scholarly journals Mathematical Modelling of Pulsatile Flow of Non-Newtonian Fluid Through a Constricted Artery

2021 ◽  
Vol 8 (3) ◽  
pp. 485-491
Author(s):  
Saktipada Nanda ◽  
Biswadip Basu Mallik ◽  
Samarpan Deb Majumder ◽  
Ramesh Kumar Karthick ◽  
Sagar Suman ◽  
...  
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Power Law ◽  
Flow Rate ◽  
Computational Models ◽  
Research Work ◽  
Flow Parameters ◽  
Wall Shear

The research work explores blood flow into a stenosed artery, or one with abnormal growth within it. At the throats and at the critical height of the stenosis, mathematical and computational models have been developed to calculate the various associated parameters such as flow rate, pressure gradient, impedance, and wall shear stress. Modeling blood as a power law fluid showed the dependency of these quantities on temporal and spatial variables, as well as the frequency of the flow oscillation in time and the key parameters of the flow mechanism. The exponential curve is the geometry of the stenosis studied in this analysis. Analytical expressions for axial velocity, volumetric flow rate, pressure gradient, blood flow resistance, and shear stress have been computed and simulated in ANSYS to generate useful results with respect to variation of flow parameters with power law indices and also for comparison between Newtonian and Non- Newtonian models of blood. Upon investigation, it was found that wall shear stress (WSS) increases with stenosis depth and therefore, plays a crucial role in affecting other flow parameters. At power law index 0.6, the highest shear stress and flow velocity were encountered at approximately 7 Pa and 0.5 m/s respectively.

scholarly journals Biorheological Model on Flow of Herschel-Bulkley Fluid through a Tapered Arterial Stenosis with Dilatation

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
S. Priyadharshini ◽  
R. Ponalagusamy
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Power Law ◽  
Flow Resistance ◽  
Velocity Profiles ◽  
Arterial Stenosis ◽  
Axial Distance ◽  
Tapered Artery ◽  
Wall Shear

An analysis of blood flow through a tapered artery with stenosis and dilatation has been carried out where the blood is treated as incompressible Herschel-Bulkley fluid. A comparison between numerical values and analytical values of pressure gradient at the midpoint of stenotic region shows that the analytical expression for pressure gradient works well for the values of yield stress till 2.4. The wall shear stress and flow resistance increase significantly with axial distance and the increase is more in the case of converging tapered artery. A comparison study of velocity profiles, wall shear stress, and flow resistance for Newtonian, power law, Bingham-plastic, and Herschel-Bulkley fluids shows that the variation is greater for Herschel-Bulkley fluid than the other fluids. The obtained velocity profiles have been compared with the experimental data and it is observed that blood behaves like a Herschel-Bulkley fluid rather than power law, Bingham, and Newtonian fluids. It is observed that, in the case of a tapered stenosed tube, the streamline pattern follows a convex pattern when we move fromr/R=0tor/R=1and it follows a concave pattern when we move fromr/R=0tor/R=-1. Further, it is of opposite behaviour in the case of a tapered dilatation tube which forms new information that is, for the first time, added to the literature.

scholarly journals Analysis of Flow Characteristics of the Blood Flowing through an Inclined Tapered Porous Artery with Mild Stenosis under the Influence of an Inclined Magnetic Field

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Neetu Srivastava
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Flow Rate ◽  
Flow Characteristics ◽  
Volumetric Flow Rate ◽  
Mhd Equations ◽  
Inclined Magnetic Field ◽  
Wall Shear

Analytical investigation of MHD blood flow in a porous inclined stenotic artery under the influence of the inclined magnetic field has been done. Blood is considered as an electrically conducting Newtonian fluid. The physics of the problem is described by the usual MHD equations along with appropriate boundary conditions. The flow governing equations are finally transformed to nonhomogeneous second-order ordinary differential equations. This model is consistent with the principles of magnetohydrodynamics. Analytical expressions for the velocity profile, volumetric flow rate, wall shear stress, and pressure gradient have been derived. Blood flow characteristics are computed for a specific set of values of the different parameters involved in the model analysis and are presented graphically. Some of the obtained results show that the flow patterns in converging region (ξ<0), diverging region (ξ>0), and nontapered region (ξ=0) are effectively influenced by the presence of magnetic field and change in inclination of artery as well as magnetic field. There is also a significant effect of permeability on the wall shear stress as well as volumetric flow rate.

