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International Conference on Mathematical Modelling and Scientific Computation

ICMMSC 2018: Mathematical Modelling and Scientific Computing with Applications pp 219–239Cite as

Finite Element Analysis of MHD Blood Flow in Stenosed Coronary Artery with the Suspension of Nanoparticles

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 308))

Abstract

The numerical study presents a two dimensional mathematical modelling and computational simulation of blood flow in a stenosed coronary artery in the presence of magnetic field. Blood flow model is considered based on second grade fluid flow and heat transfer with the suspension of nanoparticles. Vogel’s model is employed for viscosity of blood as a function of temperature. In order to complete our model, the variability in design and size of stenosis is considered. The finite element method is used to solve the transformed conservation equations numerically in conjunction of variational approach and FreeFEM++. The results show that an increase in the thermophoresis parameter (\( N_{t} \)) decreases the velocity while the increment in the Brownian motion parameter (\( N_{b} \)) increases the velocity in the whole domain. An increase in \( N_{t} \) and Brownian motion parameter (\( N_{b} \)), there is an increase in temperature values and nanoparticles concentration at the throat of the stenosis and as well as in the remaining domain. These properties changes in the domain by changing the shapes and designs of the stenosis in the domain.

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Abbreviations

A, B:

Constants in viscosity function

B r :

Brownian diffusion constant

D b :

Brownian diffusion coefficient

D T :

Thermophoretic diffusion coefficient

g:

Gravitational vector

\( \alpha_{1} ,\,\alpha_{2} \) :

Material modules

G r :

Grashof Number

\( B_{0} \) :

Magnetic field

\( \rho_{f} \) :

Density of the base fluid

\( \rho_{p} \) :

Density of the nanoparticles

M :

Magnetohydrodynamics parameter

\( N_{b} \) :

Brownian motion parameter

\( N_{t} \) :

Thermophoresis parameter

V :

Velocity vector

\( A_{1} ,\,A_{2} \) :

Rilvin Erickson Tensors

J :

Electric current density

\( \theta \) :

Temperature

\( \kappa \) :

Thermal conductivity

Φ :

Nanoparticle volume fraction

\( \lambda_{1} \) :

Viscoelastic parameter

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Authors and Affiliations

  1. Department of Mathematics, MNNIT, Allahabad, Prayagraj, 211004, India

    Ankita Dubey & B. Vasu

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  1. Ankita Dubey
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  2. B. Vasu
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Correspondence to Ankita Dubey .

Editor information

Editors and Affiliations

  1. Discipline of Mathematics, Indian Institute of Technology Indore, Indore, Madhya Pradesh, India

    Santanu Manna

  2. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, USA

    Biswa Nath Datta

  3. Discipline of Mathematics, Indian Institute of Technology Indore, Indore, Madhya Pradesh, India

    Sk. Safique Ahmad

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Dubey, A., Vasu, B. (2020). Finite Element Analysis of MHD Blood Flow in Stenosed Coronary Artery with the Suspension of Nanoparticles. In: Manna, S., Datta, B., Ahmad, S. (eds) Mathematical Modelling and Scientific Computing with Applications. ICMMSC 2018. Springer Proceedings in Mathematics & Statistics, vol 308. Springer, Singapore. https://doi.org/10.1007/978-981-15-1338-1_17

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