Rarefied gas motion in a short planar channel over the entire knudsen number range

1990 ◽  
Vol 30 (5) ◽  
pp. 713-717 ◽  
Author(s):  
V. D. Akin'shin ◽  
A. M. Makarov ◽  
V. D. Seleznev ◽  
F. M. Sharipov
Keyword(s):  
Knudsen Number ◽  
Rarefied Gas ◽  
Planar Channel ◽  
Number Range

On the Rarefied Gas Flow in Pipes

2005 ◽  
Author(s):  
Vladan D. Djordjevic
Keyword(s):  
Knudsen Number ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Natural Extension ◽  
Slip Boundary Condition ◽  
Molecular Flow ◽  
Rarefied Gas Flow ◽  
Number Range ◽  
Average Value ◽  
Linearized Boltzmann Equation

Rarefied gas flow in a pipe is treated in the paper by modeling the slip boundary condition by means of a fractional derivative. At that the order of the derivative is conveniently chosen to be a function of the average value of the Knudsen number so that the entire Knudsen number range, from continuum flow to free molecular flow, is covered. Very good agreement with the solutions of linearized Boltzmann equation is achieved. The paper represents a natural extension of the work of the same author on the rarefied micro channel flow, published earlier.

Plane Thermal Transpiration of a Rarefied Gas Between Two Walls of Maxwell-Type Boundaries With Different Accommodation Coefficients

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Toshiyuki Doi
Keyword(s):  
Boltzmann Equation ◽  
Mass Flow Rate ◽  
Knudsen Number ◽  
Mass Flow ◽  
Flow Rate ◽  
Poiseuille Flow ◽  
Rarefied Gas ◽  
Thermal Transpiration ◽  
Wide Range ◽  
Accommodation Coefficients

Plane thermal transpiration of a rarefied gas between two walls of Maxwell-type boundaries with different accommodation coefficients is studied based on the linearized Boltzmann equation for a hard-sphere molecular gas. The Boltzmann equation is solved numerically using a finite difference method, in which the collision integral is evaluated by the numerical kernel method. The detailed numerical data, including the mass and heat flow rates of the gas, are provided over a wide range of the Knudsen number and the entire range of the accommodation coefficients. Unlike in the plane Poiseuille flow, the dependence of the mass flow rate on the accommodation coefficients shows different characteristics depending on the Knudsen number. When the Knudsen number is relatively large, the mass flow rate of the gas increases monotonically with the decrease in either of the accommodation coefficients like in Poiseuille flow. When the Knudsen number is small, in contrast, the mass flow rate does not vary monotonically but exhibits a minimum with the decrease in either of the accommodation coefficients. The mechanism of this phenomenon is discussed based on the flow field of the gas.

Effect of Rarefaction, Dissipation, and Accommodation Coefficients on Heat Transfer in Microcylindrical Couette Flow

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Latif M. Jiji
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Couette Flow ◽  
Knudsen Number ◽  
Slip Flow ◽  
Accommodation Coefficient ◽  
Rotating Shaft ◽  
Number Range ◽  
Accommodation Coefficients

This paper examines the effects of rarefaction, dissipation, curvature, and accommodation coefficients on flow and heat transfer characteristics in rotating microdevices. The problem is modeled as a cylindrical Couette flow with a rotating shaft and stationary housing. The housing is maintained at uniform temperature while the rotating shaft is insulated. Thus, heat transfer is due to viscous dissipation only. An analytic solution is obtained for the temperature distribution in the gas filled concentric clearance between the rotating shaft and its stationary housing. The solution is valid in the slip flow and temperature jump domain defined by the Knudsen number range of 0.001<Kn<0.1. The important effect of the momentum accommodation coefficient on velocity reversal and its impact on heat transfer is determined. The Nusselt number was found to depend on four parameters: the momentum accommodation coefficient of the stationary surface σuo, Knudsen number Kn, ratio of housing to shaft radius ro∕ri, and the dimensionless group [γ∕(γ+1)](2σto−1)∕(σtoPr). Results indicate that curvature, Knudsen number, and the accommodation coefficients have significant effects on temperature distribution, heat transfer, and Nusselt number.

Mass Flow Rate Measurements: From Hydrodynamic to Free Molecular Regime

2008 ◽  
Author(s):  
Timothe´e Ewart ◽  
Irina A. Graour ◽  
Pierre Perrier ◽  
J. Gilbert Me´olans
Keyword(s):  
Mass Flow Rate ◽  
Knudsen Number ◽  
Mass Flow ◽  
Flow Rate ◽  
Stationary Flow ◽  
Small Mass ◽  
Accommodation Coefficient ◽  
Navier Stokes ◽  
Number Range ◽  
Free Molecular Regime

An experimental investigation in a single silica microtube in isothermal stationary flow for various gases is made from the hydrodynamic to the near free molecular regime to study the reflection/accommodation process at the wall. This kind of investigation requires, more than other Micro-Electro-Mechanical-Systems (MEMS) experiments, a powerful experimental platform to measure very small mass flow rate. A global analytic expression, based on the Navier-Stokes (NS) equations with second order boundary conditions, is used to yield the Tangential Momentum Accommodation Coefficient (TMAC) in 0.003–0.3 Knudsen number range. Otherwise, the experimental results of the mass flow rate is compared with theoretical values calculated from kinetic approaches using variable TMAC as fitting parameter over the 0.3–30 Knudsen number range. Finally, whatever the theoretical approach the TMAC values obtained from the different gas-surface pairs are rather close one to other, but the TMAC values seem decreasing when the molecular mass increases.

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