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.

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

2017 ◽  
Vol 17 (08) ◽  
pp. 1750109 ◽  
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.

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.

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.

The influence of magnetic field on wall shear stress in power law fluid flow of blood

2021 ◽  
Author(s):  
Amira Husni Talib ◽  
Ilyani Abdullah ◽  
Nik Nabilah Nik Mohd Naser
Keyword(s):  
Magnetic Field ◽  
Shear Stress ◽  
Fluid Flow ◽  
Wall Shear Stress ◽  
Power Law ◽  
Power Law Fluid ◽  
Wall Shear

A Superposition Analysis of the Turbulent Boundary Layer in an Adverse Pressure Gradient

1951 ◽  
Vol 18 (1) ◽  
pp. 95-100
Author(s):  
Donald Ross ◽  
J. M. Robertson
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Pressure Recovery ◽  
Stress Coefficient ◽  
Wall Shear

Abstract As an interim solution to the problem of the turbulent boundary layer in an adverse pressure gradient, a super-position method of analysis has been developed. In this method, the velocity profile is considered to be the result of two effects: the wall shear stress and the pressure recovery. These are superimposed, yielding an expression for the velocity profiles which approximate measured distributions. The theory also leads to a more reasonable expression for the wall shear-stress coefficient.

scholarly journals Pipe rheology of microfibrillated cellulose suspensions

Cellulose ◽  
2019 ◽  
Vol 27 (1) ◽  
pp. 141-156 ◽  
Author(s):  
Tuomas Turpeinen ◽  
Ari Jäsberg ◽  
Sanna Haavisto ◽  
Johanna Liukkonen ◽  
Juha Salmela ◽  
...  
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Yield Stress ◽  
Power Law ◽  
Slip Flow ◽  
Microfibrillated Cellulose ◽  
Flow Index ◽  
Shear Rheology ◽  
Power Law Fluids ◽  
Wall Shear

Abstract The shear rheology of two mechanically manufactured microfibrillated cellulose (MFC) suspensions was studied in a consistency range of 0.2–2.0% with a pipe rheometer combined with ultrasound velocity profiling. The MFC suspensions behaved at all consistencies as shear thinning power law fluids. Despite their significantly different particle size, the viscous behavior of the suspensions was quantitatively similar. For both suspensions, the dependence of yield stress and the consistency index on consistency was a power law with an exponent of 2.4, similar to some pulp suspensions. The dependence of flow index on consistency was also a power law, with an exponent of − 0.36. The slip flow was very strong for both MFCs and contributed up to 95% to the flow rate. When wall shear stress exceeded two times the yield stress, slip flow caused drag reduction with consistencies higher than 0.8%. When inspecting the slip velocities of both suspensions as a function of wall shear stress scaled with the yield stress, a good data collapse was obtained. The observed similarities in the shear rheology of both the MFC suspensions and the similar behavior of some pulp fiber suspensions suggests that the shear rheology of MFC suspensions might be more universal than has previously been realized.

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