Slip Flow in the Hydrodynamic Entrance Region of Circular and Noncircular Microchannels

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Zhipeng Duan ◽  
Y. S. Muzychka
Keyword(s):  
Friction Factor ◽  
Slip Flow ◽  
Velocity Slip ◽  
Mean Free Path ◽  
Momentum Equation ◽  
Linearization Method ◽  
Asymptotic Results ◽  
Cross Sectional ◽  
Practical Applications ◽  
Continuum Flow

Microscale fluid dynamics has received intensive interest due to the emergence of micro-electro-mechanical systems (MEMS) technology. When the mean free path of the gas is comparable to the channel’s characteristic dimension, the continuum assumption is no longer valid and a velocity slip may occur at the duct walls. Noncircular cross sections are common channel shapes that can be produced by microfabrication. The noncircular microchannels have extensive practical applications in MEMS. The paper deals with issues of hydrodynamic flow development. Slip flow in the entrance of circular and parallel plate microchannels is first considered by solving a linearized momentum equation. It is found that slip flow is less sensitive to analytical linearized approximations than continuum flow and the linearization method is an accurate approximation for slip flow. Also, it is found that the entrance friction factor Reynolds product is of finite value and dependent on the Kn and tangential momentum accommodation coefficient but independent of the cross-sectional geometry. Slip flow and continuum flow in the hydrodynamic entrance of noncircular microchannels has been examined and a model is proposed to predict the friction factor and Reynolds product f Re for developing slip flow and continuum flow in most noncircular microchannels. It is shown that the complete problem may be easily analyzed by combining the asymptotic results for short and long ducts. Through the selection of a characteristic length scale, the square root of cross-sectional area, the effect of duct shape has been minimized. The proposed model has an approximate accuracy of 10% for most common duct shapes.

Effects of Corrugated Roughness on Developed Laminar Flow in Microtubes

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Zhipeng Duan ◽  
Y. S. Muzychka
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Slip Flow ◽  
Velocity Slip ◽  
Momentum Equation ◽  
Analytical Models ◽  
Microchannel Flow ◽  
Compressibility Effect ◽  
Continuum Flow ◽  
Experimental Pressure

The effects of corrugated surface roughness on developed laminar flow in microtubes are investigated. The momentum equation is solved using a perturbation method with slip at the boundary. Novel analytical models are developed to predict friction factor and pressure drop in corrugated rough microtubes for continuum flow and slip flow. The developed model proposes an explanation on the observed phenomenon that some experimental pressure drop results for microchannel flow have shown a significant increase (15–50%) due to roughness. The developed model for slip flow illustrates the coupled effects between velocity slip and small corrugated roughness. Compressibility effect has also been examined and simple models are proposed to predict the pressure distribution and mass flow rate for slip flow in corrugated rough microtubes.

Effects of Axial Corrugated Roughness on Low Reynolds Number Slip Flow and Continuum Flow in Microtubes

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Zhipeng Duan ◽  
Y. S. Muzychka
Keyword(s):  
Pressure Drop ◽  
Slip Flow ◽  
Velocity Slip ◽  
Analytical Models ◽  
Axial Distance ◽  
Microchannel Flow ◽  
Compressibility Effect ◽  
Continuum Flow ◽  
Experimental Pressure ◽  
The Stokes Equation

The effect of axial corrugated surface roughness on fully developed laminar flow in microtubes is investigated. The radius of a microtube varies with the axial distance due to corrugated roughness. The Stokes equation is solved using a perturbation method with slip at the boundary. Analytical models are developed to predict friction factor and pressure drop in corrugated rough microtubes for continuum flow and slip flow. The developed model proposes an explanation on the observed phenomenon that some experimental pressure drop results for microchannel flow have shown a significant increase due to roughness. The developed model for slip flow illustrates the coupled effects between velocity slip and small corrugated roughness. Compressibility effect has also been examined and simple models are proposed to predict the pressure distribution and mass flow rate for slip flow in corrugated rough microtubes.