scholarly journals Blood flow rate and wall shear stress in seven major cephalic arteries of humans

2019 ◽  
Vol 236 (3) ◽  
pp. 522-530
Author(s):  
Roger S. Seymour ◽  
Qiaohui Hu ◽  
Edward P. Snelling
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Flow Rate ◽  
Blood Flow Rate ◽  
Wall Shear

scholarly journals Theoretical Study of Compressible Flow through Aneurysms

2021 ◽  
Author(s):  
Maria Jumani
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Theoretical Study ◽  
Reynolds Numbers ◽  
Centerline Velocity ◽  
Flow Parameters ◽  
Flow Through ◽  
Wall Shear

The goal of this research is to analyze the effect of blood flow through expansions by using the KarmanPohlhausen method. The Karman-Pohlhausen method has previously been used in several research works to analyze the flow through constrictions. In this Thesis, the effect of different flow parameters (Reynolds number, compressibility, and slip) on pressure, pressure gradient, centerline velocity, and on wall shear stress are analyzed. Our results show that the pressure gradient curves are most affected by increasing Reynolds number and compressibility, as well as for smaller slip values (ws0). Furthermore, the scaled centerline velocity was least affected by varying Reynolds and Mach numbers, whereas changes are observed in centerline velocity curves for different slip values. The wall shear stress was essentially unchanged by the Reynolds numbers, compressibility range and slip values considered in this Thesis.

scholarly journals Mathematical Modelling of Blood Flow through a Tapered Overlapping Stenosed Artery with Variable Viscosity

2014 ◽  
Vol 11 (4) ◽  
pp. 185-195 ◽  
Author(s):  
G. C. Shit ◽  
M. Roy ◽  
A. Sinha
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Variable Viscosity ◽  
Stenosed Artery ◽  
Flow Through ◽  
Wall Shear ◽  
Analytical Expressions

This paper presents a theoretical study of blood flow through a tapered and overlapping stenosed artery under the action of an externally applied magnetic field. The fluid (blood) medium is assumed to be porous in nature. The variable viscosity of blood depending on hematocrit (percentage volume of erythrocytes) is taken into account in order to improve resemblance to the real situation. The governing equation for laminar, incompressible and Newtonian fluid subject to the boundary conditions is solved by using a well known Frobenius method. The analytical expressions for velocity component, volumetric flow rate, wall shear stress and pressure gradient are obtained. The numerical values are extracted from these analytical expressions and are presented graphically. It is observed that the influence of hematocrit, magnetic field and the shape of artery have important impact on the velocity profile, pressure gradient and wall shear stress. Moreover, the effect of primary stenosis on the secondary one has been significantly observed.

An Experiment on the Pulsatile Flow at Transitional Reynolds Numbers—The Fluid Dynamical Meaning of the Blood Flow Parameters in the Aorta

1993 ◽  
Vol 115 (4A) ◽  
pp. 412-417 ◽  
Author(s):  
Masahide Nakamura ◽  
Wataru Sugiyama ◽  
Manabu Haruna
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Pulsatile Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Human Aorta ◽  
Navier Stokes Equation ◽  
Wall Shear

An experiment on the fully developed sinusoidal pulsatile flow at transitional Reynolds numbers was performed to evaluate the basic characteristics of the wall shear stress. In this experiment, the wall shear stress was calculated from the measured section averaged axial velocity and the pressure gradient by using the section averaged Navier-Stokes equation. The experimental results showed that the ratio of the amplitude of the wall shear stress to the amplitude of the pressure gradient had the maximum value when the time averaged Reynolds number was about 4000 and the Womersley number was about 10. As this condition is close to the blood flow condition in the human aorta, it is suggested that the parameter of the aorta has an effect to increase the amplitude of the wall shear stress acting on the arterial wall.

