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Pulsatile Flow of EMHD Micropolar Hybrid Nanofluid in a Porous Bifurcated Artery With an Overlapping Stenosis in the Presence of Body Acceleration and Joule Heating

  • General and Applied Physics
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Abstract

The aim of the present work is to examine the electro-kinetic pulsatile transport of hybrid a nanofluid (\(Ag-TiO_2/\)blood) in a porous bifurcated artery with an overlapping stenosis in the parent lumen subjected to a uniform magnetic field and periodic acceleration of the human body. The rheology of the base fluid (blood) is characterized by a micropolar fluid in order to model the impact of microrotation of the microelements (blood cells). The heat transfer analysis has been explored by considering viscous dissipation and Joule heating features. The electric double layer (EDL) and charge distribution are demonstrated by the Poisson–Boltzmann equation, which is linearized by means of the Debye–Hückel approximation. An analytical expression for the electric potential function is derived by solving the linearized Poisson–Boltzmann equation. The appropriate equations for the governing two-dimensional flow are normalized and simplified into the one-dimensional flow by considering the mild stenotic and low Reynolds number approximations, and a suitable coordinate conversion is utilized to convert the boundary of bifurcated artery into a well-designed boundary. The transformed coupled nonlinear partial differential equations are solved numerically by adopting the Crank–Nicolson finite difference technique subjected to appropriate initial and boundary conditions. The impact of physiological factors on the flow characteristics such as axial velocity, microrotation, temperature, wall shear stress and resistance to flow has been analyzed on both sides of the apex for \(Ag-\)blood as well as \((Ag-TiO_2)/\)blood flow models. Also, a comparative analysis between the results of nanofluid (\(Ag-\)blood) and hybrid nanofluid (\(Ag-TiO_2/\)blood) has been made. Finally, the Nusselt number is computed at the critical height of stenosis and recorded in tabular form for both \(Ag-\)blood and \((Ag-TiO_2)/\)blood flow models. These results display that axial flow, microrotation of particles and thermal performance in bifurcated arteries can be normalized by regulating the magnetic and electro-osmotic parameters. The EDL thickness (inversion of electro-osmotic parameter) plays a vital role in attenuating the wall shear stress and resistance to flow in the stenotic bifurcated artery. The heat transfer rate at the stenotic wall increases with the Brinkman and Grashof numbers and decays with the severity of stenosis and micropolar coupling number.

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Abbreviations

−:

Represents the dimensional quantities

\(\overline{z},\, \overline{r}\) :

Axial and radial coordinate, respectively

\(\overline{R}_0\) :

Radius of the parent artery in the unconstricted region

\(\overline{r}_0\) :

Radius of the daughter artery

\(\overline{R}_1,\, \overline{R}_2\) :

Radius of outer and inner walls, respectively

\(\overline{B}_0\) :

Magnetic field

\(\overline{E}_0\) :

Electric field

\(\overline{u},\, \overline{v}\) :

Axial and radial velocity, respectively

\(\overline{T}\) :

Temperature

\(\overline{p}\) :

Pressure

\(\overline{k}_p\) :

Permeability of porous medium

\(\overline{J}\) :

Microgyration parameter

\(\overline{u}_{HS}\) :

Helmholtz–Smoluchowski velocity

A :

Amplitude of body acceleration

\(Ke\) :

Electro-osmotic parameter

\(Ha\) :

Hartmann number

N :

Coupling number

\(m^2\) :

Micropolar spin parameter

Da :

Darcy number

Gr :

Grashof number

Pr :

Prandtl number

Br :

Brinkman number

Sz :

Joule heating parameter

\(Q_p,\, Q_d\) :

Volumetric flow rate in parent and daughter arteries, respectively

Nu :

Nusselt number

\(I_0,\, K_0\) :

Modified Bessel functions

\(\overline{\delta }_s\) :

Maximum height of constriction

\(\beta\) :

Half of the bifurcation angle

\(\overline{\rho }_{hnf}\) :

Density of hybrid nanofluid

\(\overline{\mu }_{hnf}\) :

Viscosity of hybrid nanofluid

\(\overline{\sigma }_{hnf}\) :

Electrical conductivity of hybrid nanofluid

\(\overline{\eta }\) :

Rotational viscosity

\(\overline{\gamma }\) :

Spin gradient viscosity

\(\overline{\nu }_{\overline{\theta }}\) :

Microrotation velocity

\(\overline{\psi }\) :

Electro-osmotic potential

\(\overline{\rho }_e\) :

Electric charge density

\(\epsilon\) :

Dielectric constant

\(\overline{\kappa }\) :

Debye–Hückel parameter

\(\overline{\lambda }_D\) :

Debye length

\(\overline{\zeta }_1,\, \overline{\zeta }_2\) :

Zeta potential on the outer and inner wall, respectively

\(\tau\) :

Shear stress

\(\lambda _p,\, \lambda _d\) :

Flow resistance in parent and daughter arteries, respectively

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Acknowledgements

The first author Mr. Ramakrishna Manchi is thankful to the MHRD, the Government of India for the grant of a fellowship to carry out this work.

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  1. Department of Mathematics, National Institute of Technology, Tamil Nadu, Tiruchirappalli, 62001, India

    Ramakrishna Manchi & R. Ponalagusamy

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  1. Ramakrishna Manchi
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Manchi, R., Ponalagusamy, R. Pulsatile Flow of EMHD Micropolar Hybrid Nanofluid in a Porous Bifurcated Artery With an Overlapping Stenosis in the Presence of Body Acceleration and Joule Heating. Braz J Phys 52, 52 (2022). https://doi.org/10.1007/s13538-022-01061-3

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