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Analytical Investigation of Nanoparticle as a Drug Carrier Suspended in a MHD Blood Flowing Through an Irregular Shape Stenosed Artery

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Abstract

In this study, a single- and discrete-phase models are used to obtain the analytical expressions of velocity, temperature, wall shear stress and stream function, to delineate the transport characteristics of Newtonian gold–blood nanofluid flowing through stenosed artery in the presence of magnetic field. The spherical gold nanoparticles are used in discrete-phase analysis for tracking the nanoparticle in the blood flow through multiple stenoses, which is not explored so far. The effect of various flow parameters on velocity profile, wall shear stress and stream function is demonstrated through mathematically and graphically for different values of interest. The effect of nanoparticle volume fraction in the presence and absence of external magnetic field is investigated. The results demonstrate that with an increase in the particle concentration in the presence of magnetic field, the temperature of the nanofluid and wall shearing stress are increased, whereas the velocity is decreased. The significant effect of Brownian motion is observed on gold nanoparticle in discrete-phase model. This study would provide valuable information for nanoparticle distribution in a vascular artery in the field of nanoparticle drug delivery for treatment of stenotic diseases.

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Abbreviations

HPM:

Homotopy perturbation method

MHD:

Magnetohydrodynamic

MSD:

Mean square displacement

\(\gamma\) :

Thermal expansion coefficient

\(\lambda\) :

Mean free path of the blood

\(\mu\) :

Viscosity

\(\nu\) :

Kinematic viscosity

\(\phi\) :

Volume fraction of nanoparticles

\(\rho\) :

Density of blood

\(\sigma\) :

Standard deviation

\(\sigma _1\) :

Electric conductivity

\(\tau\) :

Particle relaxation time

\(\tilde{D}\) :

Diffusion coefficient

\(B_0\) :

Applied magnetic field

bf:

Subscript for base fluids properties

\(C_{\mathrm{c}}\) :

Stokes–Cunningham slip correction

\(d_{\mathrm{p}}\) :

Nanoparticle diameter

E :

Electric field

g :

Acceleration of gravity

\(G_{r}\) :

Grashof number

J :

Electric current density

k :

Thermal conductivity

\(K_B\) :

Boltzmann constant

\(l_0\) :

Length of a single stenosis

M :

Hartmann number

nf:

Subscript for nanofluids properties

p:

Subscript for nanoparticle properties

\(Q_{0}\) :

Heat absorption parameter

Re :

Reynolds number

\(S_0\) :

Spectral intensity function

\(T_{\rm B}\) :

Absolute temperature of the blood

\(T_{\infty }\) :

Temperature giving to the upper wall

\(u_0\) :

Average velocity

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Acknowledgements

The authors are grateful to Dr. Samiran Ghosh, Department of Applied Mathematics, University of Calcutta for fruitful discussions. This work is partially supported by CPEPA, UGC, New Delhi.

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Authors and Affiliations

  1. Institute of Engineering and Management, Salt Lake, Kolkata, 700091, India

    Satyasaran Changdar

  2. Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata, 700009, India

    Soumen De

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  1. Satyasaran Changdar
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Correspondence to Satyasaran Changdar.

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Changdar, S., De, S. Analytical Investigation of Nanoparticle as a Drug Carrier Suspended in a MHD Blood Flowing Through an Irregular Shape Stenosed Artery. Iran J Sci Technol Trans Sci 43, 1259–1272 (2019). https://doi.org/10.1007/s40995-018-0601-1

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  • DOI: https://doi.org/10.1007/s40995-018-0601-1

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