Collision limited reaction rates for arbitrarily shaped particles across the entire diffusive Knudsen number range

2011 ◽  
Vol 135 (5) ◽  
pp. 054302 ◽  
Author(s):  
Ranganathan Gopalakrishnan ◽  
Thaseem Thajudeen ◽  
Christopher J. Hogan
Keyword(s):  
Knudsen Number ◽  
Reaction Rates ◽  
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.

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.

Rarefaction, Temperature Jump, and Viscous Dissipation Effects on Heat Transfer in Rotating Micro Devices

2006 ◽  
Author(s):  
Latif M. Jiji
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Viscous Dissipation ◽  
Knudsen Number ◽  
Temperature Jump ◽  
Slip Flow ◽  
Fluid Temperature ◽  
Rotating Shaft ◽  
Number Range ◽  
Rotating Surface

This paper examines the effects of rarefaction and dissipation on flow and heat transfer characteristics in rotating micro devices. The housing is assumed to be at uniform temperature while the rotating surface is insulated. Thus heat generation and transfer are due to viscous dissipation only. An analytic solution is obtained for the velocity and temperature distribution in the gas filled concentric clearance between a 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 Kn < 0.1. The Nusselt number was found to depend on three parameters: the Knudsen number Kn, ratio of housing to shaft radius ro / ri, and Prandtl number-specific heat ratio group γ/(γ + 1) Pr. Results indicate that curvature and Knudsen number have significant effect on the Nusselt number. However, fluid temperature rise due to dissipation is negligible.

Mass Flow Rate Measurement Through Rectangular Microchannels for Large Knudsen Number Range

2011 ◽  
Author(s):  
M. Hadj Nacer ◽  
Pierre Perrier ◽  
Irina Graur
Keyword(s):  
Boundary Condition ◽  
Mass Flow Rate ◽  
Knudsen Number ◽  
Mass Flow ◽  
Flow Rate ◽  
Stokes Equations ◽  
Rectangular Cross Section ◽  
Velocity Slip ◽  
Bgk Model ◽  
Number Range

The mass flow rate through microchannels with rectangular cross section is measured for the wide Knudsen number range (0.0025–26.2) in isothermal steady conditions. The experimental technique called ‘Constant Volume Method’ is used for the measurements. This method consists of measuring the small pressure variations in the tanks upstream and downstream of the microchannel. The measurements of the mass flow rate are carried out for three gases (Helium, Nitrogen and Argon). The microchannel internal surfaces are covered with a thin layer of gold with mean roughness Ra = 0.87nm (RMS). The continuum approach (Navier-Stokes equations) with first order velocity slip boundary condition was used in the slip regime (Knudsen number varies from 0.0025 to 0.1) to obtain the experimental velocity slip and accommodation coefficients associated to the Maxwell kinetic boundary condition. In the transitional and near free molecular regimes the linearized kinetic BGK model was used to calculate numerically the mass flow rate. From the comparison of the numerical and measured values of the mass flow rate the accommodation coefficient was also deduced.

Mass flow rate measurements in a microchannel, from hydrodynamic to near free molecular regimes

2007 ◽  
Vol 584 ◽  
pp. 337-356 ◽  
Author(s):  
TIMOTHÉE EWART ◽  
PIERRE PERRIER ◽  
IRINA A. GRAUR ◽  
J. GILBERT MÉOLANS
Keyword(s):  
Mass Flow Rate ◽  
Knudsen Number ◽  
Mass Flow ◽  
Flow Rate ◽  
Single Channel ◽  
Number Range ◽  
Free Molecular Regime ◽  
First Order ◽  
Slip Regime ◽  
Accommodation Process

Helium mass flow rates in a microchannel were measured, for a wide Knudsen-number range, in isothermal steady conditions. The flow Knudsen numbers, considered here, cover the range from continuum slip regime to the near free molecular regime. We used a single-channel system involved in an experimental platform more powerful than those previously used. The experimental errors and uncertainties were accurately investigated and estimated. In the continuum slip regime, it was found that the first-order approach is pertinent for Knudsen number between 0.03 and 0.3. Moreover, the slip coefficient was deduced by comparing the experiments with the theoretical first-order slip continuum approach. For Knudsen number between 0.03 and 0.7, a polynomial second-power form is proposed for the mass flow rate expression. Otherwise, the experimental results on the mass flow rate were compared with theoretical values calculated from kinetic approaches over the 0.03–50 Knudsen number range, and an overall agreement appears through the comparison. It was also found, when the Knudsen number increased, that the wall influence on measurement occurred first through the accommodation process in the transition regime followed by the wall influence through the aspect ratio in the free molecular regime.

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
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