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1.
A mathematical model for blood flow through an elastic artery with multistenosis under the effect of a magnetic field in a
porous medium is presented. The considered arterial segment is simulated by an anisotropically elastic cylindrical tube filled
with a viscous incompressible electrically conducting fluid representing blood. An artery with mild local narrowing in its
lumen forming a stenosis is analyzed. The effects of arterial wall parameters represent viscoelastic stresses along the longitudinal
and circumferential directions T
t
and T
θ
, respectively. The degree of anisotropy of the vessel wall γ, total mass of the vessel, and surrounding tissues M and contributions of the viscous and elastic constraints to the total tethering C and K respectively on resistance impedance, wall shear stress distribution, and radial and axial velocities are illustrated. Also,
the effects of the stenosis shape m, the constant of permeability X, the Hartmann number H
α
and the maximum height of the stenosis size δ on the fluid flow characteristics are investigated. The results show that the flow is appreciably influenced by surrounding
connective tissues of the arterial wall motion, and the degree of anisotropy of the vessel wall plays an important role in
determining the material of the artery. Further, the wall shear stress distribution increases with increasing T
t
and γ while decreases with increasing T
θ
, M, C, and K. Transmission of the wall shear stress distribution and resistance impedance at the wall surface through a tethered tube
are substantially lower than those through a free tube, while the shearing stress distribution at the stenosis throat has
inverse characteristic through totally tethered and free tubes. The trapping bolus increases in size toward the line center
of the tube as the permeability constant X increases and decreases with the Hartmann number Ha increased. Finally, the trapping bolus appears, gradually in the case of non-symmetric stenosis, and disappears in the case
of symmetric stenosis. The size of trapped bolus for the stream lines in a free isotropic tube (i.e., a tube initially unstressed)
is smaller than those in a tethered tube. 相似文献
2.
A micropolar model for axisymmetric blood flow through an axially nonsymmetreic but radially symmetric mild stenosis tapered artery is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter (referred to as the shape parameter). The model is also used to study the effect of the taper angle Ф. Flow parameters such as the velocity, the resistance to flow (the resistance impedance), the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis (stenosis throat) have been computed for different values of the shape parameter n, the taper angle Ф, the coupling number N and the micropolar parameter m. It is shown that the resistance to flow decreases with increasing the shape parameter n and the micropolar parameter m while it increases with increasing the coupling number N. So, the magnitude of the resistance impedance is higher for a micropolar fluid than that for a Newtonian fluid model. Finally, the velocity profile, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis are discussed for different values of the parameters involved on the problem. 相似文献
3.
Heat and mass transfer effects on Newtonian biomagnetic fluid of blood flow through a tapered porous artery with a stenosis
is investigated. Governing equations have been modeled by treating blood as Newtonian biomagnetic fluid. The governing equations
are simplified under the assumption of mild stenosis. Exact solutions have been evaluated for velocity, temperature, and concentration
profiles. The effects of Newtonian nature of blood on velocity, temperature, concentration profile, wall shear stress, shearing
stress at the stenosis throat and impedance of the artery are discussed graphically. Stream lines have been presented in last
section of the article. 相似文献
4.
A numerical study of laminar forced convective flows of three different nanofluids through a horizontal circular tube with
a constant heat flux condition has been performed. The effect of Al2O3 volume concentration 0 ≤ φ ≤ 0.09 in the pure water, water-ethylene glycol mixture and pure ethylene glycol as base fluids,
and Reynolds number of 100 ≤ Re ≤ 2,000 for different power inputs in the range of 10 ≤ Q(W) ≤ 400 have been investigated. In this study, all of the nanofluid properties are temperature and nanoparticle volume concentration
dependent. The governing equations have been solved using finite volume approach with the SIMPLER algorithm. The results indicate
an increase in the averaged heat transfer coefficient with increasing the mass of ethylene glycol in the water base fluid,
solid concentration and Reynolds number. From the investigations it can be inferred that, the pressure drop and pumping power
in the nanofluids at low solid volumetric concentration (φ < 3%) is approximately the same as in the pure base fluid in the
various Reynolds numbers, but the higher solid nanoparticle volume concentration causes a penalty drop in the pressure. Moreover,
this study shows it is possible to achieve a higher heat transfer rate with lower wall shear stress with the use of proper
nanofluids. 相似文献
5.
