Rheological properties of Reiner-Rivlin fluid model for blood flow through tapered artery with stenosis

Akbar, Noreen Sher; Nadeem, Sohail; Mekheimer, Kh. S.

doi:10.1016/j.joems.2014.10.007

Cited by 23 publications

(10 citation statements)

References 18 publications

(11 reference statements)

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“…14 shows the axial velocity profile across cross section of artery for non-tapered, divergent and convergent artery. The trend shows similarity to the earlier reported trend [27,28].…”

Section: Numerical Results and Discussionsupporting

confidence: 90%

“…18 and with respect to ratio of cross viscosity to viscosity in Fig. 19 show similar trend line reported in earlier literature [28].…”

Section: Numerical Results and Discussionsupporting

confidence: 86%

“…The equations governing steady flow of incompressible Reiner -Rivlin in cylindrical coordinate considering suitable transformation for non-dimensional parameters and mild stenosis conditions reduce to [27,28]…”

Section: Formulation Of Problemmentioning

confidence: 99%

“…Resistance impedence [27,28]: The effect of viscosity, flow rate, degree of stenosis and type of tapered artery on velocity, resistance impedence and wall shear stress are studied by using Equations 7, 8 and 9 respectively.…”

Section: Solution Of Problemmentioning

confidence: 99%

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Analytical Study of Non-Newtonian Reiner–Rivlin Model for Blood flow through Tapered Stenotic Artery

Dash¹,

Singh²

2020

Math.Biol.Bioinf.

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Stenosis, the abnormal narrowing of artery, significantly affects dynamics of blood flow due to increasing resistance to flow of blood. Velocity of blood flow, arterial pressure distribution, wall shear stress and resistance impedance factors are altered at different degree of stenosis. Prior knowledge of flow parameters such as velocity, flow rate, pressure drop in diseased artery is acknowledged to be crucial for preventive and curative medical intervention. The present paper develops the solution of Navier–Stokes equations for conservation of mass and momentum for axis-symmetric steady state case considering constitutive relation for Reiner–Rivlin fluid. Reiner–Rivlin constitutive relation renders the conservation equations non-linear partial differential equations. Few semi-analytical and numerical solutions are found to be reported in literature but no analytical solution. This has motivated the present research to obtain a closed-form solution considering Reiner–Rivlin constitutive relation. Solution yields an expression for axial velocity, which is utilized to obtain pressure gradient, resistance impedance and wall shear stress by considering volumetric flow rate as initial condition. The effect of viscosity, cross viscosity, flow rate, taper angle of artery and degree of stenosis on axial velocity, resistance impedance and wall shear stress are studied.

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“…14 shows the axial velocity profile across cross section of artery for non-tapered, divergent and convergent artery. The trend shows similarity to the earlier reported trend [27,28].…”

Section: Numerical Results and Discussionsupporting

confidence: 90%

“…18 and with respect to ratio of cross viscosity to viscosity in Fig. 19 show similar trend line reported in earlier literature [28].…”

Section: Numerical Results and Discussionsupporting

confidence: 86%

Section: Formulation Of Problemmentioning

confidence: 99%

Section: Solution Of Problemmentioning

confidence: 99%

See 2 more Smart Citations

Analytical Study of Non-Newtonian Reiner–Rivlin Model for Blood flow through Tapered Stenotic Artery

Dash¹,

Singh²

2020

Math.Biol.Bioinf.

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“…This type of flow can be found in many parts of living body such as, the muscular layers of the digestive track that comprise smooth muscle tissue, the one way movement of the food mass which is called a bolus controlled by a wave-like involuntary muscle contraction, transport of urine from kidney to bladder, transport of cilia and blood flow in small vessels. There are a large number of simulation techniques which may be aimed at analyzing the impedance of peristaltic flow of various fluid models [13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Entropy Generation in the Flow of Peristaltic Nanofluids in Channels With Compliant Walls

Abbas

Bai

Rashidi

et al. 2016

Entropy

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The role of radiation and bioconvection as an external agent to control the temperature and motion of fluid over the radially spinning circular surface: A theoretical analysis via Chebyshev spectral approach

Usman

Bhatti

Ghaffari

et al. 2022

Math Methods in App Sciences

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The usage of nanoparticles is effectively increased in industries because of their high thermal performance. Moreover, the bioconvection phenomenon in nanomaterials leads to innovative biotechnology applications, such as biofuels, biosensors, the petroleum industry, etc. Because of the nanoparticle's exceptional performance and bioconvection phenomenon, the magnetohydrodynamics bioconvection Reiner–Rivlin nanofluid flow is considered over the rotatory stretchable disk contains the motile gyrotactic microorganisms. The heat and mass transport phenomenon with thermal radiation and activation energy is also investigated under convective‐Nield's boundary conditions. The governing partial differential equations (PDEs) are transmuted with specific similarity transformation into ordinary differential equations (ODEs). The obtained ODEs are solved numerically through the assistance of the Chebyshev spectral collocation method. The effects of the flow parameters on the boundary layer profiles are reported graphically. The graphical illustration elucidates that the dimensionless parameters have significantly affected the nondimensional boundary layer profiles. The fluid velocity, temperature, concentration of nanoparticles, and motile density of microorganisms are effectively controlled through the proper alteration of the pertinent parameters. The thermophoresis parameter decreases the heat and mass transport rates, whereas the Brownian motion parameter helps to increase them. Finally, the current research can successfully fill a gap in the existing literature.

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Rheological properties of Reiner-Rivlin fluid model for blood flow through tapered artery with stenosis

Cited by 23 publications

References 18 publications

Analytical Study of Non-Newtonian Reiner–Rivlin Model for Blood flow through Tapered Stenotic Artery

Analytical Study of Non-Newtonian Reiner–Rivlin Model for Blood flow through Tapered Stenotic Artery

Analysis of Entropy Generation in the Flow of Peristaltic Nanofluids in Channels With Compliant Walls

The role of radiation and bioconvection as an external agent to control the temperature and motion of fluid over the radially spinning circular surface: A theoretical analysis via Chebyshev spectral approach

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