Numerical solution of magnetohydrodynamics effects on a generalised power law fluid model of blood flow through a bifurcated artery with an overlapping shaped stenosis

This paper presents a numerical analysis of blood flow in a diseased vessel within the presence of an external magnetic field. The blood flow was considered to be incompressible and fully developed, in that the non-Newtonian nature of the fluid was characterised as a generalised power law model for...

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Bibliographic Details
Published in:PloS one 2023-02, Vol.18 (2), p.e0276576-e0276576
Main Authors: Zain, Norliza Mohd, Ismail, Zuhaila
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Arteries
Behavior
Bifurcations
Biology and Life Sciences
Blood
Blood flow
Blood Flow Velocity - physiology
Blood vessels
Cardiovascular diseases
Computer Simulation
Constriction, Pathologic
Disease
Extremities
Fluid flow
Galerkin method
Hemodynamics
Humans
Incompressible flow
Laws, regulations and rules
Magnetic fields
Magnetohydrodynamics
Mathematical models
Mathematics
Medicine and Health Sciences
Methods
Models, Cardiovascular
Newton-Raphson method
Newtonian fluids
Numerical analysis
Numerical methods
Physical Sciences
Power law
Prevention
Pulmonary arteries
Quadratures
Rheology
Risk factors
Shear stress
Shear thickening (liquids)
Shear thinning (liquids)
Stenosis
Stress, Mechanical
Structure
Thinning
Thromboembolism
Thrombosis
Veins & arteries
Viscosity
Viscous flow
Wall shear stresses
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Summary:This paper presents a numerical analysis of blood flow in a diseased vessel within the presence of an external magnetic field. The blood flow was considered to be incompressible and fully developed, in that the non-Newtonian nature of the fluid was characterised as a generalised power law model for shear-thinning, Newtonian, and shear-thickening fluids. The impact of a transverse directed external magnetic field on blood flow through a stenosed bifurcated artery was investigated. The arterial geometry was considered as a bifurcated channel with overlapping shaped stenosis. The problem was treated mathematically using the Galerkin Least-Squares (GLS) method. The implementation of this numerical method managed to overcome the numerical instability faced by the classical Galerkin technique when adopted to a highly viscous flow. The benefit of GLS in circumventing the Ladyzhenskaya-Babuška-Brezzi (LBB) condition was utilized by evaluating both the velocity and pressure components at corner nodes of a unstructured triangular element. The non-linearity that emerged from the convective terms was then treated using the Newton-Raphson method, while the numerical integrals were computed using a Gaussian quadrature rule with six quadrature points. The findings obtained from this study were then compared with available results from the literature as well as Comsol multiphysics software to verify the accuracy and validity of the numerical algorithms. It was found that the application of magnetic field was able to overcome flow reversal by 39% for a shear-thinning fluid, 26% for a Newtonian fluid, and 27% for a shear-thickening fluid. The negative pressure and steep wall shear stress which occurs at the extremities of an overlapping stenosis throat were diminished by rise in magnetic intensity. This prevented thrombosis occurrence and produced a uniform calm flow.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0276576