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

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (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.

## Keywords

Blood flow Vogel’s model Nanoparticles Magnetohydrodynamics Thermophoresis Brownian motion Coronary artery Stenosis

## Nomenclature

A, B

Constants in viscosity function

Br

Brownian diffusion constant

Db

Brownian diffusion coefficient

DT

Thermophoretic diffusion coefficient

g

Gravitational vector

$$\alpha_{1} ,\,\alpha_{2}$$

Material modules

Gr

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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