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Numerical Investigation on Electro-Magneto Hydrodynamic Flow of Jeffrey Nanofluid in an Inclined Tapered Arterial Stenosis with Variable Viscosity, Variable Magnetic Field and Periodic Body Force

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Abstract

In the present study, electromagnetic effects on blood flow along with iron oxide nanoparticles through tapered arterial stenosis inclined at an angle. The rheology of blood is treated as Jeffrey fluid. The governing equations of the flow under the assumptions of mild stenosis and slight tapering are solved numerically and solutions for velocity, wall shear stress, flow resistance, temperature and concentration profiles are obtained. The influences of variable viscosity and radially variable magnetic field are analyzed in detail. From the obtained numerical results, it is significant that the magnitude of shear stress at the arterial wall enhances with increase in the values of stenotic height, tapering parameter, viscosity parameter, viscosity index and electrokinetic parameter. Also, the values of Grashof numbers, Jeffrey parameter, inclination parameters, Womersley number and Prandtl number help in reducing the magnitudes of wall shear stress and resistive impedance. It is worthy to note that the temperature profile decreases with increase in the values of thermophoresis parameter and the concentration profile enhances with a rise in the values of Brownian motion parameter and Schmidt number. The obtained significant results can be used to control the hydrodynamic factors namely the wall shear stress, velocity and flow impedance which, inturn will be useful in the diagnosis and treatment of atherosclerosis.

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Acknowledgements

I thank the anonymous reviewers for their valuable suggestions in improving the standard of the paper.

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  1. Department of Mathematics, Mepco Schlenk Engineering College, Sivakasi, Tamilnadu, 626005, India

    S. Priyadharshini

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Appendix

Appendix

Finite Difference Schemes used in the study: The spatial (radial) derivatives are approximated by the central difference and time derivatives with a forward difference (for velocity) as given below:

$$\begin{aligned} \begin{aligned}&\frac{\partial u_f}{\partial t} = \frac{(u_f)_{i,j}^{(s+1)}-(u_f)_{i,j}^{(s)}}{\varDelta t}, \\&\frac{\partial u_f}{\partial \xi } = \frac{(u_f)_{i,j+1}^{(s)}-(u_f)_{i,j-1}^{(s)}}{2\varDelta \xi } = (uffp)_{i,j}^{(s)} (say),\\&\frac{\partial ^2 u_f}{\partial \xi ^2} = \frac{(u_f)_{i,j+1}^{(s)}-2(u_f)_{i,j}^{(s)}+(u_f)_{i,j-1}^{(s)}}{(\varDelta \xi )^2} = (ufsp)_{i,j}^{(s)}\\ \end{aligned} \end{aligned}$$

The formula used in the above study are as follow: Wall shear stress distribution:

$$\begin{aligned} S_{rz} = \left[ \frac{1+K-K(R\xi )^n}{R(1+\lambda _1)}\right] \frac{\partial u_f}{\partial \xi } \end{aligned}$$

Flow Rate:

$$\begin{aligned} Q = 2R^2 \int _0^1{\xi u d\xi } \end{aligned}$$

Flow resistance:

$$\begin{aligned} \lambda = \int _{0}^{L}\frac{-\frac{\partial p}{\partial z}}{Q}dz, \end{aligned}$$

L is the length of the artery.

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Priyadharshini, S. Numerical Investigation on Electro-Magneto Hydrodynamic Flow of Jeffrey Nanofluid in an Inclined Tapered Arterial Stenosis with Variable Viscosity, Variable Magnetic Field and Periodic Body Force. Int. J. Appl. Comput. Math 7, 182 (2021). https://doi.org/10.1007/s40819-021-01123-1

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