Laminar Flow in Microchannels With Noncircular Cross Section

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Ali Tamayol ◽  
Majid Bahrami
Keyword(s):  
Experimental Data ◽  
Cross Section ◽  
Cross Sections ◽  
Analytical Solutions ◽  
Point Matching ◽  
Fully Developed Flow ◽  
Closed Form Solutions ◽  
Wide Range ◽  
Matching Technique ◽  
Simply Connected

Analytical solutions are presented for laminar fully developed flow in micro-/minichannels of hyperelliptical and regular polygonal cross sections in the form of compact relationships. The considered geometries cover a wide range of common simply connected shapes including circle, ellipse, rectangle, rectangle-with-round-corners, rhombus, star-shape, equilateral triangle, square, pentagon, and hexagon. A point matching technique is used to calculate closed form solutions for the velocity distributions in the above-mentioned channel cross sections. The developed relationships for the velocity distribution and pressure drop are successfully compared with existing analytical solutions and experimental data collected from various sources for a variety of geometries, including polygonal, rectangular, circular, elliptical, and rhombic cross sections. The present compact solutions provide a convenient and power tool for performing hydrodynamic analyses in a variety of fundamental and engineering applications such as in microfluidics, transport phenomena, and porous media.

Analytical Solutions for Laminar Fully-Developed Flow in Microchannels With Non-Circular Cross-Section

2009 ◽  
Author(s):  
A. Tamayol ◽  
M. Bahrami
Keyword(s):  
Experimental Data ◽  
Pressure Drop ◽  
General Solution ◽  
Cross Section ◽  
Cross Sections ◽  
Analytical Solutions ◽  
Circular Cross Section ◽  
Fully Developed Flow ◽  
Wide Range ◽  
Simply Connected

Analytical solutions are presented for laminar fully-developed flow in micro/minichannels of hyperelliptical and regular polygonal cross-sections. The considered geometries cover a wide range of common simply connected shapes including circle, ellipse, rectangle, rhomboid, star-shape, equilateral triangle, square, pentagon, and hexagon. Therefore, the present approach can be considered as a general solution. Predicted results for the velocity distribution and pressure drop are successfully compared with existing analytical solutions and experimental data collected from various sources for a variety of geometries, including: polygonal, rectangular, circular, elliptical, and rhombic cross-sections.

Point-matching technique for rectangular-cross-section dielectric rod

1971 ◽  
Vol 7 (17) ◽  
pp. 497 ◽  
Author(s):  
A.L. Cullen ◽  
O. Özkan ◽  
L.A. Jackson
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Point Matching ◽  
Matching Technique

MOMENTUM-TRANSFER STRUCTURE OF POMERON AT ACCELERATOR ENERGIES

2004 ◽  
Vol 19 (40) ◽  
pp. 3001-3010 ◽  
Author(s):  
M. KAWASAKI ◽  
T. MAEHARA ◽  
M. YONEZAWA
Keyword(s):  
Experimental Data ◽  
Differential Cross Section ◽  
Momentum Transfer ◽  
Cross Section ◽  
Mass Parameter ◽  
Low Energy ◽  
Peripheral Part ◽  
Wide Range ◽  
Diffraction Picture ◽  
Transfer Structure

A representation of Pomeron amplitude derived asymptotically in the framework of the geometrical diffraction picture is shown to be consistent with the gross feature of the experimental data of the differential cross-section of pp and [Formula: see text] scattering in the low energy region [Formula: see text] over a wide range of momentum transfer. It is found that the most peripheral part of the diffraction interaction is characterized by a mass parameter of 0.4–0.5 GeV indicating the dominance of the two-pion states.