scholarly journals Pressure Drop of Microchannel Plate Fin Heat Sinks

Micromachines ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 80 ◽  
Author(s):  
Zhipeng Duan ◽  
Hao Ma ◽  
Boshu He ◽  
Liangbin Su ◽  
Xin Zhang
Keyword(s):  
Fluid Dynamics ◽  
Pressure Drop ◽  
Slip Flow ◽  
Numerical Data ◽  
Velocity Slip ◽  
Fundamental Solutions ◽  
Momentum Equation ◽  
Channel Length ◽  
Microchannel Plate ◽  
Heat Sinks

The entrance region constitutes a considerable fraction of the channel length in miniaturized devices. Laminar slip flow in microchannel plate fin heat sinks under hydrodynamically developing conditions is investigated semi-analytically and numerically in this paper. The semi-analytical model for the pressure drop of microchannel plate fin heat sinks is obtained by solving the momentum equation with the first-order velocity slip boundary conditions at the channel walls. The simple pressure drop model utilizes fundamental solutions from fluid dynamics to predict its constitutive components. The accuracy of the model is examined using computational fluid dynamics (CFD) simulations and the experimental and numerical data available in the literature. The model can be applied to either apparent liquid slip over hydrophobic and superhydrophobic surfaces or gas slip flow in microchannel heat sinks. The developed model has an accuracy of 92 percent for slip flow in microchannel plate fin heat sinks. The developed model may be used to predict the pressure drop of slip flow in microchannel plate fin heat sinks for minimizing the effort and expense of experiments, especially in the design and optimization of microchannel plate fin heat sinks.

Low-Speed Slip Flow Over a Wedge

1970 ◽  
Vol 37 (2) ◽  
pp. 454-460 ◽  
Author(s):  
K. E. Kasza ◽  
W. L. Chow
Keyword(s):  
Boundary Layer ◽  
Free Path ◽  
Asymptotic Method ◽  
Slip Velocity ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Velocity Slip ◽  
Mean Free Path ◽  
Low Speed ◽  
Boundary Layer Equations

The problem of low-speed slip flow of a rarefied gas over a wedge has been solved using Meksyn’s asymptotic method of integrating the boundary-layer equations. Detailed results are given for slip velocity and developing velocity profiles for various wedge angles. The solution tends far downstream asymptotically to the Falkner and Skan profiles of conventional nonslip flow. In addition, the first correction to the skin friction due to velocity slip is found to be of the order of the first power of the molecular mean free path of the gas.

Models for Gaseous Slip Flow in Non-Circular Microchannels

2007 ◽  
Author(s):  
Zhipeng Duan ◽  
Y. S. Muzychka
Keyword(s):  
Friction Factor ◽  
Cross Sections ◽  
Slip Flow ◽  
Analytical Models ◽  
Roughness Effects ◽  
Practical Applications ◽  
Micro Channels ◽  
Mems Technology ◽  
Compressibility Effects ◽  
Circular Microchannels

Micro-scale fluid dynamics has received intensive interest due to the emergence of Micro-Electro-Mechanical Systems (MEMS) technology. Non-circular cross sections are common channel shapes that can be produced through a variety of micro-fabrication techniques. Non-circular microchannels have extensive practical applications in MEMS. Slip flow in noncircular microchannels has been examined by the authors and a review of several new models obtained by the authors is presented. These models are general and robust, and can be used by the research community for practical engineering design of microchannel flow systems. The reviewed models address: (i) fully developed slip flow in non-circular microchannels, (ii) hydrodynamically developing slip flow in non-circular microchannels, (iii) compressibility effects, and (iv) roughness effects. A model is proposed to predict the friction factor and Reynolds product fRe for fully developed and developing slip flow in most non-circular micro-channels. Compressibility effects on slip flow in non-circular microchannels have been examined and simple models are proposed to predict the pressure distribution and mass flow rate for slip flow in most non-circular microchannels. Finally, the effect of corrugated surface roughness on fully developed laminar flow in microtubes is examined. Simple analytical models are developed to predict friction factor and pressure drop in corrugated rough microtubes for continuum flow and slip flow.

scholarly journals Prediction of Windage Losses of an Enclosed High Speed Composite Rotor in Low Air Pressure Environments