The boundary layer problem of a power-law fluid flow with fluid injection on a wedge whose surface is moving with a constant
velocity in the opposite direction to that of the uniform mainstream is analyzed. The free stream velocity, the injection
velocity at the surface, moving velocity of the wedge surface, the wedge angle and the power law index of non-Newtonian fluid
are assumed variables. The fourth order Runge–Kutta method modified by Gill is used to solve the non-dimensional boundary
layer equations for non-Newtonian flow field. Without fluid injection, for every angle of wedge β, a limiting value for velocity ratio λ
cr
(velocity of the wedge surface/velocity of the uniform flow) is found for each power-law index n. The value of λ
cr
increases with the increasing wedge angle β. The value of wedge angle also restricts the physical characteristics of the fluid to be used. The effects of the different
parameters on velocity profile and on skin friction are studied and the drag reduction is discussed. In case of C = 2.5 and velocity ratio λ = 0.2 for wedge angle β = 0.5 with the fluid with power law-index n = 0.5, 48.8% drag reduction is obtained. 相似文献
6.
In this paper, the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized
Maxwell fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. Initially,
the fluid is at rest, and the motion is produced by the rotation of the cylinder about its axis with a unsteady angular velocity.
The solutions that have been obtained are presented under series form in terms of the generalized G
a,b,c
(, t)-functions. The similar solutions for the ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained
as special cases, when β → 1, respectively β → 1 and λ → 0, from general solutions. Finally, the solutions that have been obtained are compared by graphical illustrations,
and the influence of the pertinent parameters on the fluid motion is also underlined by graphical illustrations. 相似文献
7.
Here the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized second
grade fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. At time
t=0 the fluid is at rest and the motion is produced by the rotation of the cylinder around its axis. The solutions that have
been obtained are presented under series form in terms of the generalized G-functions. The similar solutions for ordinary second grade and Newtonian fluids are obtained from general solution for β→1, respectively, β→1 and α
1→0. Finally, the influences of the pertinent parameters on the fluid motion, as well as a comparison between models, is underlined
by graphical illustrations. 相似文献
8.
Ilkay Bak?rta? 《International Journal of Non》2005,40(6):785-793
In the present work, treating the artery as a tapered, thin walled, long and circularly conical prestressed elastic tube and using the longwave approximation, we have studied the propagation of weakly non-linear waves in such a fluid-filled elastic tube by employing the reductive perturbation method. By considering the blood as an incompressible inviscid fluid, the evolution equation is obtained as the Korteweg-de Vries equation with a variable coefficient. It is shown that this type of equation admits a solitary wave-type solution with variable wave speed. It is observed that, the wave speed decreases with distance for positive tapering while it increases for negative tapering. It is further observed that, the progressive wave profile for expanding tubes (a>0) becomes more steepened whereas for narrowing tubes (a<0) it becomes more flattened. 相似文献
9.
The flow of an incompressible couple stress fluid in an annulus with local constriction at the outer wall is considered. This
configuration is intended as a simple model for studying blood flow in a stenosed artery when a catheter is inserted into
it. The effects couple stress fluid parameters α and σ, height of the constriction (ε), and ratio of radii (k) on the impedance and wall shear stresses are studied graphically. Graphical results show that the resistance to the flow
as well as the wall shear stress increases as the ratio of the radii increases and decreases as the couple stress fluid parameters
increases. 相似文献
10.
M. M. Carroll 《Journal of Elasticity》2011,103(2):173-187
A three-parameter strain energy function is developed to model the nonlinearly elastic response of rubber-like materials.
The development of the model is phenomenological, based on data from the classic experiments of Treloar, Rivlin and Saunders,
and Jones and Treloar on sheets of vulcanized rubber. A simple two-parameter version, similar to the Mooney-Rivlin and Gent-Thomas
strain energies, provides an accurate fit with all of the data from Rivlin and Saunders and Jones and Treloar, as well as
with Treloar’s data for deformations for which the principal deformation invariant I
1 has values in the range 3≤I
1≤20. 相似文献
11.
