scholarly journals Erratum: ‘‘Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation’’ [Phys. Fluids A 2, 2061 (1990)]

1991 ◽  
Vol 3 (11) ◽  
pp. 2825-2825 ◽  
Author(s):  
S. K. Loyalka ◽  
S. A. Hamoodi
Keyword(s):  
Boltzmann Equation ◽  
Poiseuille Flow ◽  
Rarefied Gas ◽  
Cylindrical Tube ◽  
Linearized Boltzmann Equation

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.

Numerical Analysis of the Time-Dependent Energy and Momentum Transfers in a Rarefied Gas Between Two Parallel Planes Based on the Linearized Boltzmann Equation

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
Toshiyuki Doi
Keyword(s):  
Energy Transfer ◽  
Boltzmann Equation ◽  
Rarefied Gas ◽  
Numerical Data ◽  
Time Dependent ◽  
Sound Waves ◽  
Low Frequencies ◽  
Resonance Effects ◽  
Linearized Boltzmann Equation ◽  
Wide Range

Periodic time-dependent behavior of a rarefied gas between two parallel planes caused by an oscillatory heating of one plane is numerically studied based on the linearized Boltzmann equation. Detailed numerical data of the energy transfer from the heated plane to the unheated plane and the forces of the gas acting on the boundaries are provided for a wide range of the gas rarefaction degree and the oscillation frequency. The flow is characterized by a coupling of heat conduction and sound waves caused by repetitive expansion and contraction of the gas. For a small gas rarefaction degree, the energy transfer is mainly conducted by sound waves, except for very low frequencies, and is strongly affected by the resonance of the waves. For a large gas rarefaction degree, the resonance effects become insignificant and the energy transferred to the unheated plane decreases nearly monotonically as the frequency increases. The force of the gas acting on the heated boundary shows a remarkable minimum with respect to the frequency even in the free molecular limit.

Finite Element Solution for the Rarefied Gas Lubrication Problem

1988 ◽  
Vol 110 (2) ◽  
pp. 335-341 ◽  
Author(s):  
Masahiro Kubo ◽  
Y. Ohtsubo ◽  
N. Kawashima ◽  
H. Marumo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Boltzmann Equation ◽  
Rarefied Gas ◽  
Finite Width ◽  
Pressure Equation ◽  
Linearized Boltzmann Equation ◽  
The Boltzmann Equation ◽  
Element Method

This paper is useful in analyzing the performance of finite-width-air bearings in the rarefied gas region, using a newly developed finite element method. The linearized Boltzmann equation was solved by numerical iteration and a pressure equation was obtained, coupled with a continuous equation. The finite element method was developed for solving the pressure equation. The results were compared with a two moment approximate solution for the Boltzmann equation, which corresponds to the conventional slip flow analysis developed by Burgdorfer. An analysis of tapered flat slider flying characteristics in the rarefied gas regime, e.g., when the inverse Knudsen number in the trailing edge = 1, showed that the present exact solution for the Boltzmann equation was different from the two moment approximate solution by more than 10 percent in load capacity value, when the dimensionless load was not so large as when it is used for actual slider design.

Sign in / Sign up

Export Citation Format

Share Document