Non Newtonian Fluid Model for the Effect of Resistance Parameter on Different Portion of Arteries of Blood Flow Through an Arterial Stenosis

A theoretical study of an unsteady two-layered blood flow through a stenosed artery is presented in this article. The geometry of a rigid stenosed artery is assumed to be$w$-shaped. The flow regime is assumed to be laminar, unsteady and uni-directional. The characteristics of blood are modelled by the generalized Oldroyd-B non-Newtonian fluid model in the core region and a Newtonian fluid model in the periphery region. The governing partial differential equations are derived for each region by using mass and momentum conservation equations. In order to facilitate numerical solutions, the derived differential equations are nondimensionalized. A well-tested explicit finite-difference method (FDM) which is forward in time and central in space is employed for the solution of a nonlinear initial boundary value problem corresponding to each region. Validation of the FDM computations is achieved with a variational finite element method algorithm. The influences of the emerging geometric and rheological parameters on axial velocity, resistance impedance and wall shear stress are displayed graphically. The instantaneous patterns of streamlines are also presented to illustrate the global behaviour of the blood flow. The simulations are relevant to haemodynamics of small blood vessels and capillary transport, wherein rheological effects are dominant.

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JEFFREY FLUID MODEL FOR BLOOD FLOW THROUGH A TAPERED ARTERY WITH A STENOSIS

Journal of Mechanics in Medicine and Biology ◽

10.1142/s0219519411003879 ◽

2011 ◽

Vol 11 (03) ◽

pp. 529-545 ◽

Cited By ~ 34

Author(s):

NOREEN SHER AKBAR ◽

S. NADEEM ◽

MOHAMED ALI

Keyword(s):

Blood Flow ◽

Newtonian Fluid ◽

Fluid Model ◽

Time Derivative ◽

Jeffrey Fluid ◽

Retardation Time ◽

Tapered Artery ◽

Convective Derivative ◽

Flow Through ◽

Two Parameters

In this article, we have studied a non-Newtonian fluid model for blood flow through a tapered artery with a stenosis by assuming blood as Jeffrey fluid. The main purpose of our study was to follow the idea of Mekheimer and El Kot (2008), for Jeffrey fluid model, mean to study Jeffrey fluid model for blood flow through a tapered artery with a stenosis, Jeffrey fluid model is a non-Newtonian fluid model in which we consider convective derivative instead of time derivative. It is capable of describing the phenomena of relaxation and retardation time. The Jeffrey fluid has two parameters, the relaxation time λ1 and retardation time [Formula: see text]. Perturbation method is used to solve the resulting equations. The effects of non-Newtonian nature of blood on velocity profile, wall shear stress, shearing stress at the stenosis throat, and impedance of the artery are discussed. The results for Newtonian fluid are obtained as special case from this model.

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Comparison of Newtonian and Non-newtonian Fluid Models in Blood Flow Simulation in Patients With Intracranial Arterial Stenosis

Frontiers in Physiology ◽

10.3389/fphys.2021.718540 ◽

2021 ◽

Vol 12 ◽

Author(s):

Haipeng Liu ◽

Linfang Lan ◽

Jill Abrigo ◽

Hing Lung Ip ◽

Yannie Soo ◽

...

Keyword(s):

Blood Flow ◽

Newtonian Fluid ◽

Fluid Model ◽

Arterial Stenosis ◽

Cfd Modeling ◽

Patient Specific ◽

Fluid Models ◽

Cfd Models ◽

Atherosclerotic Stenosis ◽

Transient Simulations

BackgroundNewtonian fluid model has been commonly applied in simulating cerebral blood flow in intracranial atherosclerotic stenosis (ICAS) cases using computational fluid dynamics (CFD) modeling, while blood is a shear-thinning non-Newtonian fluid. We aimed to investigate the differences of cerebral hemodynamic metrics quantified in CFD models built with Newtonian and non-Newtonian fluid assumptions, in patients with ICAS.MethodsWe built a virtual artery model with an eccentric 75% stenosis and performed static CFD simulation. We also constructed CFD models in three patients with ICAS of different severities in the luminal stenosis. We performed static simulations on these models with Newtonian and two non-Newtonian (Casson and Carreau-Yasuda) fluid models. We also performed transient simulations on another patient-specific model. We measured translesional pressure ratio (PR) and wall shear stress (WSS) values in all CFD models, to reflect the changes in pressure and WSS across a stenotic lesion. In all the simulations, we compared the PR and WSS values in CFD models derived with Newtonian, Casson, and Carreau-Yasuda fluid assumptions.ResultsIn all the static and transient simulations, the Newtonian/non-Newtonian difference on PR value was negligible. As to WSS, in static models (virtual and patient-specific), the rheological difference was not obvious in areas with high WSS, but observable in low WSS areas. In the transient model, the rheological difference of WSS areas with low WSS was enhanced, especially during diastolic period.ConclusionNewtonian fluid model could be applicable for PR calculation, but caution needs to be taken when using the Newtonian assumption in simulating WSS especially in severe ICAS cases.