This paper reports results of DPIV measurements on a two-dimensional elliptic airfoil rotating about its own axis of symmetry
in a fluid at rest and in a parallel freestream. In the former case, we examined three rotating speeds (Re
c,Ω = 400, 1,000 and 2,000), and in the later case, four rotating speeds (Ro
c,Ω = 2.4, 1.2, 0.6 and 0.4), together with two freestream velocities (Re
c,u
= 200 and 1,000) and two starting configurations of the airfoil (i.e., chord parallel to (α
0 = 0°) or normal (α
0 = 90°) to the freestream). Results show that a rotating airfoil in a stationary fluid produces two distinct types of vortex
structures depending on the Reynolds number. The first type occurs at the lowest Reynolds number (Re
c,Ω = 400), where vortices shed from the two edges or tips of the airfoil dissipated quickly, resulting in the airfoil rotating
in a layer of diffused vorticity. The second type occurs at higher Reynolds numbers (i.e., Re
c,Ω = 1,000 and 2,000), where the corresponding vortices rotated together with the airfoil. Due to the vortex suction effect,
the torque characteristics are likely to be heavily damped for the first type because of the rapidly subsiding vortex shedding,
and more oscillatory for the second type due to persistent presence of tip vortices. In a parallel freestream, increasing
the tip-speed ratio (V/U) of the airfoil (i.e., decreasing the Rossby number, Ro
c,Ω) transformed the flow topology from periodic vortex shedding at Ro
c,Ω = 2.4 to the generation of a “hovering vortex” at Ro
c,Ω = 0.6 and 0.4. The presence of the hovering vortex, which has not been reported in literature before, is likely to enhance
the lift characteristics of the airfoil. Freestream Reynolds number is found to have minimal effect on the vortex formation
and shedding process, although it enhances shear layer instability and produces more small-scale flow structures that affect
the dynamics of the hovering vortex. Likewise, initial starting configuration of the airfoil, while affecting the flow transient
during the initial phase of rotation, has insignificant effect on the overall flow topology. Unfortunately, technical constraint
of our apparatus prevented us from carrying out complimentary force measurements; nevertheless, the results presented herein,
which are more extensive than those computed by Lugt and Ohring (1977), will provide useful benchmark data, from which more advanced numerical calculations can be carried out to ascertain the
corresponding force characteristics, particularly for those conditions with the presence of hovering vortex. 相似文献
12.
Two hot-wire flow diagnostics have been developed to measure a variety of turbulence statistics in the buoyancy driven, air-helium
Rayleigh–Taylor mixing layer. The first diagnostic uses a multi-position, multi-overheat (MPMO) single wire technique that
is based on evaluating the wire response function to variations in density, velocity and orientation, and gives time-averaged
statistics inside the mixing layer. The second diagnostic utilizes the concept of temperature as a fluid marker, and employs
a simultaneous three-wire/cold-wire anemometry technique (S3WCA) to measure instantaneous statistics. Both of these diagnostics
have been validated in a low Atwood number (A
t
≤ 0.04), small density difference regime, that allowed validation of the diagnostics with similar experiments done in a hot-water/cold-water
water channel facility. Good agreement is found for the measured growth parameters for the mixing layer, velocity fluctuation
anisotropy, velocity fluctuation p.d.f behavior, and measurements of molecular mixing. We describe in detail the MPMO and S3WCA diagnostics, and the validation
measurements in the low Atwood number regime (A
t
≤ 0.04). We also outline the advantages of each technique for measurement of turbulence statistics in fluid mixtures with
large density differences. 相似文献
13.
《ournal of non Newtonian Fluid Mechanics》2006,133(1):1-13
In 1963 Giesekus [H. Giesekus, Die simultane Translations- und Rotationsbewegung einer Kugel in einer elastikoviskosen Flüssigkeit, Rheol. Acta 3 (1962) 59–71] showed that a Stokes velocity field also satisfies the equilibrium equation for the flow of a restricted form of the second order fluid. The same result was found by Tanner [R.I. Tanner, Plane creeping flows of incompressible second order fluids, Phys. Fluids 9 (1966) 1246–1247] in 1966 in the context of plane flow for which the restrictions on the second order fluid are not relevant. Tanner [R.I. Tanner, Some extended Giesekus-type theorems for non-Newtonian fluids, Rheol. Acta 28 (1989) 449–452] later showed that the velocity field for the inertialess, plane flow of the generalized Newtonian fluid is also the velocity field for the flow of a special form of the Criminale–Ericksen–Filbey (CEF) stress system [W.O. Criminale Jr., J.L. Ericksen, G.L. Filbey Jr., Steady flow of non-Newtonian fluids, Arch. Rat. Mech. 1 (1958) 410–417]. In this paper it will be shown that the results of Giesekus and Tanner are special cases of a more general theorem in which the velocity field, in any dimension, of the equilibrium Reiner–Rivlin problem also satisfies the corresponding problem for the materially steady stress system (a generalization of the CEF system) provided the coefficients of the Reiner–Rivlin stress [M. Reiner, A mathematical theory of dilatancy, Am. J. Math. 67 (1945) 350–362; R.S. Rivlin, The hydrodynamics of non-Newtonian fluids, Proc. R. Soc. Lond. 193 (1948) 260–281] are derivable from a strain-rate potential. As with the Giesekus–Tanner theorems the new theorem holds generally for velocity boundary conditions, but in some cases, such as the free jet, stress boundary conditions can be imposed. 相似文献
14.
