Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers

In this paper, the blood flow through a tapered artery with a stenosis by considering axially non-symmetric but radially symmetric mild stenosis on blood flow characteristics is analyzed, assuming the flow is steady and blood is treated as Williamson fluid. Perturbation solutions have been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different type of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest.

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Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers

Journal of Engineering Mathematics ◽

10.1007/s10665-004-7952-7 ◽

2005 ◽

Vol 52 (1) ◽

pp. 63-91 ◽

Cited By ~ 4

Author(s):

G. M. Cox ◽

S. W. Mccue ◽

N. Thamwattana ◽

J.M. Hill

Keyword(s):

Flow Through ◽

Perturbation Solutions

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Radial flow through deformable porous shells

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000008936 ◽

1993 ◽

Vol 34 (3) ◽

pp. 333-354 ◽

Cited By ~ 18

Author(s):

S. I. Barry ◽

G. K. Aldis

Keyword(s):

Nonlinear Diffusion ◽

Perturbation Methods ◽

Radial Flow ◽

Small Time ◽

Diffusion Equations ◽

Nonlinear Diffusion Equations ◽

Flow Perturbation ◽

Flow Through ◽

Planar Geometries ◽

Perturbation Solutions

AbstractThe problem of radially directed fluid flow through a deformable porous shell is considered. General nonlinear diffusion equations are developed for spherical, cylindrical and planar geometries. Solutions for steady flow are found in terms of an exact integral and perturbation solutions are also developed. For unsteady flow, perturbation methods are used to find approximate small-time solutions and a solution valid for slow compression rates. These solutions are used to investigate the deformation of the porous material with comparisons made between the planar and the cylindrical geometries.

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Mixed convection analysis for blood flow through arteries on Williamson fluid model

International Journal of Biomathematics ◽

10.1142/s179352451550045x ◽

2015 ◽

Vol 08 (04) ◽

pp. 1550045 ◽

Cited By ~ 4

Author(s):

Noreen Sher Akbar

Keyword(s):

Blood Flow ◽

Mixed Convection ◽

Fluid Model ◽

Flow Characteristics ◽

Williamson Fluid ◽

Tapered Artery ◽

Impedance Wall ◽

Different Types ◽

Flow Through ◽

Perturbation Solutions

In this paper, the blood flow through a tapered artery with a stenosis by considering axially non-symmetric but radially symmetric mild stenosis on blood flow characteristics is analyzed, assuming the flow is steady and blood is treated as Williamson fluid. The effects of mixed convection heat and mass transfer are also carried out. Perturbation solutions have been calculated for velocity, temperature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different types of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest. Streamlines have been plotted at the end of the paper.

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Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers

Journal of Engineering Mathematics ◽

10.1007/bf02694031 ◽

2005 ◽

Vol 52 (1-3) ◽

pp. 63-91

Author(s):

G. M. Cox ◽

S. W. McCue ◽

N. Thamwattana ◽

J. M. Hill

Keyword(s):

Flow Through ◽

Perturbation Solutions

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Perturbation solutions for highly frictional granular media

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2004.1368 ◽

2005 ◽

Vol 461 (2053) ◽

pp. 21-42 ◽

Cited By ~ 6

Author(s):

Ngamta Thamwattana ◽

James M. Hill

Keyword(s):

Internal Friction ◽

Granular Media ◽

Numerical Solutions ◽

Solution Procedure ◽

Perturbation Series ◽

Regular Perturbation ◽

Approximate Analytical Solutions ◽

Leading Term ◽

Flow Through ◽

Perturbation Solutions

In this paper, we deal with the materials possessing angles of internal friction ϕ for which 1 − sin ϕ is close to zero, and we use the solution for sin ϕ = 1 as the leading term in a regular perturbation series, where the correction terms are of order 1 − sin ϕ . In this way we obtain approximate analytical solutions which can be used to describe the behaviour of real granular materials. The solution procedure is illustrated with reference to quasi–static flow through wedge–shaped and conical hoppers. For these two problems, the obtained perturbation solutions are shown to be graphically indistinguishable from the numerical solutions for high angles of internal friction, and for moderately high angles of internal friction the perturbation solutions still provide excellent approximations.

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Development of apical pits in chloride cells of the gills of Pimephales promelas after chronic exposure to acid water

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100076044 ◽

1983 ◽

Vol 41 ◽

pp. 462-463

Author(s):

Richard L. Leino ◽

Jon G. Anderson ◽

J. Howard McCormick

Keyword(s):

Confidence Interval ◽

Chronic Exposure ◽

Lake Superior ◽

Pimephales Promelas ◽

Chloride Cells ◽

Fathead Minnows ◽

Secondary Lamellae ◽

Untreated Water ◽

Water Ph ◽

Flow Through

Groups of 12 fathead minnows were exposed for 129 days to Lake Superior water acidified (pH 5.0, 5.5, 6.0 or 6.5) with reagent grade H2SO4 by means of a multichannel toxicant system for flow-through bioassays. Untreated water (pH 7.5) had the following properties: hardness 45.3 ± 0.3 (95% confidence interval) mg/1 as CaCO3; alkalinity 42.6 ± 0.2 mg/1; Cl- 0.03 meq/1; Na+ 0.05 meq/1; K+ 0.01 meq/1; Ca2+ 0.68 meq/1; Mg2+ 0.26 meq/1; dissolved O2 5.8 ± 0.3 mg/1; free CO2 3.2 ± 0.4 mg/1; T= 24.3 ± 0.1°C. The 1st, 2nd and 3rd gills were subsequently processed for LM (methacrylate), TEM and SEM respectively.Three changes involving chloride cells were correlated with increasing acidity: 1) the appearance of apical pits (figs. 2,5 as compared to figs. 1, 3,4) in chloride cells (about 22% of the chloride cells had pits at pH 5.0); 2) increases in their numbers and 3) increases in the % of these cells in the epithelium of the secondary lamellae.

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