Solution of the linearized couette-flow problem in a rarefied gas by the integral-diffusion method

1966 ◽  
Vol 6 (2) ◽  
pp. 38-40 ◽  
Author(s):  
A. T. Onufriev
Keyword(s):  
Couette Flow ◽  
Flow Problem ◽  
Rarefied Gas ◽  
Diffusion Method

Modeling of Flow Characteristic and Heat Transfer for Micro Couette Flow

2001 ◽  
Author(s):  
Hong Xue ◽  
Ling Xie ◽  
S. K. Chou
Keyword(s):  
Heat Transfer ◽  
Couette Flow ◽  
Flow Characteristic ◽  
Rarefied Gas ◽  
Characteristic Length ◽  
Velocity Slip ◽  
Flow And Heat Transfer ◽  
Wide Range ◽  
Perturbation Velocity ◽  
Rarefaction Effects

Abstract Gaseous flow encountered in micro/nano electromechanical systems experiences change in Kn number across a wide range of flow regime due to variation in characteristic length in the system and significant compressibility of the rarefied gas. In this study, we attempt to develop a general, physics-based model to predict the flow and heat transfer in the slip and transition regimes. Such an extension is constructed on the fact that Chapman-Enskog’s approximation of the Boltzmann equation can be revised using a function of Kn number as a perturbation. Velocity slip and temperature jump at the solid boundaries are modified accordingly. Rarefaction effects on dynamic viscosity and thermal conductivity are considered. As a first step to evaluate the model, it is applied to the simplest shear-driven flow, micro Couette flow. Compared with the results of DSMC, satisfactory agreement has been achieved in a wide range of Kn and Ma numbers.

THE INFLUENCE OF SLIP AND JUMP BOUNDARY CONDITIONS ON THE CYLINDRICAL COUETTE FLOW

2002 ◽  
Vol 12 (03) ◽  
pp. 445-459 ◽  
Author(s):  
LILIANA M. GRAMANI CUMIN ◽  
GILBERTO M. KREMER ◽  
FELIX SHARIPOV
Keyword(s):  
Angular Velocity ◽  
Boundary Conditions ◽  
Couette Flow ◽  
Rarefied Gas ◽  
Thermodynamic Force ◽  
Heat Conducting ◽  
Field Equations ◽  
Viscous Stress Tensor ◽  
Heat Flux Vector ◽  
Cylindrical Couette Flow

The solution of the field equations of the cylindrical Couette flow problem for a rarefied gas is found when the state of equilibrium between the cylinders is perturbed by the following small thermodynamic forces: (i) a pressure difference; (ii) an angular velocity difference; and (iii) a temperature difference. The flow is analyzed within the framework of continuum mechanics by using the field equations that follow from the balance equations of mass, momentum and energy of a viscous and heat conducting gas. These equations are solved analytically by considering slip and jump boundary conditions. The fields of density, velocity, temperature, heat flux vector and viscous stress tensor are calculated as functions of the Knudsen number and of the angular velocity of the rotating cylinders for each thermodynamic force. The asymptotic behaviors of these fields are compared with those obtained from a kinetic model of the Boltzmann equation. The influence of the slip and jump boundary conditions on the solutions is also discussed.

Cylindrical Couette Flow of a Rarefied Gas

1967 ◽  
Vol 10 (6) ◽  
pp. 1200 ◽  
Author(s):  
Carlo Cercignani
Keyword(s):  
Couette Flow ◽  
Rarefied Gas ◽  
Cylindrical Couette Flow

The cylindrical couette flow of a rarefied gas consisting of charged particles inside walls with arbitrary reflection coefficients

1991 ◽  
Vol 69 (12) ◽  
pp. 1429-1440
Author(s):  
M. A. Mahmoud ◽  
G. A. Shalaby
Keyword(s):  
Shear Stress ◽  
Distribution Function ◽  
Reflection Coefficient ◽  
Couette Flow ◽  
Method Of Moments ◽  
Rarefied Gas ◽  
Charged Particles ◽  
Reflection Coefficients ◽  
Model Kinetic Equation ◽  
Cylindrical Couette Flow

A kinetic-theory treatment of the cylindrical Couette flow is considered. A generalization of the case of a surface with an arbitrary reflection coefficient that depends on the nature of the surface. In this paper we consider that the reflection coefficients of the inner and outer walls are different. A model kinetic equation of the BGK (Bhatnger–Gross–Krook) type is solved using the method of moments with a two-sided distribution function. The dependence of the velocity and shear stress on the reflection coefficient is obtained.

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