The onset of buoyancy-driven convection in an initially quiescent ferrofluid saturated horizontal porous layer in the presence
of a uniform vertical magnetic field is investigated. The Brinkman-Lapwood extended Darcy equation with fluid viscosity different
from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed
to be rigid-paramagnetic, while the upper paramagnetic boundary is considered to be either rigid or stress-free. The thermal
conditions include fixed heat flux at the lower boundary, and a general convective–radiative exchange at the upper boundary,
which encompasses fixed temperature and fixed heat flux as particular cases. The resulting eigenvalue problem is solved numerically
using the Galerkin technique. It is found that increase in the Biot number Bi, porous parameter σ, viscosity ratio Λ, magnetic susceptibility χ, and decrease in the magnetic number M
1 and non-linearity of magnetization M
3 is to delay the onset of ferroconvection in a porous medium. Further, increase in M
1, M
3, and decrease in χ, Λ, σ and Bi is to decrease the size of convection cells. 相似文献
15.
Mixing by secondary flow is studied by particle image velocimetry (PIV) in a developing laminar pulsating flow through a circular curved pipe. The pipe curvature ratio is η = r
0/r
c
= 0.09, and the curvature angle is 90°. Different secondary flow patterns are formed during an oscillation period due to
competition among the centrifugal, inertial, and viscous forces. These different secondary-flow structures lead to different
transverse-mixing schemes in the flow. Here, transverse mixing enhancement is investigated by imposing different pulsating
conditions (Dean number, velocity ratio, and frequency parameter); favorable pulsating conditions for mixing are introduced.
To obviate light-refraction effects during PIV measurements, a T-shaped structure is installed downstream of the curved pipe.
Experiments are carried out for the Reynolds numbers range 420 ≤ Rest ≤ 1,000 (Dean numbers 126.6 ≤ Dn ≤ 301.5) corresponding to non-oscillating flow, velocity component ratios 1 ≤ (β = U
max,osc/U
m,st) ≤ 4 (the ratio of velocity amplitude of oscillations to the mean velocity without oscillations), and frequency parameters
8.37 < (α = r
0(ω/ν)0.5) < 24.5, where α2 is the ratio of viscous diffusion time over the pipe radius to the characteristic oscillation time. The variations in cross-sectional
average values of absolute axial vorticity (|ζ|) and transverse strain rate (|ε|) are analyzed in order to quantify mixing.
The effects of each parameter (Rest, β, and α) on transverse mixing are discussed by comparing the dimensionless vorticities (|ζ
P
|/|ζ
S
|) and dimensionless transverse strain rates (|ε
P
|/|ε
S
|) during a complete oscillation period. 相似文献
16.
We study the flow of yield stress fluids over a rotating surface when both the viscoelastic solid behavior below a critical
deformation (γ
c) and liquid properties beyond γ
c can play a significant role. We review the detailed characteristics of the flow in the solid regime in the specific case
of a pure elongational strain (large height to radius ratio). We, in particular, show that there exists a critical rotation
velocity (ω
c) associated with the transition from the solid to the liquid regime. We then consider the specific case of lubricational
regime (small height to radius ratio) in the liquid regime. In that case we describe the different possible evolutions of
the equilibrium shape of the material as a function of the rotation velocity (ω), from which we extrapolate the transient shape evolutions as ω increases. We show that for a sufficiently large rotation velocity the sample separates into two parts, one remaining at
rest around the rotation axis, the other going on moving radially. These predictions are then compared with systematic spin-coating
tests under increasing rotation velocity ramps followed by a plateau at ω
f with typical yield stress fluids. It appears that there exists a critical velocity below which the material undergoes a limited
elongation and beyond which it starts to spread significantly over the solid surface. For a larger ω
f value the sample forms a thick peripheral roll, leaving behind it a thin layer of fluid at rest relatively to the disc. These
characteristics are in qualitative agreement with the theoretical predictions. Beyond a sufficiently large ω
f value this roll eventually spreads radially in the form of thin fingers. Moreover, in agreement with the theory in the lubricational
regime, the different curves of deformation vs ω fall along a master curve when the rotation velocity is scaled by ω
c for different accelerations, different sample radii, or different material yield stress. The final thickness of the deposit
seems to be mainly governed by the displacement of the roll, the characteristics of which take their origin in the initial
stage of the spreading, including the solid–liquid transition. 相似文献
17.
