MATHEMATICAL ANALYSIS OF BLOOD FLOW THROUGH AN ARTERIAL SEGMENT WITH TIME‐DEPENDENT STENOSIS

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.

THEORETICAL ANALYSIS OF BLOOD FLOW THROUGH AN ARTERIAL SEGMENT HAVING MULTIPLE STENOSES

The present paper is concerned with the study of a mathematical model for the flow of blood through a multi-stenosed artery. Blood is considered here to consist of a peripheral plasma layer which is free from red cells, and a core region which is represented by a Casson fluid. A suitable generalized geometry of multiple stenoses existing in the arterial segment under consideration is taken for the study. A thorough quantitative analysis has been made through numerical computations of the variables involved in the analysis that are of special interest in the study. The computational results are presented graphically.