2003 ◽  
Author(s):  
Hsing-Pang Liu ◽  
Mike Werst ◽  
Jonathan J. Hahne ◽  
David Bogard
Keyword(s):  
Free Path ◽  
High Speed ◽  
Rarefied Gas ◽  
Flow Instability ◽  
Slip Flow ◽  
Mean Free Path ◽  
Air Gap ◽  
Air Pressure ◽  
General Interest ◽  
Continuum Flow

The frictional windage losses associated with non-ventilated airflows in the air gaps between the rotor and stator of a high speed rotating machine can greatly influence the rotor outer and stator inner surface temperatures. The characteristics of the radial and axial air-gap flows have been of general interest in many engineering applications. A rotating air gap flow is very complex, and in general, can be categorized as a continuum flow, slip flow, and free molecule flow, depending on the ratio of its mean free path to the air gap dimension. For a continuum flow between concentric rotating cylinders, secondary flow of rows of circumferential Taylor vortices in the air gap due to centrifugal flow instability of a curved flow at relatively high rotating speeds will typically be formed. As the air pressure in the air gap drops significantly, rarefied gas flow, departure from continuum flow, occurs when the mean free path becomes relatively large compared to the air gap dimension. This paper has developed and summarized an analytical approach to predict high speed windage losses (rotor tip velocities up to 900 m/s) at low rotor cavity air pressures (0.1 torr to 10 torr). The predicted transient windage losses at various air pressures and high rotor speeds are compared with measured windage losses generated in continuum and slip flow regimes. The agreements between the predicted and measured windage losses are relatively well.

Numerical Study of Gaseous Microchannel Flows on the Dimensional and Physical Effects

2009 ◽  
Author(s):  
Kuan-Hung Lin ◽  
Jiunn-Chi Wu
Keyword(s):  
Friction Factor ◽  
Numerical Study ◽  
Pressure Ratio ◽  
Slip Flow ◽  
Applied Pressure ◽  
Flow Characteristics ◽  
Velocity Slip ◽  
Analytic Solutions ◽  
Transition Flow ◽  
Aspect Ratios

In this article, we perform a series of simulations to analyze the gaseous flow in two-dimensional (2D) and three-dimensional (3D) microchannels. The geometry effects of entrance and exit, applied pressure ratios and rarefaction effects on the flow characteristics are thoroughly investigated. In addition, a modified Poiseuille number correlation for air flows is obtained. This calculation solves the compressible Navier-Stokes and energy equations under velocity slip and temperature jump conditions with varying inlet to outlet pressure ratios (from 1.76 to 20), the outlet Knudsen numbers (from 0 to 0.22) and the aspect ratios (from 0 to 0.47). The calculated mass flow rate, pressure distribution and friction factor are compared with analytic solutions and experimental data in both the slip flow and earlier transition flow regimes. In the case of higher applied pressure ratio, both experiments and numerical modeling show pressure drop at upstream and downstream. Finally, we discuss the adequacy of the friction factor correlation for the 2D flow and the 3D flow in microchannels with both inlet and outlet chambers.

Diagnostics of metal samples using the results of experimental and theoretical study of positively charged microparticles formed upon sample destruction

2018 ◽  
Vol 84 (10) ◽  
pp. 23-28
Author(s):  
D. A. Golentsov ◽  
A. G. Gulin ◽  
Vladimir A. Likhter ◽  
K. E. Ulybyshev
Keyword(s):  
Experimental Data ◽  
Early Stage ◽  
Experimental Studies ◽  
Material Model ◽  
Total Charge ◽  
Cross Sectional ◽  
Practical Applications ◽  
Mechanical And Electrical Properties ◽  
Order Of Magnitude ◽  
Using Data

