MATHEMATICAL AND NUMERICAL MODELLING OF FLOW PROBLEMS IN BIOLOGICAL SYSTEMS

Abstract

The thesis consists of a study of modelling of flow problems of Newtonian and non-Newtonian fluids in biological systems through constricted arteries. It consists of nine chapters. The first chapter is introductory and deals with the fundamental concepts of flow and transfer processes of Newtonian and non-Newtonian biological fluids. Power—law and biviscous models have been used as a constitutive equation of blood. The constitutive equation and equations of conservation of mass, momentum and energy have been used for the Newtonian and non-Newtonian biological fluids. Integral momentum technique, finite difference and quasi=linearization methods have been used in the solutions of bio-fluid problems. In Chapter II, an analysis has been carried out for establishing the laminar start-up flow in constricted artery due to elastic reservoir (aorta). In this chapter, study of axially symmetric unsteady flow into the lumen of tube of varying cross-section with axial distance with start-up flow is calculated. An analytical expression for the velocity profile, pressure gradient and wall shear stress have been derived by employing momentum integral' technique and effect of growth of stenosis has been broughtout in comparison to normal flow of blood into the abdominal aorta.