Improved Slip-Flow Boundary Conditions for Thin Lubrication Layers

1986 ◽  
Vol 53 (3) ◽  
pp. 723-724
Author(s):  
B. Nageswara Rao
Keyword(s):  
Boundary Conditions ◽  
Slip Flow ◽  
Flow Boundary

Slip-flow boundary conditions for non-Newtonian lubrication layers

1999 ◽  
Vol 24 (4) ◽  
pp. 211-217 ◽  
Author(s):  
Helge I Andersson ◽  
Ole Andreas Valnes
Keyword(s):  
Boundary Conditions ◽  
Slip Flow ◽  
Flow Boundary

Simulation of Micro-Scale Jet Impingement Heat Transfer

2000 ◽  
Author(s):  
Paul A. Boeschoten ◽  
Deborah V. Pence ◽  
James A. Liburdy
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Mach Number ◽  
Boundary Conditions ◽  
Slip Velocity ◽  
Slip Flow ◽  
Local Maximum ◽  
Jet Impingement ◽  
Micro Scale ◽  
Flow Boundary

Abstract The heat transfer performance of a micro-scale, axisymmetric, confined jet impinging on a flat surface at high Mach numbers (0.2 to 0.6) and low Reynolds numbers (419 to 1310) was computationally studied. The flow is characterized by Knudsen numbers, based on the jet radius, large enough (0.0013) to warrant slip-flow boundary conditions at the impinging surface. The effects of Mach number, compressibility, and slip-flow on heat transfer results are presented, along with the local Nusselt number distributions, and velocity and temperature fields near the impingement surface. Results for uniform wall heat flux show that the wall temperature decreases with increasing Mach number, with a local minimum at r/D = 0.7. The slip velocity also increases with Mach number with peak values also near r/D = 0.7. The resulting Nusselt number increases with increasing Mach number, and a local maximum in the Nusselt number is observed at r/D = 0.6, not at the centerline. In general, compressibility improves heat transfer due to increased fluid density near the impinging surface. Also, inclusion of slip-velocity increases the rate of heat transfer. However, the accompanying temperature-jump condition at the wall is found to reduce the local heat transfer rate. The net effect of the slip-flow boundary conditions applied in this study was an overall reduction in heat transfer.

Laminar Forced Convection in Annular Microchannels With Slip Flow Regime

2009 ◽  
Author(s):  
Arman Sadeghi ◽  
Abolhassan Asgarshamsi ◽  
Mohammad Hassan Saidi
Keyword(s):  
Nusselt Number ◽  
Fluid Flow ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Gas Flow ◽  
Slip Flow ◽  
Outer Wall ◽  
Graphical Form ◽  
Uniform Temperature

Fluid flow and heat transfer at microscale have attracted an important research interest in recent years due to the rapid development of microelectromechanical systems (MEMS). Fluid flow in microdevices has some characteristics which one of them is rarefaction effect related with gas flow. In this research, hydrodynamically and thermally fully developed laminar rarefied gas flow in annular microducts is studied using slip flow boundary conditions. Two different cases of the thermal boundary conditions are considered, namely: uniform temperature at the outer wall and adiabatic inner wall (Case A) and uniform temperature at the inner wall and adiabatic outer wall (Case B). Using the previously obtained velocity distribution, energy conservation equation subjected to relevant boundary conditions is numerically solved using fourth order Runge-Kutta method. The Nusselt number values are presented in graphical form as well as tabular form. It is realized that for the case A increasing aspect ratio results in increasing the Nusselt number, while the opposite is true for the case B. The effect of aspect ratio on Nusselt number is more notable at smaller values of Knudsen number, while its effect becomes slighter at large Knudsen numbers. Also increasing Knudsen number leads to smaller values of Nusselt number for the both cases.

