Nanoscale and Microscale Thermophysical Engineering

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The ability to capture nonequilibrium phenomena in rarefied gas flow using hydrodynamic models based on the Navier-Stokes-Fourier (NSF) equations and the regularized 13 moment equations (R13) are assessed. Results from the hydrodynamic models are compared against direct simulation Monte Carlo data obtained for planar Couette flow. The study shows that the R13 equations are able to capture the phenomenon of non-gradient heat flux up to a Knudsen number (Kn) of unity. In contrast, the NSF equations completely fail to predict this effect. For low Mach numbers, the R13 equations can reliably predict the temperature jump up to Kn = 1 and are also able to capture the correct trend at higher Mach numbers. However, the NSF equations can only provide an adequate description of the temperature jump for Kn , 0.25 and fail to exhibit the correct trend above this Knudsen number. For velocity slip, the R13 equations are in better agreement with the DSMC data but both hydrodynamic approaches fail to capture the nonlinearity of the velocity profile within the Knudsen layer. Overall, the R13 equations provide a much improved hydrodynamic description of the flow physics in the transition regime.

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“…Planar Couette flow represents a classical problem in rarefied gas dynamics and it has often been used to investigate features such as velocity-slip, temperature jump and Knudsen layers [32][33][34]. In the present study, the coordinates are chosen such that the upper plate moves with velocity u w in the x 1 direction and x 2 is the direction perpendicular to the plates.…”

Section: Calibration Of the Boundary Valuesmentioning

confidence: 99%