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Analytical solution of Newtonian nanofluid flow in a tapered artery based on a consistent couple stress theory

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Abstract

Reduction of the stenosis in arteries is one of the most important applications of nanoparticles in medicine. Thus, investigating nanoparticles in stenosed arteries is a subject attracting so much attention from the researchers nowadays. However, considering the small size of arteries, it seems that non-classical theories demonstrate better results when compared to the classical Navier-Stokes theory. The present paper aims at investigating the Newtonian nanofluid flow through divergent and convergent, non-tapered and tapered arteries with mild stenosis according to the consistent couple stress theory. Concentration, temperature, and velocity profiles, as well as the impact of various parameters such as the height of the stenosis, the shape of the stenosis curve, Brownian distribution parameter, thermophoresis distribution parameter, Darcy number, and the length scale were calculated for all the three geometries. Results demonstrate that an increase in the height of the stenosis and an increase in the Darcy coefficient, respectively, lead to a decrease and an increase in the axial velocity in all three artery geometries. Moreover, an increase in the impact of the length scale leads to a decrease in the axial velocity. The impact of the length scale on the velocity profile shows the significance of the length parameter on the flow within the geometries with small sizes which is not present in the classical Navier-Stokes theory.

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Abbreviations

Br :

Local nanoparticle Grashof number

c :

Volumetric volume expansion coefficient

C :

Concentration

D a :

Darcy number

D ij :

Symmetric part of velocity gradient tensor

f :

Body force per unit mass

Gr :

Local temperature Grashof number

h :

Heat source per unit mass

k :

Fluid permeability

K nf :

Thermal conductivity

l :

Characteristic material length

L 0 :

Length of stenosis

M ij :

Coupe stress tensor

n :

Shape parameter

N b :

Brownian motion parameter

N t :

Thermophoresis parameter

P :

Pressure

q i :

Heat flux vector

R 0 :

Radius of non-tapered artery

R(z):

Radius of tapered artery

t :

Time

T :

Temperature

T ij :

Force stress tensor

u :

Axial velocity

v :

Radial velocity

V k :

Velocity vector

α :

Slip parameter

γ :

Coefficient of thermal expansion

δ :

The height of the stenosis

ε :

The internal energy per unit mass

μ :

Viscosity

ξ :

Tapering parameter

ρ :

Density

Ω ij :

Skew-symmetric part of velocity gradient tensor

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Authors and Affiliations

  1. Department of Mechanical Engineering, Shahrekord University, P.O. B 115, Shahrekord, Iran

    Fatemeh Karami, Afshin Ahmadi Nadooshan & Yaghuob Tadi Beni

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  1. Fatemeh Karami
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  2. Afshin Ahmadi Nadooshan
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  3. Yaghuob Tadi Beni
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Correspondence to Afshin Ahmadi Nadooshan.

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Karami, F., Nadooshan, A.A. & Beni, Y.T. Analytical solution of Newtonian nanofluid flow in a tapered artery based on a consistent couple stress theory. Heat Mass Transfer 56, 459–476 (2020). https://doi.org/10.1007/s00231-019-02713-y

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