Fluid Mechanics of Flow Through Rectangular Hydrophobic Microchannels

2011 ◽  
Author(s):  
Navid Kashaninejad ◽  
Weng Kong Chan ◽  
Nam-Trung Nguyen
Keyword(s):  
Aspect Ratio ◽  
Rectangular Cross Section ◽  
Expansion Method ◽  
Channel Height ◽  
Parallel Plates ◽  
Laminar Regime ◽  
Dimensional Solution ◽  
Eigenfunction Expansion Method ◽  
Flow Through ◽  
Liquid Flows

In this study, the effect of two important parameters have been evaluated for pressure driven liquid flows in microchannel in laminar regime by analytical modeling, followed by experimental measurement. These parameters are wettability conditions of microchannel surfaces and aspect ratio of rectangular microchannels. For small values of aspect ratio, the channel was considered to have a rectangular cross-section, instead of being two parallel plates. Novel expressions for these kinds of channels were derived using eigenfunction expansion method. The obtained two-dimensional solutions based on dual finite series were then extended to the case of a constant slip velocity at the bottom wall. In addition, for large values of aspect ratio, a general equation was obtained which is capable of accounting for different values of slip lengths for both upper and lower channel walls. Firstly, it was found out that for low aspect ratio microchannels, the results obtained by analytical rectangular 2-D model agree well with the experimental measurements as compared to one dimensional solution. For high aspect ratio microchannels, both models predict the same trend. This finding indicates that using the conventional 1-D solution may not be accurate for the channels where the width is of the same order as the height. Secondly, experimental results showed that up to 2.5% and 16% drag reduction can be achieved for 1000 and 250 micron channel height, respectively. It can be concluded that increasing the surface wettability can reduce the pressure drop in laminar regime and the effect is more pronounced by decreasing the channel height.

Stokes flow through periodic orifices in a channel

1994 ◽  
Vol 263 ◽  
pp. 207-226 ◽  
Author(s):  
Y. Zeng ◽  
S. Weinbaum
Keyword(s):  
Aspect Ratio ◽  
Stokes Flow ◽  
Three Dimensional ◽  
Plane Wall ◽  
Channel Height ◽  
Infinite Plane ◽  
Electron Microscopic ◽  
Dimensional Solution ◽  
Aspect Ratios ◽  
Flow Through

This paper develops a three-dimensional infinite series solution for the Stokes flow through a parallel walled channel which is obstructed by a thin planar barrier with periodically spaced rectangular orifices of arbitrary aspect ratio B’/d’ and spacing D’. Here B’ is the half-height of the channel and d’ is the half-width of the orifice. The problem is motivated by recent electron microscopic studies of the intercellular channel between vascular endothelial cells which show a thin junction strand barrier with discontinuities or breaks whose spacing and width vary with the tissue. The solution for this flow is constructed as a superposition of Hasimoto's (1958) general solution for the two-dimensional flow through a periodic slit array in an infinite plane wall and a new three-dimensional solution which corrects for the top and bottom boundaries. In contrast to the well-known solutions of Sampson (1891) and Hasimoto (1958) for the flow through zero-thickness orifices of circular or elliptic cross-section or periodic slits in an infinite plane wall, which exhibit characteristic viscous velocity profiles, the present bounded solutions undergo a fascinating change in behaviour as the aspect ratio B’/d’ of the orifice opening is increased. For B’/d’ [Lt ] 1 and (D’ –- d’)/B’ of O(1) or greater, which represents a narrow channel, the velocity has a minimum at the orifice centreline, rises sharply near the orifice edges and then experiences a boundary-layer-like correction over a thickness of O(B’) to satisfy no-slip conditions. For B’/d’ of O(1) the profiles are similar to those in a rectangular duct with a maximum on the centreline, whereas for B’/d’ [Gt ] 1, which describes widely separated channel walls, the solution approaches Hasimoto's solution for the periodic infinite-slit array. In the limit (D’ –- d’)/B’ [Lt ] 1, where the width of the intervening barriers is small compared with the channel height, the solutions exhibit the same behaviour as Lee & Fung's (1969) solution for the flow past a single cylinder. The drag on the zero-thickness barriers in this case is nearly the same as for the cylinder for all aspect ratios.