MEMS-Scale Turbomachinery Based Vacuum Roughing Pump

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Anthony J. Gannon ◽  
Garth V. Hobson ◽  
Michael J. Shea ◽  
Christopher S. Clay ◽  
Knox T. Millsaps
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
3D Simulations ◽  
Slip Boundary ◽  
Wall Shear

This study forms part of a program to develop a micro-electro-mechanical systems (MEMS) scale turbomachinery based vacuum pump and investigates the roughing portion of such a system. Such a machine would have many radial stages with the exhaust stages operating near atmospheric conditions while the inlet stages operate at near vacuum conditions. In low vacuum such as those to the inlet of a roughing pump, the flow can still be treated as a continuum; however, the no-slip boundary condition is not accurate. The Knudsen number becomes a dominant nondimensional parameter in these machines due to their small size and low pressures. As the Knudsen number increases, slip-flow becomes present at the walls. The study begins with a basic overview on implementing the slip wall boundary condition in a commercial code by specifying the wall shear stress based on the mean-free-path of the gas molecules. This is validated against an available micro-Poiseuille classical solution at Knudsen numbers between 0.001 and 0.1 with reasonable agreement found. The method of specifying the wall shear stress is then applied to a generic MEMS scale roughing pump stage that consists of two stators and a rotor operating at a nominal absolute pressure of 500 Pa. The zero flow case was simulated in all cases as the pump down time for these machines is small due to the small volume being evacuated. Initial transient two-dimensional (2D) simulations are used to evaluate three boundary conditions, classical no-slip, specified-shear, and slip-flow. It is found that the stage pressure rise increased as the flow began to slip at the walls. In addition, it was found that at lower pressures the pure slip boundary condition resulted in very similar predictions to the specified-shear simulations. As the specified-shear simulations are computationally expensive it is reasonable to use slip-flow boundary conditions. This approach was used to perform three-dimensional (3D) simulations of the stage. Again the stage pressure increased when slip-flow was present compared with the classical no-slip boundaries. A characteristic of MEMS scale turbomachinery are the large relative tip gaps requiring 3D simulations. A tip gap sensitivity study was performed and it was found that when no-slip boundaries were present the pressure ratio increased significantly with decreasing tip gap. When slip-flow boundaries were present, this relationship was far weaker.

scholarly journals Unsteady Ferrofluid Slip Flow in the Presence of Magnetic Dipole With Convective Boundary Conditions

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 138551-138562
Author(s):  
Saeed Islam ◽  
Muhammad Zubair ◽  
Asifa Tassaddiq ◽  
Zahir Shah ◽  
Hussam Alrabaiah ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Magnetic Dipole ◽  
Slip Flow ◽  
Convective Boundary Conditions ◽  
Convective Boundary

Poiseuille Number Correlations of Gas Flow in Concentric Micro Annular Tubes

2008 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Koichi Suzuki
Keyword(s):  
Boundary Conditions ◽  
Gas Flow ◽  
Slip Flow ◽  
Tube Length ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Rarefaction Effect ◽  
Wide Range ◽  
Poiseuille Number ◽  
Fast Flow

Poiseuille number, the product of friction factor and Reynolds number (f · Re) for quasi-fully developed concentric micro annular tube flow was obtained for both no-slip and slip boundary conditions. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for both isothermal flow and no heat conduction flow conditions. The detail of the incompressible slip Poiseuille number is kindly documented and its value defined as a function of r* and Kn is represented. The outer tube radius ranges from 50 to 150μm with the radius ratios of 0.2, 0.5 and 0.8 and selected tube length is 0.02m. The stagnation pressure, pstg is chosen in such away that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmospheric pressure. In the case of fast flow, the value of f · Re is higher than that of incompressible slip flow theory due to the compressibility effect. However in the case of slow flow the value of f · Re is slightly lower than that of incompressible slip flow due to the rarefaction effect, even the flow is accelerated. The value of f · Re obtained for no-slip boundary conditions is compared with that of obtained for slip boundary conditions. The values of f · Re obtained for slip boundary conditions are predicted by f · Re correlations obtained for no-slip boundary conditions since rarefaction effect is relatively small for the fast flow.

Shear flow near solids: Epitaxial order and flow boundary conditions

1990 ◽  
Vol 41 (12) ◽  
pp. 6830-6837 ◽  
Author(s):  
Peter A. Thompson ◽  
Mark O. Robbins
Keyword(s):  
Shear Flow ◽  
Boundary Conditions ◽  
Flow Boundary
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