Destruction of bodies is accompanied by formation of both large and microscopic fragments. Numerous experiments on the rupture of different samples show that those fragments carry a positive electric charge. his phenomenon is of interest from the viewpoint of its potential application to contactless diagnostics of the early stage of destruction of the elements in various technical devices. However, the lack of understanding the nature of this phenomenon restricts the possibility of its practical applications. Experimental studies were carried out using an apparatus that allowed direct measurements of the total charge of the microparticles formed upon sample rupture and determination of their size and quantity. The results of rupture tests of duralumin and electrical steel showed that the size of microparticles is several tens of microns, the particle charge per particle is on the order of 10–14 C, and their amount can be estimated as the ratio of the cross-sectional area of the sample at the point of discontinuity to the square of the microparticle size. A model of charge formation on the microparticles is developed proceeding from the experimental data and current concept of the electron gas in metals. The model makes it possible to determine the charge of the microparticle using data on the particle size and mechanical and electrical properties of the material. Model estimates of the total charge of particles show order-of-magnitude agreement with the experimental data.

Detecting common breaks in the means of high dimensional cross-dependent panels

2021 ◽  
Author(s):  
Lajos Horváth ◽  
Zhenya Liu ◽  
Gregory Rice ◽  
Yuqian Zhao
Keyword(s):  
Panel Data ◽  
Common Factors ◽  
Real Data ◽  
Change Points ◽  
High Dimensional ◽  
Asymptotic Results ◽  
Cross Sectional ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Cross Sectional Dependence

Abstract The problem of detecting change points in the mean of high dimensional panel data with potentially strong cross–sectional dependence is considered. Under the assumption that the cross–sectional dependence is captured by an unknown number of common factors, a new CUSUM type statistic is proposed. We derive its asymptotic properties under three scenarios depending on to what extent the common factors are asymptotically dominant. With panel data consisting of N cross sectional time series of length T, the asymptotic results hold under the mild assumption that min {N, T} → ∞, with an otherwise arbitrary relationship between N and T, allowing the results to apply to most panel data examples. Bootstrap procedures are proposed to approximate the sampling distribution of the test statistics. A Monte Carlo simulation study showed that our test outperforms several other existing tests in finite samples in a number of cases, particularly when N is much larger than T. The practical application of the proposed results are demonstrated with real data applications to detecting and estimating change points in the high dimensional FRED-MD macroeconomic data set.

scholarly journals Program Quality and Developmental Outcomes Related to Youth Volleyball in Ethiopia: Assessing Relationships and Variations

2021 ◽  
Vol 11 (4) ◽  
pp. 1388-1405
Author(s):  
Abdulaziz Mussema ◽  
Tefera Tadesse ◽  
Zelalem Melkamu
Keyword(s):  
Developmental Outcomes ◽  
Central Zone ◽  
Youth Sport ◽  
Program Quality ◽  
Cross Sectional Survey ◽  
Cross Sectional ◽  
Practical Applications ◽  
The Mean ◽  
Project Site

This study aims to assess program quality and developmental outcomes of a youth volleyball project in one of the regional states in Ethiopia, and further examine variations between groups across gender and project site zones. We applied a cross-sectional survey design, collecting quantitative data from youth volleyball players (n = 215) with a mean age of 16.18 years (SD = 0.69) through a self-reported questionnaire. The results indicated that young players’ perceptions did not vary significantly across gender, except for the mean score of the perceived experience variable for girls (M = 2.68, SD = 0.318) was significantly higher than the mean score of boys (M = 2.58, SD = 0.258). One-way (project site zone) analyses of variance (ANOVAs) identified that youth volleyball projects in the central zone were consistently rated higher than those in the western zone, except for the current practice rating. Moreover, correlation analysis results indicated the presence of a significant relationship, both within and between program quality and developmental outcome variables. Furthermore, the results of regression analysis indicated that the program quality variables together predicted each of the developmental outcomes, accounting for 18.9% to 31.7% of the variances. It is concluded that the quality of the youth volleyball program in Ethiopia varies considerably across the project site zones and the program quality variables significantly relate to the developmental outcomes measured with differential effects. The data from this study reveals several practical applications for Ethiopia and beyond in terms of guiding youth volleyball projects. Moreover, the findings of the study showed that youth sport and the manner in which it is structured and delivered to youth players influences the attainment of positive developmental outcomes. These results suggest that contextual differences really do have an effect on the quality of youth sport program processes and developmental outcomes.

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