Mathematical Analysis of Blood Flow Through an Arterial Segment With Time‐dependent Stenosis

Abstract

Abstract. A mathematical model is developed here with an aim to study the pulsatile flow of blood through an arterial segment having a time-dependent stenosis. Blood is considered to consist of a core layer where erythrocytes are concentrated and a peripheral plasma layer that is free from erythrocytes. The plasma layer is taken to behave as a Newtonian fluid,while the core layer is represented by as a Casson fluid (non-Newtonian) model. The pulsatile flow is analyzed by considering a periodic pressure gradient, which is a function of time. A perturbation analysis is employed to solve the governing differential equations by taking the Womersley frequency parameter to be small (α < 1). This is a realistic assumption for physiological fluid flows, particularly for flow of blood in small vessels. Using appropriate boundary conditions, analytical expressions for the velocity profile, the volumetric flow rate, the wall shear stress and the flow resistance have been derived. These expressions are computed numerically and the computational results are presented graphically, in order to illustrate the variation of different quantities that are of particular interest in the study.

The Effects of Magnetic Casson Blood Flow in an Inclined Multi-stenosed Artery by using Caputo-Fabrizio Fractional Derivatives

“…As blood flows at low shear rate into narrow arteries, it behaves like a Casson fluid [16]. Many researchers [17][18][19] have been working on the Casson fluid model for modelling blood flow through narrow arteries. Nagarani and Sarojamma [20] studied the effect of body acceleration on pulsatile flow of Casson fluid through a mild stenosed artery.…”

A review on non-Newtonian fluid models for multi-layered blood rheology in constricted arteries

“…Singh [ 89 ] addressed a two-fluid model of movement of blood in which both the peripheral plasma and core layers were treated as Casson fluids. Many researchers have proposed single and multi-phase Casson fluid models of blood motion in various situations [ 90 – 95 ].…”

The Effects of Magnetic Casson Blood Flow in an Inclined Multi-stenosed Artery by using Caputo-Fabrizio Fractional Derivatives

“…As blood flows at low shear rate into narrow arteries, it behaves like a Casson fluid [16]. Many researchers have been working on the Casson fluid model for modelling blood flow through narrow arteries [17][18][19]. Nagarani and Sarojamma [20] studied the effect of body acceleration on pulsatile flow of Casson fluid through a mild stenosed artery.…”