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A note on the pulsatile flow of hydromagnetic Eyring–Powell nanofluid through a vertical porous channel

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Abstract

In this study, the pulsating flow of hydromagnetic nanofluid in a vertical porous channel has been investigated. Blood is considered as a base fluid that is non-Newtonian, and alumina \((\mathrm{Al}_{2}\mathrm{O}_{3})\), copper (Cu), silver (Ag) and gold (Au) are considered as nanoparticles. The effects of Joule’s heating and velocity slip at the walls are taken into consideration. Numerical results are obtained by solving the transformed differential equations using the Runge–Kutta fourth-order in addition to the shooting method. Influences of several flow controlling parameters including Grashof number, cross-flow Reynolds number, Hartmann number and frequency parameter on velocity and temperature profiles are examined graphically. The results elucidates that the velocity-slip plays an important role in increasing the heat transfer and velocity of the nanofluid. Further, the heat transfer rate by means of Nusselt number against different parameters is studied and the numerical results obtained are presented. It shows that heat transfer rate at the injection wall increased with increasing Grashof number, frequency parameter and radiation parameter.

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Abbreviations

\( \hat{u} \) :

Velocity along \( \hat{x} \)-axis

\( \gamma , C \) :

Eyring–Powell fluid parameters

\( q_r \) :

Radiative heat flux

\( \hat{v} \) :

Velocity along \( \hat{y} \)-axis

M :

Hartmann number

u :

Dimensionless velocity

\( \hat{t} \) :

Time

R :

Reynold’s number

\( \hat{p} \) :

Dimensional pressure

t :

Dimensionless time

k :

Permeability of porous walls

p :

Dimensionless pressure

\( \phi \) :

Nanoparticle volume fraction

\( \kappa \) :

Thermal conductivity

Gr:

Grashof number

\( \sigma \) :

Electrical conductivity

\( \upsilon \) :

Kinematic viscosity

Pr:

Prandtl number

\( \mu \) :

Dynamic viscosity

\( \hat{\tau }_{xy} \) :

Stress tensor

L :

Slip parameter

g :

Acceleration due to gravity

\( \hat{T} \) :

Temperature

Ec:

Eckert number

\( \theta \) :

Dimensionless temperature

\( k_1 \) :

Non-Newtonian parameter

\( \beta \) :

Thermal expansion coefficient

\( c_p \) :

Specific heat

a :

Slip coefficient

\( \hat{\sigma } \) :

Stefan–Boltzmann constant

\( B_0 \) :

Magnetic field strength

\( \rho \) :

Density

\( \omega \) :

Frequency

\(\hat{k}\) :

Rosseland mean absorption coefficient

\( v_0 \) :

Suction/injection velocity

H :

Frequency parameter

Rd:

Radiation parameter

nf:

Nanofluid

f :

Base fluid

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Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences,VIT-AP University, Inavolu, Vijayawada, Andhra Pradesh, 522 237, India

    P. Bharath Kumar & Srinivas Suripeddi

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  1. P. Bharath Kumar
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  2. Srinivas Suripeddi
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Both authors contributed equally to this paper.

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Correspondence to Srinivas Suripeddi.

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Kumar, P.B., Suripeddi, S. A note on the pulsatile flow of hydromagnetic Eyring–Powell nanofluid through a vertical porous channel. Eur. Phys. J. Spec. Top. 230, 1465–1474 (2021). https://doi.org/10.1140/epjs/s11734-021-00057-5

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