Gaseous Slip Flow in a Micro-Channel

2003 ◽  
Author(s):  
Shou-Shing Hsieh ◽  
Huang-Hsiu Tsai ◽  
Chih-Yi Lin ◽  
Ching-Fang Huang ◽  
Cheng-Ming Chien
Keyword(s):  
Gas Flow ◽  
Perturbation Methods ◽  
Flow Model ◽  
Slip Flow ◽  
Micro Channel ◽  
Slip Boundary Conditions ◽  
Nitrogen Gas ◽  
Slip Boundary ◽  
Mass Flow Rates ◽  
Good Agreement

An experimental and theoretical study of low Reynolds number compressible gas flow in a micro channel is presented. Nitrogen gas was used. The channel was microfabricated on silicon wafers and were 50 μm deep, 200 μm wide and 24000 μm long. The Knudsen number ranged from 0.001 to 0.02. Pressure drop were measured at different mass flow rates in terms of Re and found in good agreement with those predicted by analytical solutions in which a 2-D continuous flow model with first slip boundary conditions are employed and solved by perturbation methods.

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.

A Micro-Channel Flow and Heat Transfer Study by Lattice Boltzmann Method

2003 ◽  
Author(s):  
Ru Yang ◽  
Chin-Sheng Wang
Keyword(s):  
Heat Transfer ◽  
Lattice Boltzmann Method ◽  
Channel Flow ◽  
Lattice Boltzmann ◽  
Slip Flow ◽  
Navier Stokes ◽  
Micro Channel ◽  
Parallel Plates ◽  
Boltzmann Method ◽  
Good Agreement

A Lattice Boltzmann method is employed to investigate the flow characteristics and the heat transfer phenomenon between two parallel plates separated by a micro-gap. A nine-velocity model and an internal energy distribution model are used to obtain the mass, momentum and temperature distributions. It is shown that for small Knudsen numbers (Kn), the current results are in good agreement with those obtained from the traditional Navier-Stokes equation with non-slip boundary conditions. As the value of Kn is increased, it is found that the non-slip condition may no longer be valid at the wall boundary and that the flow behavior changes to one of slip-flow. In slip flow regime, the present results is still in good agreement with slip-flow solution by Navier Stokes equations. The non-linear nature of the pressure and friction distribution for micro-channel flow is gieven. Finally, the current investigation presents a prediction of the temperature distribution for micro-channel flow under the imposed conditions of an isothermal boundary.

A Friction Factor Correlation for Gas Flow in Parallel Plate Microchannels by Considering Combined Effects of Compressibility and Rarefaction

2008 ◽  
Author(s):  
Xiaohong Yan ◽  
Qiuwang Wang
Keyword(s):  
Friction Factor ◽  
Velocity Gradient ◽  
Parallel Plate ◽  
Gas Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Combined Effects ◽  
Slip Boundary

The effects of compressibility and rarefaction for gas flow in microchannels have been extensively studied separately. However, these two effects are always combined for gas flow in microchannels. In this paper, the two-dimensional compressible Navier-Stokes equations are solved for gas flow in parallel plate channels with a slip boundary condition to study the combined effects of compressibility and rarefaction on the friction factor. The numerical methodology is based on the control volume finite difference scheme. It is found that the effect of compressibility increases the velocity gradient near the wall which then increases the friction factor. On the other hand, increasing the velocity gradient near the wall leads to a much larger slip velocity and implies a stronger rarefaction effect and a corresponding decrease in the friction factor. These two opposite effects make the effect of compressibility on friction factor for slip flow weaker than that for no-slip compressible flow. A correlation among fRe, Kn and Ma is presented. The correlation is validated with available experimental and analytical results.

AN ELASTIC-COLLISION SCHEME FOR LATTICE BOLTZMANN METHODS

2001 ◽  
Vol 12 (03) ◽  
pp. 387-401 ◽  
Author(s):  
J. G. ZHOU
Keyword(s):  
Experimental Data ◽  
Lattice Boltzmann ◽  
Elastic Collision ◽  
Complex Geometries ◽  
Slip Boundary Conditions ◽  
Lattice Boltzmann Methods ◽  
Slip Boundary ◽  
Arbitrary Complex ◽  
Bounce Back ◽  
Good Agreement

An elastic-collision scheme is developed to achieve slip and semi-slip boundary conditions for lattice Boltzmann methods. Like the bounce-back scheme, the proposed scheme is efficient, robust and generally suitable for flows in arbitrary complex geometries. It involves an equivalent level of computation effort to the bounce-back scheme. The new scheme is verified by predicting wind-driven circulating flows in a dish-shaped basin and a flow in a strongly bent channel, showing good agreement with analytical solutions and experimental data. The capability of the scheme for simulating flows through multiple bodies has also been demonstrated.

Liquid Transport Properties in Sub-Micron Channel Flows

2001 ◽  
Author(s):  
K. Johan A. Westin ◽  
Kenneth S. Breuer ◽  
Chang-Hwan Choi ◽  
Peter Huang ◽  
Zhiqiang Cao ◽  
...  
Keyword(s):  
Flow Rate ◽  
Low Flow ◽  
Slip Boundary Conditions ◽  
Liquid Transport ◽  
Flow Rates ◽  
Slip Boundary ◽  
Laminar Channel Flow ◽  
Flow Through ◽  
Set Up ◽  
Good Agreement

Abstract An experimental set-up for pressure driven liquid flow through microchannels have been designed and tested. The flow rate is determined by tracking the free liquid surface in a precision bore hole using a laser distance meter. Measurements of the flow rate through silicon microchannels with a height of less than 0.9 μm show good results for Newtonian fluids (silicon oil, ethanol) at flow rates as low as 0.2 nl/s. The experimental results are also in very good agreement with predictions based on laminar channel flow using no-slip boundary conditions, indicating that standard macroscopic assumptions are still valid for these fluids under these conditions. However, experiments with aqueous solutions show anomalies in the form of unexpectedly low flow rates and time dependent variations. Possible explanations to these observations are discussed.

