Rarefied gas flow between parallel plates

1969 ◽  
Vol 66 (1) ◽  
pp. 189-196 ◽  
Author(s):  
M. M. R. Williams
Keyword(s):  
Boundary Condition ◽  
Integral Equation ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Volumetric Flow Rate ◽  
Slip Boundary Condition ◽  
General Boundary Condition ◽  
Boltzmann Transport ◽  
Parallel Plates ◽  
Slip Boundary

AbstractThe flow of a rarefied gas between parallel plates has been studied via the linearized Boltzmann transport equation. Using a general boundary condition, which includes an arbitrary ratio of specular to diffuse reflection from the wall, we have derived an integral equation for the mass flow velocity. The integral equation is solved by using a replication property of the kernel and application of the method of Muskelishvili.The total volumetric flow rate is obtained and a slip boundary condition is deduced for use with the hydrodynamic equations.Certain aspects of the eigenvalue spectrum associated with the Boltzmann equation are discussed.

New slip boundary condition in high-speed rarefied gas flow simulations

2019 ◽  
Vol 234 (3) ◽  
pp. 840-856
Author(s):  
Nam TP Le ◽  
Nam H Tran ◽  
Thoai N Tran ◽  
Toan T Tran
Keyword(s):  
Boundary Condition ◽  
High Speed ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Slip Boundary Condition ◽  
Mean Free Path ◽  
Slip Condition ◽  
Monte Carlo Data ◽  
Flow Simulations ◽  
Slip Boundary

In this paper, we propose a new slip boundary condition in hypersonic gas flow simulations. It is derived by considering the Langmuir isotherm adsorption into the Kaniadarkis et al. model of the kinetic theory of gas. Moreover, the motion of the adsorbed molecules over the surface (i.e. surface diffusion) is considered for the calculation of the mean free path in new slip condition. Three aerodynamic configurations are selected for evaluating new slip condition such as (1) the sharp-leading-edge flat plate, (2) circular cylinder in cross-flow, and (3) the sharp 25°–55° biconic cases. Hypersonic gas flows have the Mach number ranging from 6.1 to 15.6, and the working gases are argon and nitrogen. The simulation results show that new slip condition predicts better slip velocity than the Maxwell slip condition and gives good agreement with the direct simulation Monte-Carlo data for all cases considered in the present work.

scholarly journals Slip boundary condition of heat flux in Knudsen layers

2014 ◽  
Vol 470 (2161) ◽  
pp. 20130578 ◽  
Author(s):  
Mingtian Xu
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Mean Free Path ◽  
Knudsen Layer ◽  
Boltzmann Transport ◽  
Slip Boundary ◽  
The Mean ◽  
Solid Walls

In a Knudsen layer with thickness comparable to the mean free path, collisions between heat carriers and solid walls play an important role in nanoscale heat transports. An interesting question is that whether these collisions also induce the slip of heat flow similar to the velocity slip condition of the rarefied gases on solid walls. In this work based on the discrete Boltzmann transport equation, the slip boundary condition of heat flux on solid walls in the Knudsen layer is established. This result is exemplified by the slip boundary condition of heat flux in nanowires, which has been proposed in a phenomenological way.

Simulation of Rarefied Gas Flow in Microchannel Based on Vorticity-Stream Function Method

2007 ◽  
Author(s):  
Xueyong Wei ◽  
Mike C. L. Ward ◽  
Dejiang Lu ◽  
Zhuangde Jiang
Keyword(s):  
Stream Function ◽  
Function Method ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Taylor Series Expansion ◽  
Accommodation Coefficient ◽  
Parallel Plates ◽  
Slip Boundary ◽  
Tangential Momentum ◽  
New Formula

Vorticity-stream function method is successfully used to solve an incompressible gas flow in the parallel-plates micro-channel. A new formula in finite difference scheme is developed to describe the boundary vorticity based on the slip boundary theory and Taylor series expansion. Results show that the boundary vorticity are not only influenced by the Knudsen number (Kn) but also influenced by the tangential momentum accommodation coefficient (TMAC).

