| Newton (1687) proposed a linear relationship between the stress tensor sigma ij and the strain rate tensor eij for isotropic viscous incompressible fluids as (n/a) p being undetermined hydrostatic pressure, mu the coefficient of viscosity and eij defined by (n/a).;The constitutive equation for Walters liquid (Model B') with short memories is (n/a), where (n/a).;Here sigmaik is the stress tensor, p is an isotropic pressure, gik is the metric tensor of a fixed coordinate system xi, vi is the velocity vector, the contravariant form of (n/a).;It is convected derivative of the deformation rate tensor eik . Here eta0 is the limiting viscosity at small rate of shear, which is given by (n/a).;But the above classical linear theory fails to explain a number of phenomena such as Merrington effect, Weissenberg effect, normal stress effect, centripetal pump effect etc., which were realised long back. The inadequacy of the classical linear theory of Newtonian fluid has led to the necessity of generalizing the linear relationship between stress and strain rate tensor. Many rheological models have been proposed to describe the mechanical behaviours of non-Newtonian fluids. But in this study, we have chosen the model of Walters liquid (Model B') with short memories to investigate the flow behaviours in specific problems for different geometries.;N(tau) being the relaxation spectrum as introduced by Walters. This idealized model is a valid approximation of Walters fluid (Model B') taking very short memories into account, so that terms involving (n/a) are ignored.;In this thesis, our endeavour is to investigate the flow patterns of Walters liquid and analyse their behaviour under different valid and suitable boundary conditions. The thesis consists of six chapters.;In chapter I, a brief note on the classical linear theory of fluid flow has been given with its limitations. The outline of various theories proposed to explain the non-linear effects such as normal stress effects, Merrington effect, Weissenberg effect etc. and their advantages and demerits are given. A brief deduction of the constitutive equation of Walters liquid (Model B') has been done. Also, the equations of motion in cartesian, cylindrical polar and spherical polar coordinates are given. A brief review of the relevant literature and the motivation of the present work have been given in the last section. |
