The thesis entitled "Rheological Aspects of Viscous Non-Newtonian Fluid Flow in Narrow Gaps" submitted for the award of degree of Doctor of philosophy in mathematics embodies the results of research work carried out by me under the supervision of Dr. Prem Shankar Singh, Reader and Head, Department of Mathematics S.G.R.P.G. College Dobhi, Jaunpur (U.P.), India.

The whole thesis is divided into seven chapters. The number inside the bracket [ ] refers to the references given at the end of each chapter.

The first chapter is introduction which contains definition concept and basic information about the different types of fluid model. Equation of motion in different co-ordinate system are given. The rheological property of blood, plasma-peripheral layer, and historical background of microcirculation are also discussed in this chapter. The previous works done on the subject, mathematical tools and equation of fluid motion have been given.

In the second chapter, two phase flow of blood in cylindrical tube of uniform radius R is considered. A central core fluid viscosity is surrounded by cell free plasma fluid viscosity & thickness to the adjacent wall is discussed. The expression for core velocity and plasma fluid velocity have been obtained. Expression for volumetric flow rate is also found out. The variation of bluntness parameter w.r.t. to different parameter are shown by table & graphs. Microscopic study of blood flow in narrow vessels reveals that bluntness of the velocity profile in core region deviated from parabolic flow.

In the third chapter, micropolar fluid model of Newtonian fluid sphere has been discussed. The flow field within the Newtonian fluid sphere and flow field of the micropolar fluid out side the sphere are determinded. The expression for drag and terminal velocity are found out. Where the value of drag decreases with increasing viscosity.

The fourth chapter is devoted to the mild stenosis of blood flow through narrow vessels. The steady of blood flow in an uniform circular tube of radius R is considered. The expression for velocity and flow rate is found out. We also find out the apparent fluidity at maximum height of stenosis. The expression of wall shear stress at maximum height of stenosis have been obtained.

In the fifth chapter, the Poiseuille flow of micropolar fluid through a rigid circular tube of radius R is considered. The expression for velocity and apparent viscosity have been calculated. The expression for flow rate is also calculate. In this analysis we observed that slip in velocity at the boundary Wall affects the velocity field where as the particles rotational velocity is unaffected. The variation in pressure gradient w.r.t. velocity of the axis are shown by graph. The value of pressure gradient decreases when the velocity increases suddenly decreases for constant value of S¯. .

Six chapter is devoted to the blood vessels A model of straight long rigid circular tubes whose radii are constant & plasma layer is assumed to be constant & independent of time R location. The expression of shear stress, velocity distribution, wall shear stress, pluge core radius and flow rate at any time for small values of Womersley frequency parameter alpha have been calculated.

The last chapter is devoted to the study of velocity profiles in the core and PPL regions. Flow rates for different regions have been obtained. The effective viscosities for one and two phase flows obeying Bingham plastic constitutive equation have been obtained. Bingham flow model of visco-elastic fluid flow in narrow gap with rheological effect has been analysed.