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A non-newtonian fluid model for blood flow through arteries under stenotic conditions

Journal of Biomechanics ◽

10.1016/s0021-9290(05)80011-9 ◽

1993 ◽

Vol 26 (9) ◽

pp. 1129-1141 ◽

Cited By ~ 75

Author(s):

J.C. Misra ◽

M.K. Patra ◽

S.C. Misra

Keyword(s):

Blood Flow ◽

Newtonian Fluid ◽

Fluid Model ◽

Flow Through

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COUPLE STRESS FLUID MODEL FOR PULSATILE FLOW OF BLOOD IN A POROUS TAPERED ARTERIAL STENOSIS UNDER MAGNETIC FIELD AND PERIODIC BODY ACCELERATION

Journal of Mechanics in Medicine and Biology ◽

10.1142/s0219519417501093 ◽

2017 ◽

Vol 17 (08) ◽

pp. 1750109 ◽

Cited By ~ 3

Author(s):

R. PONALAGUSAMY ◽

S. PRIYADHARSHINI

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Newtonian Fluid ◽

Couple Stress ◽

Flow Resistance ◽

Fluid Model ◽

Arterial Stenosis ◽

Couple Stress Fluid ◽

Flow Through ◽

Wall Shear

In this paper, a magnetic and non-Newtonian fluid model for pulsatile flow of blood with periodic body acceleration has been investigated by adopting Laplace transform and finite Hankel transform. A closed form of analytic solution is obtained for physiologically important quantities such as velocity profile, flow rate, wall shear stress and flow resistance. Effects of different physical parameters reflecting couple stress parameter, Darcy number, Hartman number, tapering angle (divergent tapered tube or convergent tapered tube), shape stenosis parameter and amplitude of periodic acceleration on wall shear stress and flow resistance have been emphasized. For any value of taper angle ([Formula: see text]) and stenotic height ([Formula: see text]), it is pertinent to point out here that the wall shear stress is less in the case of flow through the asymmetric stenosed tube as compared to the case of flow through the symmetric stenosed tube when one is in the up-stream of flow region, but it is of opposite behavior as one moves in the down-stream of flow region. It is important to note that the flow resistance increases significantly and more nonlinearly with the increase in the axial distance in the case of flow through a converging tapered artery with stenosis as compared to that of the same flow through a stenosed artery. The size of trapping bolus becomes larger for the flow of couple stress fluid through a converging tapered arterial stenosis than that of the same flow through a stenosed artery. Another important result is that as compared to the case of Newtonian fluid, the couple stress fluid behaviour plays a key role in increasing the size of trapping bolus. This investigation puts forward important observations that the asymmetric nature of stenosis considered plays a predominant role in reducing the flow resistance in the case of diseased blood vessel and the flow resistance is higher for the case of couple stress fluid than that of Newtonian fluid. Finally, some applications of the present model have been briefly discussed.

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INFLUENCE OF HEAT AND CHEMICAL REACTIONS ON HYPERBOLIC TANGENT FLUID MODEL FOR BLOOD FLOW THROUGH A TAPERED ARTERY WITH A STENOSIS

Heat Transfer Research ◽

10.1615/heattransres.2012004295 ◽

2012 ◽

Vol 43 (1) ◽

pp. 69-94 ◽

Cited By ~ 5

Author(s):

Noreen Sher Akbar ◽

Sohail Nadeem ◽

Mohamed Ali

Keyword(s):

Blood Flow ◽

Chemical Reactions ◽

Fluid Model ◽

Hyperbolic Tangent ◽

Tapered Artery ◽

Flow Through

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A Non-Newtonian Fluid Flow Model for the Slip Condition on Blood Flow through a Stenosed Artery using Power-law Fluid

Journal of Computer and Mathematical Sciences ◽

10.29055/jcms/823 ◽

2018 ◽

Vol 9 (7) ◽

pp. 871-879

Author(s):

Rajesh Shrivastava ◽

R. S. Chandel ◽

Ajay Kumar ◽

Keerty Shrivastava and Sanjeet Kumar

Keyword(s):

Blood Flow ◽

Fluid Flow ◽

Newtonian Fluid ◽

Power Law ◽

Flow Model ◽

Slip Condition ◽

Power Law Fluid ◽

Stenosed Artery ◽

Flow Through

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Mechanics of non-Newtonian blood flow in an artery having multiple stenosis and electroosmotic effects

Science Progress ◽

10.1177/00368504211031693 ◽

2021 ◽

Vol 104 (3) ◽

pp. 003685042110316

Author(s):

Salman Akhtar ◽

Luthais B McCash ◽

Sohail Nadeem ◽

Salman Saleem ◽

Alibek Issakhov

Keyword(s):

Blood Flow ◽

Flow Problem ◽

Fluid Model ◽

Casson Fluid ◽

Viscous Effects ◽

Heating Effects ◽

Casson Fluid Model ◽

Flow Through ◽

Mathematical Equations ◽

Mathematica Software

The electro-osmotically modulated hemodynamic across an artery with multiple stenosis is mathematically evaluated. The non-Newtonian behaviour of blood flow is tackled by utilizing Casson fluid model for this flow problem. The blood flow is confined in such arteries due to the presence of stenosis and this theoretical analysis provides the electro-osmotic effects for blood flow through such arteries. The mathematical equations that govern this flow problem are converted into their dimensionless form by using appropriate transformations and then exact mathematical computations are performed by utilizing Mathematica software. The range of the considered parameters is given as [Formula: see text]. The graphical results involve combine study of symmetric and non-symmetric structure for multiple stenosis. Joule heating effects are also incorporated in energy equation together with viscous effects. Streamlines are plotted for electro-kinetic parameter [Formula: see text] and flow rate [Formula: see text]. The trapping declines in size with incrementing [Formula: see text], for symmetric shape of stenosis. But the size of trapping increases for the non-symmetric case.

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