Department of Mathematics, Bangladesh University of Engineering and Technology, Bangladesh
*Corresponding author: R Nasrin, Department of Mathematics, Bangladesh University of Engineering and Technology, Bangladesh
Submission: March 13, 2020;Published: April 03, 2020
ISSN : 2576-8840Volume13 Issue1
This paper is devoted to study numerically a recent development of a non-Newtonian blood flow model for a stenosed artery in human blood vessel. For numerical investigation the blood flow modeling method of this research begins with non-Newtonian power-law model. The governing system of equation based on incompressible Navier-Stokes equations with externally imposed magnetic resonance has been generalized to take into account the mechanical properties of blood. The intent of this research is to examine the effects of inlet velocity and imposed magnetic field on the blood flow throughout the artery. The Galerkin’s weighted residual method of finite element system has been employed to resolve the governing system of equation with proper boundary conditions. The numerical simulation has been conducted for various inlet velocities from 0.005 to 0.1m/s and magnetic field strength from 0 to 6 tesla with superior convergence of the iterative structure. Results have been shown in terms of velocity, surface plot of velocity, pressure and viscosity contours. Cross-sectional plots of velocity and viscosity magnitudes across the stenotic contraction have also been displayed graphically. Obtained results of the blood flow simulations indicate that viscosity increases due to increasing values of inlet velocity of blood and magnetic strength.
Keywords: Non-newtonian fluid; Stenotic artery; Power law model; Magnetic field; Finite element method
Nomenclature
B: Magnetic field intensity [tesla]; K: Consistency coefficient; m=Blood consistency coefficient; n= Blood flow behavior index; 𝑝=Blood flow pressure [𝑃𝑎]; u=Velocity components (along x direction) [m/s]; v=Velocity components (along y direction) [m/s]
Greek symbol
= Shear stress (normal) [Pa]; 𝛾̇=Shear rate [𝑠−1]; = Lower shear rate limit; = Shear stress (tangential) [𝑃𝑎]; = Wall shear stress [𝑃𝑎]; 𝜇=Fluid viscosity [𝑁𝑠/m2]; 𝜌=Blood density [kg/m3]; σ=Electrical conductivity; λ=Curve fitting parameters
Abbreviation: BFD: Biomagnetic Fluid Dynamic; CT: Computed Tomography; EMF: Electro Magnetic Field; HCT: Hematocrite; MRI: Magnetic Resonance Imaging; WSS: Wall Shear Stress; 2D: Two Dimensional