Mathematical analysis of blood flow through an arterial segment with time‐dependent stenosis

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.

Key words:

• Pulsatile flow
• Casson model
• Two‐layer model
• Time‐dependent stenosis