Steady flow through distorted rectangular tubes of large aspect ratio

1983 ◽  
Vol 385 (1788) ◽  
pp. 107-127 ◽  
Keyword(s):  
Aspect Ratio ◽  
Boundary Layers ◽  
Rectangular Cross Section ◽  
Two Dimensional ◽  
Large Aspect Ratio ◽  
Dimensional Solution ◽  
Method Of Solution ◽  
Flow Through ◽  
High Reynolds ◽  
Sharp Corners

High Reynolds number ( Re ) flows through large aspect ratio ( λμ ) tubes of rectangular cross section are studied. One wall of the tube is slightly deformed to produce a two-dimensional distortion of length λ . We determine conditions for the flow at the centre of the tube and near the distortion to approximate the appropriate two-dimensional solution: namely, λμ ≫ ( λ -1 Re ) 1/6 if Re 1/7 ≲ λ and μ ≫ 1 if Re 1/7 ≳ λ . However, the latter condition needs to be strengthened to λμ ≫ Re 1/7 if the flow is additionally to be approximately two-dimensional far up- and down-stream. The method of solution includes a numerical calculation for the flow in the sharp corners of the tube. We deduce that for sufficiently short distortions ( λ ≪ Re 1/9 (ln Re ) 11/9 ), the sharp corners can effectively isolate disturbances in the wall boundary layers from each other. However, for larger distortions the disturbances in the boundary layers are all of comparable magnitude owing to interactions at the corners. Our examination of the corner regions also enables us to confirm a hypothesis, due to Hocking (1977) and others, that to leading order the pressure is constant in approximately square regions at the sides of the tube.

scholarly journals Flow through a helical pipe with rectangular cross-section

1970 ◽  
Vol 4 (2) ◽  
pp. 99-110
Author(s):  
Md Mahmud Alam ◽  
Delowara Begum ◽  
K Yamamoto
Keyword(s):  
Aspect Ratio ◽  
Iterative Method ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Main Tool ◽  
Numerical Approach ◽  
Dean Number ◽  
Helical Pipe ◽  
Flow Through ◽  
Marine Engineering

The effects of torsion, aspect ratio and curvature on the flow in a helical pipe of rectangular cross- section are studied by introducing a non-orthogonal helical coordinate system. Spectral method is applied as main tool for numerical approach where Chebyshev polynomial is used. The numerical calculations are obtained by the iterative method. The calculations are carried out for 0≤ δ ≤0.02, 1≤ λ ≤ 2.85, 1≤ γ ≤2.4, at Dn = 50 & 100 respectively, where d is the non-dimensional curvature, l the torsion parameter, g the aspect ratio and  Dn the pressure driven parameter (Dean number).DOI: http://dx.doi.org/10.3329/jname.v4i2.991 Journal of Naval Architecture and Marine Engineering Vol.4(2) 2007 p.99-110

On Timoshenko Beams of Rectangular Cross-Section

2004 ◽  
Vol 71 (3) ◽  
pp. 359-367 ◽  
Author(s):  
James R. Hutchinson
Keyword(s):  
Aspect Ratio ◽  
Timoshenko Beam ◽  
Rectangular Cross Section ◽  
Wave Length ◽  
Three Dimensional ◽  
Mindlin Plate ◽  
Dimensional Solution ◽  
Simply Supported ◽  
Shear Coefficient ◽  
Free Beam

