Mathematical Analysis for MHD Flow of Blood in Constricted Arteries

Abstract

The unsteady oscillatory magneto-hydrodynamic flow of blood in small diameter arteries with mild constriction is analyzed, blood being modelled as a HerschelBulkley fluid. Finite difference method is employed for solving the associated initial boundary value problem. Explicit finite difference schemes for velocity distribution, flow rate, skin friction and longitudinal impedance to the flow are obtained. The effects of pressure gradient, yield stress, magnetic field, power law index and maximum depth of the stenosis on the aforesaid flow quantities are discussed through appropriate graphs. It is found that the velocity and flow rate decrease and the skin friction and longitudinal impedance to flow increase with the increase of the magnetic field parameter. It was recorded that the flow rate increases and the skin friction decreases with the increase of the phase angle. It was also noted the skin friction and longitudinal impedance to flow that increase almost linearly with the increase of maximum depth of the stenosis. The estimates of the increase in the longitudinal impedance to flow and skin friction are increased considerably by the presence of the magnetic field.

Sinusoïdal flow of blood in a cylindrical deformable vessel exposed to an external magnetic field

“…His code has been tested using the theoretical results that are presented in Abi-Abdallah et al [32]. Using the Finite Difference Method, Sankar et al [33] analyzed the pulsatile flow of blood through stenosed arteries in the presence of magnetic field. Due to the presence of the stenosis, they consider the vessel wall as rigid, and, for low Reynolds numbers, they neglect the radial velocity component.…”

Modelling and simulation of myocardial infarction in the human cardiovascular system

“…In addition, the assumption that blood is a two-layer fluid (which can be considered as the suspension of erythrocytes that behave like a non-Newtonian fluid in the core region and as a Newtonian fluid in the peripheral region of plasma) was used to study the pulsatile flow of blood through a catheterized artery [6]. The result is a mathematical model of nonlinear implicit system of partial differential equations.…”