Non-Newtonian Flow Patterns Associated With an Arterial Stenosis

1992 ◽  
Vol 114 (4) ◽  
pp. 512-514 ◽  
Author(s):  
X. Y. Luo ◽  
Z. B. Kuang
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Constitutive Equation ◽  
Wall Shear Stress ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Flow Patterns ◽  
Arterial Stenosis ◽  
Newtonian Flow ◽  
Wall Shear

A non-Newtonian constitutive equation for blood has been introduced in this paper. Using this equation, blood flow attributes such as velocity profiles, flowrate, pressure gradient, and wall shear stress in both straight and stenotic (constricted) tubes have been examined. Results showed that compared with Newtonian flow at the same flowrate, the non-Newtonian normally features larger pressure gradient, higher wall shear stress, and different velocity profile, especially in stenotic tube. In addition, the non-Newtonian stenotic flow appears to be more stable than Newtonian flow.

MATHEMATICAL MODELING OF BLOOD FLOW IN ARTERIES SUBJECT TO A VIBRATING ENVIRONMENT

2018 ◽  
Vol 18 (01) ◽  
pp. 1850001 ◽  
Author(s):  
J. C. MISRA ◽  
S. D. ADHIKARY ◽  
B. MALLICK ◽  
A. SINHA
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Couple Stress ◽  
Harmonic Oscillation ◽  
External Pressure ◽  
Arterial Blood Flow ◽  
Arterial Blood ◽  
Wall Shear

A mathematical model has been developed in this paper with an aim to study arterial blood flow in a vibration environment. Blood is treated as a couple stress fluid. Oscillatory flow in a porous channel is considered in the study, when the flow takes place under the action of an external pressure gradient. The fluid flows between two porous plates lying parallel to each other. The fluid is considered to be injected on one plate with a constant velocity. The plates are considered to be oscillating with the same frequency in their own planes. However, the plate velocity of single-harmonic oscillation is not constant. The effects of various parameters representing couple stress, suction and magnitude of the oscillating pressure gradient on the velocity profile and wall shear stress are discussed. It is found that the presence of couple stress in the fluid enhances the velocity of the fluid in both axial and transverse directions, while a reverse phenomenon is observed for the wall shear stress.

Non-Newtonian Blood Modeling in Intracranial Aneurysm Hemodynamics: Impact On the WSS and OSI Metrics for Ruptured and Unruptured Cases

2021 ◽  
Author(s):  
Iago Oliveira ◽  
Gabriel B Santos ◽  
José Luiz Gasche ◽  
Julio Militzer ◽  
Carlos Eduardo Baccin
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Oscillatory Shear ◽  
Patient Specific ◽  
Oscillatory Shear Index ◽  
Hemodynamic Variables ◽  
Flow Parameters ◽  
Newtonian Model ◽  
Wall Shear

Abstract When simulating blood flow in intracranial aneurysms, the Newtonian model seems to be ubiquitous. However, analyzing the results from the few studies on this subject, the doubt remains on whether it is necessary to use non-Newtonian models in wall shear stress (WSS) simulations of cerebral vascular flows. Another open question related to this topic is whether different rheology models would influence the flow parameters for ruptured and unruptured cases, especially because ruptured aneurysms normally have morphological features that could trigger non-Newtonian phenomena in the blood flow due to low shear rates. The objective of this study is to investigate such flows. By using Computational Fluid Dynamics (CFD) in an open-source framework, we simulated an equal number of ruptured and unruptured patient-specific aneurysms to assess the influence of the blood modeling on the main hemodynamic variables associated with aneurysm formation, growth, and rupture. Results for wall shear stress and oscillatory shear index and their metrics were obtained using Casson and Carreau-Yasuda non-Newtonian models and were compared with those obtained using the Newtonian model. We found that the wall shear stress at peak systole is overestimated by more than 50% by using the non-Newtonian models, but its metrics based on time and surface averaged values remain unaffected. On the other hand, the surface-averaged oscillatory shear index (OSI) is underestimated by more than 40% by the non-Newtonian models. In addition, all differences were consistent among all aneurysms cases irrespective of their rupture status.

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