Production cross-section of heavy flavored hadrons in pp collision at s = 7 TeV

2019 ◽  
Vol 34 (19) ◽  
pp. 1950150 ◽  
Author(s):  
Muhammad Ajaz ◽  
Irfan Khan ◽  
M. K. Suleymanov
Keyword(s):  
Experimental Data ◽  
Transverse Momentum ◽  
Differential Cross Section ◽  
Cross Section ◽  
Momentum Distribution ◽  
Cross Sections ◽  
Production Cross ◽  
Center Of Mass ◽  
Transverse Momentum Distribution ◽  
Mass Frame

The transverse momentum distribution of the differential production cross-sections of heavy flavored charm hadrons [Formula: see text], [Formula: see text] in pp collisions at 7 TeV are simulated. Predictions of DPMJETIII.17-1, HIJING1.383 and Sibyll2.3c are compared to the differential cross-section measurements of the LHCb experimental data presented in the region of [Formula: see text] and [Formula: see text], where the pp center of mass frame is used to measure the transverse momentum and rapidity. The models reproduce only some regions of [Formula: see text] and/or bins of [Formula: see text] but none of them predict completely all the [Formula: see text] bins over the entire [Formula: see text] range.

QCD JETS AT HERA I.: O(αs) RADIATIVE CORRECTIONS TO ELECTROWEAK CROSS SECTIONS AND JET RATES

1989 ◽  
Vol 04 (07) ◽  
pp. 1781-1825 ◽  
Author(s):  
JÜRGEN G. KÖRNER ◽  
ERWIN MIRKES ◽  
GERHARD A. SCHULER
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Neutral Current ◽  
High Energy ◽  
Coupling Constant ◽  
Bjorken Scaling ◽  
Born Cross Section ◽  
Wide Range ◽  
Lepton Polarization ◽  
Jet Cross Sections

We present the complete O(αs) corrections to the electroweak cross sections of both neutral current and charged current deep inelastic e±p scattering including lepton polarization effects. Changes in the cross section due to the inclusion of next-to-leading-log (NLL) effects are parametrized by K factors, which are defined as the ratio of the NLL O(αs) cross sections and the Born cross section. Using the standard redefinition scheme of the parton densities, we find that the K factors deviate substantially from unity for small values of the Bjorken-Scaling variable x. We also elaborate on problems that arise when defining jet cross sections in ep scattering and present numerical results for the O(αs) 3-jet and 2-jet rates. We observe that the Q2-dependence of the 3-jet rate is dominated by the running strong coupling constant αs(Q2) allowing for its determination over a wide range in Q2 at high energy ep colliders.

Evaluation of Optical Model Potential Using Neutron Induced Cross Section Reaction for Spherical Uranium-238 Isotope up to 20MeV

2015 ◽  
Vol 59 ◽  
pp. 26-34
Author(s):  
Iman Tarik Al-Alawy ◽  
Ronak Ikram Ali
Keyword(s):  
Experimental Data ◽  
Energy Range ◽  
Cross Section ◽  
Cross Sections ◽  
Optical Model ◽  
Threshold Energy ◽  
Model Potential ◽  
Model Parameters ◽  
Incident Neutron ◽  
Optical Model Potential

The evaluation are based on mainly on the calculations of the nuclear optical model potential and relevant parameters are collected and selected from References Input Parameter Library (RIPL) which is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The analyzing of a complete energy range has done starting from threshold energy for each reaction. The cross sections are reproduced in fine steps of incident neutron energy with 0.01MeV intervals with their corresponding errors. The recommended cross sections for available experimental data taken from EXFOR library have been calculated for all the considered neutron induced reactions for U-238 isotopes. The calculated results are analyzed and compared with the experimental data. The optimized optical potential model parameters give a very good agreement with the experimental data over the energy range 0.001-20MeV for neutron induced cross section reactions (n,f), (n,tot), (n,el), (n,inl), (n,2n), (n,3n), and (n,γ) for spherical U-238 target elements.

Electron energy distributions in uniform electric fields and the Townsend ionization coefficient

1958 ◽  
Vol 244 (1237) ◽  
pp. 166-185 ◽  
Keyword(s):  
Differential Equation ◽  
Cross Section ◽  
Electric Fields ◽  
Cross Sections ◽  
Collision Cross Section ◽  
Present Theory ◽  
Uniform Electric Field ◽  
Ionization Coefficient ◽  
Special Cases ◽  
Wide Range