It was recently shown that the shear coefficient for a rectangular Timoshenko beam is highly dependent on the aspect ratio of the beam. This research investigates the reasons for that behavior by comparison of the Timoshenko beam solution with a new three-dimensional solution for a simply supported beam. The new solution is a series solution that converges to any desired accuracy. Comparisons are also made to both elementary and Mindlin plates. The Mindlin plate solution is in excellent agreement with the three-dimensional solution for the simply supported case, and is used as a basis of comparison for a free-free beam. It is found that a shear coefficient which would cause matching of the three-dimensional and Mindlin solutions would have to be a function of the wave length as well as the aspect ratio. Physical explanations are given for the high dependence on aspect ratio and for the dependence on wave length.

scholarly journals Theoretical Hydrodynamic Analysis of a Surface-Piercing Porous Cylindrical Body

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 320
Author(s):  
Dimitrios N. Konispoliatis ◽  
Ioannis K. Chatjigeorgiou ◽  
Spyridon A. Mavrakos
Keyword(s):  
Water Waves ◽  
Wave Attenuation ◽  
Three Dimensional ◽  
Cylindrical Body ◽  
Expansion Method ◽  
Wave Theory ◽  
Linear Wave ◽  
Wave Loads ◽  
Dimensional Solution ◽  
Eigenfunction Expansion Method

In the present study, the diffraction and the radiation problems of water waves by a surface-piercing porous cylindrical body are considered. The idea conceived is based on the capability of porous structures to dissipate the wave energy and to minimize the environmental impact, developing wave attenuation and protection. In the context of linear wave theory, a three-dimensional solution based on the eigenfunction expansion method is developed for the determination of the velocity potential of the flow field around the cylindrical body. Numerical results are presented and discussed concerning the wave elevation and the hydrodynamic forces on the examined body for various values of porosity coefficients. The results revealed that porosity plays a key role in reducing/controlling the wave loads on the structure and the wave run-up, hence porous barriers can be set up to protect a marine structure against wave attack.

Effect of aspect ratio on flow through and around a porous disk

2021 ◽  
Vol 6 (7) ◽  
Author(s):  
Tingting Tang ◽  
Jin Xie ◽  
Shimin Yu ◽  
Jianhui Li ◽  
Peng Yu
Keyword(s):  
Aspect Ratio ◽  
Porous Disk ◽  
Flow Through

Dependence of AC losses on aspect ratio in superconducting wires with rectangular cross section

2004 ◽  
Vol 412-414 ◽  
pp. 1045-1049 ◽  
Author(s):  
K. Kajikawa ◽  
T. Hayashi ◽  
K. Funaki ◽  
E.S. Otabe ◽  
T. Matsushita
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Ac Losses ◽  
Superconducting Wires

scholarly journals Heat Transfer From Low Aspect Ratio Pin Fins

2007 ◽  
Author(s):  
Michael E. Lyall ◽  
Alan A. Thrift ◽  
Atul Kohli ◽  
Karen A. Thole
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Gas Turbines ◽  
Channel Height ◽  
Internal Cooling ◽  
Number Range ◽  
Pin Fin ◽  
Heat Transfer Augmentation ◽  
Low Aspect Ratio ◽  
Pin Fins

The performance of many engineering devices from power electronics to gas turbines is limited by thermal management. Heat transfer augmentation in internal flows is commonly achieved through the use of pin fins, which increase both surface area and turbulence. The present research is focused on internal cooling of turbine airfoils using a single row of circular pin fins that is oriented perpendicular to the flow. Low aspect ratio pin fins were studied whereby the channel height to pin diameter was unity. A number of spanwise spacings were investigated for a Reynolds number range between 5000 to 30,000. Both pressure drop and spatially-resolved heat transfer measurements were taken. The heat transfer measurements were made on the endwall of the pin fin array using infrared thermography and on the pin surface using discrete thermocouples. The results show that the heat transfer augmentation relative to open channel flow is the highest for smallest spanwise spacings and lowest Reynolds numbers. The results also indicate that the pin fin heat transfer is higher than the endwall heat transfer.

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