Navier–Stokes modeling of a Gaede pump stage in the viscous and transitional flow regimes using slip-flow boundary conditions

2005 ◽  
Vol 23 (2) ◽  
pp. 336-346 ◽  
Author(s):  
S. Giors ◽  
F. Subba ◽  
R. Zanino
Keyword(s):  
Boundary Conditions ◽  
Slip Flow ◽  
Flow Regimes ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Flow Boundary ◽  
Pump Stage

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.

scholarly journals Compressibility Effects in 2d Wall Heating Microchannel flow

2016 ◽  
Vol 35 ◽  
pp. 57-71
Author(s):  
Md Tajul Islam
Keyword(s):  
Boundary Conditions ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Control Volume ◽  
Pressure Ratio ◽  
Slip Flow ◽  
Navier Stokes ◽  
Slip Boundary ◽  
Wall Heating ◽  
Compressibility Effects

In this article we present a numerical solution of the Navier-Stokes equations and energy equation in parallel plate microchannels with the first order slip boundary conditions on the walls, adopting control volume scheme of CFD technique. Wall heating condition was considered on the walls. Noslip boundary conditions for compressible and incompressible flows were also solved to compare the effect of slip conditions. Compressibility effects were also investigated for compressible slip and compressible noslip flow conditions. A series of simulations were performed for different heights and lengths of channels and pressure ratios. Results are presented in graphs and tables and are compared with the available analytical and experimental results. It was found that the friction constants are the highest for noslip compressible flow and lowest for the slip flow against pressure ratio and mach numbers. Friction constant decreases continuously for compressible slip flow but it approaches to an asymptotic value of 96 for compressible noslip flow for the decrease of aspect ratio.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 57-71

New boundary conditions in the transition régime

1968 ◽  
Vol 2 (3) ◽  
pp. 293-310 ◽  
Author(s):  
Carlo Cercignani ◽  
Gino Tironi
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Slip Flow ◽  
Navier Stokes ◽  
Main Body ◽  
Parallel Plates ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Flow Heat

Starting from the Boltzmann equation, new boundary conditions are derived to be matched with the Navier—Stokes equations, that are supposed to hold in the main body of a gas. The idea upon which this method is based goes back to Maxwell and Langmuir. Since the distribution function is supposed to be completely determined by the Navier—Stokes equations, this new set of boundary conditions extends in some sense the validity of the macroscopic equations to the transition and free molecular régimes. In fact, it is shown that the free molecular and slip flow régimes are correctly described by this method; the latter is also supposed to give a reasonable approximation for the complete range of Knudsen numbers. The new procedure is applied to different problems such as plane Couette flow, plane and cylindrical Poiseuile flow, heat transfer between parallel plates and concentric cylinders. Results are obtained and compared with the exact numerical solutions for the above-mentioned problems.

scholarly journals Slip-Flow Regimes in Nanofluidics: A Universal Superexponential Model

2021 ◽  
Vol 15 (5) ◽  
Author(s):  
Mohammad Aminpour ◽  
Sergio Andres Galindo Torres ◽  
Alexander Scheuermann ◽  
Ling Li
Keyword(s):  
Slip Flow ◽  
Flow Regimes

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

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