scholarly journals Application of Daftardar Jafari Method to First Grade MHD Squeezing Fluid Flow in a Porous Medium with Slip Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Inayat Ullah ◽  
M. T. Rahim ◽  
Hamid Khan
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Velocity Profile ◽  
Nonlinear Boundary ◽  
Slip Boundary Condition ◽  
First Grade ◽  
Squeezing Flow ◽  
Parallel Plates ◽  
Governing Equations ◽  
Slip Boundary

In the present work, in the presence of magnetic field and with slip boundary condition, squeezing flow of a Newtonian fluid in a porous medium between two large parallel plates is investigated. The governing equations are transformed to a single nonlinear boundary value problem. Daftardar Jafari Method (DJM) is used to solve the problem in order to obtain the velocity profile of the fluid. By using residual of the problem, the validity of solution is established. The velocity profile is argued through graphs for various values of parameters.

Experimental and Numerical Studies on Gas Flow Through Silicon Microchannels

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
K. Srinivasan ◽  
P. M. V. Subbarao ◽  
S. R. Kale
Keyword(s):  
Boundary Condition ◽  
Gas Flow ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Flow Characteristics ◽  
Slip Boundary Condition ◽  
Second Order ◽  
Navier Stokes ◽  
Slip Boundary ◽  
Aspect Ratios

The present work investigates the extension of Navier–Stokes equations from slip-to-transition regimes with higher-order slip boundary condition. To achieve this, a slip model based on the second-order slip boundary condition was derived and a special procedure was developed to simulate slip models using FLUENT®. The boundary profile for both top and bottom walls was solved for each pressure ratio by the customized user-defined function and then passed to the FLUENT® solver. The flow characteristics in microchannels of various aspect ratios (a = H/W = 0.002, 0.01, and 0.1) by generating accurate and high-resolution experimental data along with the computational validation was studied. For that, microchannel system was fabricated in silicon wafers with controlled surface structure and each system has several identical microchannels of same dimensions in parallel and the processed wafer was bonded with a plane wafer. The increased flow rate reduced uncertainty substantially. The experiments were performed up to maximum outlet Knudsen number of 1.01 with nitrogen and the second-order slip coefficients were found to be C1 = 1.119–1.288 (TMAC = 0.944–0.874) and C2 = 0.34.

Numerical study on the rotating electro-osmotic flow of third grade fluid with slip boundary condition

2020 ◽  
Vol 75 (7) ◽  
pp. 649-655
Author(s):  
Juan Song ◽  
Shaowei Wang ◽  
Moli Zhao ◽  
Ning Li
Keyword(s):  
Boundary Condition ◽  
Velocity Profile ◽  
Slip Boundary Condition ◽  
Third Grade ◽  
Parallel Plates ◽  
Third Grade Fluid ◽  
Osmotic Flow ◽  
Slip Boundary ◽  
Grade Fluid ◽  
Electro Osmotic Flow

AbstractConsidering the slip boundary condition, the rotating electro-osmotic flow of a third grade fluid in a channel formed by two parallel plates is investigated in the present study. The charge distribution is treated with the Debye–Hückel approximation analytically. Based on the finite difference method, the velocity profile for rotating electro-osmotic flow of third grade fluid is obtained numerically. It is shown that the non-Newtonian parameter of third grade fluid and the velocity slip factor play the important roles for the rotating electro-osmotic flow. The increasing non-Newtonian parameter slows down the flow and decreases the velocity magnitude, and the increasing slip parameter β has the similar influence on the velocity profile. Furthermore, the effect of the inclusion of third grade on the velocity profile is more conspicuous in the area near the walls.

A New Slip Model for Gas Lubrication

Tribology ◽  
2006 ◽  
Author(s):  
Sheng Shen ◽  
Robert M. Crone ◽  
Gang Chen ◽  
Manuel Anaya-Dufresne
Keyword(s):  
Gas Flow ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Rarefied Gas ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Slip Model ◽  
Slip Boundary ◽  
Physical Mechanisms ◽  
Gas Lubrication

In this paper, a new slip boundary condition is derived using the solution of the Boltzmann equation. The physical mechanisms of velocity slip in rarefied gas flow are discussed and emphasized. The Poiseuille flow rates predicted by the new slip model show better agreements with those calculated from the existing slip models such as 1st, 2nd, and 1.5th slip order. Based on the new slip model, a new modified Reynolds equation is also proposed to predict the pressure field in gas lubrication problem.

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