Mathematical modelling of blood flow is developed by treating the blood as a Newtonian fluid. In this study, stenosis has been accounted as an overlapping shaped in two-dimensional Cartesian coordinate system. Blood are assumed as steady laminar flow, fully developed and incompressible which flowing through an arterial bifurcation where the wall considered rigid with no-slip condition. Galerkin weighted residual method is performed and a Matlab code is developed to solve the problem. To validate the code, comparison has been made with the results obtained by COMSOL Multiphysics. Results on the velocity profiles and the streamlines pattern are observed and discussed in details.
Education is a process that develops human abilities and attitudes. Higher education began expanding its reach after WWII due to the growing political awareness of its importance for a nation’s future prospects. This study focuses on how higher education impacted Malaysian graduates by reviewing the system’s development from 1957 to present day and even beyond to 2025. A qualitative approach is used, based mostly on books, journals and qualified papers. We identify how Malaysia’s system of higher education system ensured the future employment of its graduates. In addition, we provide the set of governmental guidelines that help maintain and enhance the system’s production of marketable graduates; thus, ensuring their employability in the global job market.
A stabilized form of finite element formulation known as the Galerkin least-squares (GLS) method is implemented here for solving the two-dimensional incompressible non-Newtonian fluid model of blood flow in a diseased artery. The modelling for this type of flow is based on the conservation of mass and momentum equations, coupled with the generalised Newtonian liquid (GNL) constitutive equation characterized by the generalised power law (GPL) model. The flow of blood in this present study are assumed as steady, laminar and fully developed. The finite element algorithms considered herein are first solved for the Newtonian fluid in a straight artery with a bell shaped stenosis for validation purposes. As the efficiency and validity of the proposed algorithms are obtained through comparison with the findings from existing literature and COMSOL Multiphysics 5.2 software. Then, the algorithms are being implemented to the generalised power law fluid model of blood flow in a bifurcated artery with overlapping stenosis located at the parent's arterial lumen. The numerical results illustrate the arising of distinct sizes of vortex shedding downstream of the stenotic region for each generalised power law index.
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.
Blood flow through a bifurcated artery with the presence of an overlapping stenosis located at parent’s arterial lumen under the action of a uniform external magnetic field is studied in this paper. Blood is treated as an electrically conducting fluid which exhibits the Magnetohydrodynamics principle and it is characterized by a Newtonian fluid model. The governing equations are discretized using a stabilization technique of finite element known as Galerkin least-squares. The maximum velocity and pressure drop evaluated in this present study are compared with the results found in previous literature and COMSOL Multiphysics. The solutions found in a satisfactory agreement, thus verify the source code is working properly. The effects of dimensionless parameters of Hartmann and Reynolds numbers in the fluid’s velocity and pressure are examined in details with further scientific discussions.
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