Natural convection in a partially filled porous square cavity is numerically investigated using SIMPLEC method. The Brinkman-Forchheimer
extended model was used to govern the flow in the porous medium region. At the porous-fluid interface, the flow boundary condition
imposed is a shear stress jump, which includes both the viscous and inertial effects, together with a continuity of normal
stress. The thermal boundary condition is continuity of temperature and heat flux. The results are presented with flow configurations
and isotherms, local and average Nusselt number along the cold wall for different Darcy numbers from 10−1 to 10−6, porosity values from 0.2 to 0.8, Rayleigh numbers from 103 to 107, and the ratio of porous layer thickness to cavity height from 0 to 0.50. The flow pattern inside the cavity is affected
with these parameters and hence the local and global heat transfer. A modified Darcy–Rayleigh number is proposed for the heat
convection intensity in porous/fluid filled domains. When its value is less than unit, global heat transfer keeps unchanged.
The interfacial stress jump coefficients β
1 and β
2 were varied from −1 to +1, and their effects on the local and average Nusselt numbers, velocity and temperature profiles
in the mid-width of the cavity are investigated. 相似文献
18.
The near-field flow structure of a tip vortex behind a sweptback and tapered NACA 0015 wing was investigated and compared
with a rectangular wing at the same lift force and Re=1.81×105. The tangential velocity decreased with the downstream distance while increased with the airfoil incidence. The core radius
was about 3% of the root chord c
r, regardless of the downstream distance and α for α<8°. The core axial velocity was always wake-like. The core Γc and total Γo circulation of the tip vortex remained nearly constant up to x/c
r=3.5 and had a Γc/Γo ratio of 0.63. The total circulation of the tip vortex accounted for only about 40% of the bound root circulation Γb. For a rectangular wing, the axial flow exhibited islands of wake- and jet-like velocity distributions with Γc/Γo=0.75 and Γo/Γb=0.70. For the sweptback and tapered wing tested, the inner region of the tip vortex flow exhibited a self-similar behavior
for x/c
r≥1.0. The lift force computed from the spanwise circulation distributions agreed well with the force-balance data. A large
difference in the lift-induced drag was, however, observed between the wake integral method and the inviscid lifting-line
theory. 相似文献
19.
Steady mixed convection boundary layer flow from an isothermal horizontal circular cylinder embedded in a porous medium filled
with a nanofluid has been studied for both cases of a heated and cooled cylinder. The resulting system of nonlinear partial
differential equations is solved numerically using an implicit finite-difference scheme. The solutions for the flow and heat
transfer characteristics are evaluated numerically for various values of the governing parameters, namely the nanoparticle
volume fraction φ and the mixed convection parameter λ. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It is found that for each particular nanoparticle, as the nanoparticle volume fraction φ increases, the magnitude of the skin friction coefficient decreases, and this leads to an increase in the value of the mixed
convection parameter λ which first produces no separation. On the other hand, it is also found that of all the three types
of nanoparticles considered, for any fixed values of φ and λ, the nanoparticle Cu gives the largest values of the skin friction coefficient followed by TiO2 and Al2O3. Finally, it is worth mentioning that heating the cylinder (λ > 0) delays separation of the boundary layer and if the cylinder
is hot enough (large values of λ > 0), then it is suppressed completely. On the other hand, cooling the cylinder (λ < 0) brings
the boundary layer separation point nearer to the lower stagnation point and for a sufficiently cold cylinder (large values
of λ < 0) there will not be a boundary layer on the cylinder. 相似文献
20.
Andrew J. Onstad Christopher J. Elkins Frank Medina Ryan B. Wicker John K. Eaton 《Experiments in fluids》2011,50(6):1571-1585
Open-celled foam geometries show great promise in heat/mass transfer, chemical treatment, and enhanced mixing applications.
Flow measurements on these geometries have consisted primarily of observations of the upstream and downstream effects the
foam has on the velocity field. Unfortunately, these observations give little insight into the flow inside the foam. We have
performed quantitative flow measurements inside a scaled replica of a metal foam, ϕ = 0.921, D
Cell = 2.5 mm, by Magnetic Resonance Velocimetry to better understand the fluid motion inside the foam and give an alternative
method to determine the foam cell and pore sizes. Through these 3-D, spatially resolved measurements of the flow field for
a cell Reynolds number of 840, we have shown that the transverse motion of the fluid has velocities 20–30% of the superficial
velocity passing through the foam. This strong transverse motion creates and dissipates streamwise jets with peak velocities
2–3 times the superficial velocity and whose coherence length is strongly correlated to the cell size of the foam. This complex
fluid motion is described as “mechanical mixing” and is attributed to the geometry of the foam. A mechanical dispersion coefficient,
D
M, was formed which demonstrates the transverse dispersion of this geometry to be 14 times the kinematic viscosity and 10 times
the thermal diffusivity of air at 20°C and 1 atm. 相似文献