The second-order differential equation which expresses the equilibrium condition of an electron swarm in a uniform electric field in a gas, the electrons suffering both elastic and inelastic collisions with the gas molecules, is solved by the Jeffreys or W.K.B. method of approximation. The distribution function F(ε) of electrons of energy ε is obtained immediately in a general form involving the elastic and inelastic collision cross-sections and without any restriction on the range of E/p (electric strength/gas pressure) save that introduced in the original differential equation. In almost all applications the approximation is likely to be of high accuracy, and easy to use. Several of the earlier derivations of F(ε) are obtained as special cases. Using the function F(ε) an attempt is made to relate the Townsend ionization coefficient a to the properties of the gas in a more general manner than hitherto, using realistic functions for the collision cross-section. It is finally expressed by the equation α/ p = A exp ( — Bp/E ) in which A and B are functions involving the properties of the gas and the ratio E/p . The important coefficient B is directly related to the form and magnitude of the total inelastic cross-section below the ionization potential and can be evaluated for a particular gas once the cross-section is known experimentally. The present theory shows clearly the influence of E/p on both A and B, a matter which has not been satisfactorily discussed previously. The theory is illustrated by calculations of F (ε) and a/p for hydrogen over a range of E/p from 10 to 1000. The agreement between the calculated results and recent reliable observations of α/ p is surprisingly good considering the nature of the calculations and the wide range of E/p .

Analytical Solution for Newtonian Laminar Flow Through the Concave and Convex Ducts

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
M. Firouzi ◽  
S. H. Hashemabadi
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Friction Factor ◽  
Cross Section ◽  
Cross Sections ◽  
Fully Developed Flow ◽  
Pipe Flows ◽  
Dimensionless Velocity ◽  
Flow Through ◽  
Fanning Friction Factor

In this paper, the motion equation for steady state, laminar, fully developed flow of Newtonian fluid through the concave and convex ducts has been solved both numerically and analytically. These cross sections can be formed due to the sedimentation of heavy components such as sand, wax, debris, and corrosion products in pipe flows. The influence of duct cross section on dimensionless velocity profile, dimensionless pressure drop, and friction factor has been reported. Finally based on the analytical solutions three new correlations have been proposed for the product of Reynolds number and Fanning friction factor (Cf Re) for these geometries.

On Non-Boussinesq Gravity Currents in Non-Rectangular Cross-Section Channels

2014 ◽  
Author(s):  
T. Zemach
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Gravity Current ◽  
Classical Formulation ◽  
Wide Range ◽  
Front Condition ◽  
Significant Generalization ◽  
Self Similar ◽  
Cross Section Geometry

We consider the propagation of a gravity current of density ρc from a lock length x0 and height h0 into an ambient fluid of density ρa in a horizontal channel of height H along the horizontal coordinate x. The bottom and top of the channel are at z = 0, H, and the cross-section is given by the quite general −f1(z) ≤ y ≤ f2(z) for 0 ≤ z ≤ H. When the Reynolds number is large, the resulting flow is governed by the parameters R = ρc/ρa, H* = H/h0 and f(z) = f1(z) + f2(z). We show that the shallow-water one-layer model, combined with a Benjamin-type front condition, provides a versatile formulation for the thickness h and speed u of the current. The results cover in a continuous manner the range of light ρc/ρa ≪ 1, Boussinesq ρc/ρa ≈ 1 and heavy ρc/ρa ≫ 1 currents in a fairly wide range of depth ratio in various cross-section geometries. We obtain analytical solutions for the initial dam-break stage of propagation with constant speed, which appears for any cross-section geometry, and derive explicitly the trend for small and large values of the governing parameters. For large time, t, a self-similar propagation is feasible for f(z) = bzα cross-sections only, with t(2+2α)/(3+2α). The present approach is a significant generalization of the classical non-Boussinesq gravity current problem. The classical formulation for a rectangular (or laterally unbounded) channel is now just a particular case, f(z) = const., in the wide domain of cross-sections covered by this new model.

In-Plane Vibrations of Thick Circular Rings With T or I Cross Sections

1979 ◽  
Vol 46 (2) ◽  
pp. 470-472
Author(s):  
H. Lecoanet ◽  
J. Piranda
Keyword(s):  
Experimental Data ◽  
Eigenvalue Problem ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Circular Rings ◽  
Theoretical Results ◽  
Good Agreement

This paper deals with the problem of eigenfrequencies and eigenvectors for rings whose cross section may be decomposed in basic rectangular cross sections. The solution is derived from a solution of the in-plane eigenvalue problem for rectangular cross-section thick rings. A good agreement between theoretical results and experimental data is obtained.

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