Effect of Wall Conduction on the Stability of a Fluid in a Rectangular Region Heated from Below

1972 ◽  
Vol 94 (4) ◽  
pp. 446-452 ◽  
Author(s):  
Ivan Catton
Keyword(s):  
Lateral Wall ◽  
Rectangular Region ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Aspect Ratios ◽  
Usual Manner ◽  
Vertical Walls ◽  
The Stability ◽  
The Galerkin Method ◽  
Good Agreement

The initiation of natural convection in a fluid confined above and below by rigid, perfectly conducting surfaces and laterally by vertical walls of arbitrary thermal conductivity which form a rectangle is examined. The linearized perturbation equations are obtained in the usual manner and reduced to an eigenvalue problem. The Rayleigh number is the eigenvalue and is a function of the lateral-wall conductance and horizontal plan form (aspect ratios). The problem associated with satisfying the no-slip boundary conditions on all surfaces is surmounted by using the Galerkin method. Results are compared with experiments and shown to be in good agreement.

Leakage Predictions for Static Gasket Based on the Porous Media Theory

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Pascal Jolly ◽  
Luc Marchand
Keyword(s):  
Porous Media ◽  
Gas Flow ◽  
Molecular Flow ◽  
Intrinsic Permeability ◽  
Slip Boundary Conditions ◽  
Apparent Permeability ◽  
Slip Boundary ◽  
Porous Media Theory ◽  
Porous Media Model ◽  
Different Gases

In the present work, the annular static gaskets are considered as porous media and Darcy’s law is written for a steady radial flow of a compressible gas with a first order slip boundary conditions. From this, a simple equation is obtained that includes Klinkenberg’s intrinsic permeability factor kv of the gasket and the Knudsen number Kn′o defined with a characteristic length ℓ. The parameters kv and ℓ of the porous gasket are calculated from experimental results obtained with a reference gas at several gasket stress levels. Then, with kv and ℓ, the inverse procedure is performed to predict the leakage rate for three different gases. It is shown that the porous media model predicts leak rates with the same accuracy as the laminar-molecular flow (LMF) model of Marchand et al. However, the new model has the advantage of furnishing phenomenological information on the evolution of the intrinsic permeability and the gas flow regimes with the gasket compressive stress. It also enables quick identification of the part of leakage that occurs at the flange-gasket interface at low gasket stresses. At low gas pressure, the behavior of the apparent permeability diverges from that of Klinkenberg’s, indicating that the rarefaction effect becomes preponderant on the leak.

Gaseous Slip Flow Mixed Convection in Vertical Microducts With Constant Axial Energy Input

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Arman Sadeghi ◽  
Mostafa Baghani ◽  
Mohammad Hassan Saidi
Keyword(s):  
Nusselt Number ◽  
Pressure Drop ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Cross Sections ◽  
Slip Flow ◽  
Constant Heat Flux ◽  
Slip Boundary Conditions ◽  
First Order ◽  
Slip Boundary

The present investigation is devoted to the fully developed slip flow mixed convection in vertical microducts of two different cross sections, namely, polygon, with circle as a limiting case, and rectangle. The two axially constant heat flux boundary conditions of H1 and H2 are considered in the analysis. The velocity and temperature discontinuities at the boundary are incorporated into the solutions using the first-order slip boundary conditions. The method considered is mainly analytical in which the governing equations in cylindrical coordinates along with the symmetry conditions and finiteness of the flow parameter at the origin are exactly satisfied. The first-order slip boundary conditions are then applied to the solution using the point matching technique. The results show that both the Nusselt number and the pressure drop parameter are increasing functions of the Grashof to Reynolds ratio. It is also found that, with the exception of the H2 Nusselt number of the triangular duct, which shows an opposite trend, both the Nusselt number and the pressure drop are decreased by increasing the Knudsen number. Furthermore, the pressure drop of the H2 case is found to be higher than that obtained by assuming an H1 thermal boundary condition.

The Effect of Viscous Dissipation on Two-Dimensional Microchannel Heat Transfer

2006 ◽  
Author(s):  
Jennifer van Rij ◽  
Tim Ameel ◽  
Todd Harman
Keyword(s):  
Heat Transfer ◽  
Viscous Dissipation ◽  
Slip Flow ◽  
Second Order ◽  
Slip Boundary Conditions ◽  
Pressure Work ◽  
Axial Conduction ◽  
Slip Boundary ◽  
Nusselt Numbers ◽  
Slip Flow Regime

Microchannel convective heat transfer characteristics in the slip flow regime are numerically evaluated for two-dimensional, steady state, laminar, constant wall heat flux and constant wall temperature flows. The effects of Knudsen number, accommodation coefficients, viscous dissipation, pressure work, second-order slip boundary conditions, axial conduction, and thermally/hydrodynamically developing flow are considered. The effects of these parameters on microchannel convective heat transfer are compared through the Nusselt number. Numerical values for the Nusselt number are obtained using a continuum based three-dimensional, unsteady, compressible computational fluid dynamics algorithm that has been modified with slip boundary conditions. Numerical results are verified using analytic solutions for thermally and hydrodynamically fully developed flows. The resulting analytical and numerical Nusselt numbers are given as a function of Knudsen number, the first- and second-order velocity slip and temperature jump coefficients, the Peclet number, and the Brinkman number. Excellent agreement between numerical and analytical data is demonstrated. Viscous dissipation, pressure work, second-order slip terms, and axial conduction are all shown to have significant effects on Nusselt numbers in the slip flow regime.

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