Analysis of Viscous Incompressible Fluid Flows and Heat Transfer

Abstract

We first present a brief ideas and principles in "Fluid Mechanics" which may serve as the background materials of viscous, incompressible laminar Newtonian or non-Newtonian fluid flow problems considered in the present thesis. The basic equations viz, the continuity equation and the momentum equation for the motion of viscous incompressible fluid under the limits of continuum hypothesis are presented. The laws of classical mechanics apply throughout the continuous medium under consideration. The length scale of the flow is always taken to be large compared with the molecular mean-free-path. so that the fluid can be considered as a continuum. It excludes the flow of gases at very tow pressures i.e., rarefied gases. Liquid flows can usually be treated as incompressible fluid. The classification of fluids, say, Newtonian and non-Newtonian, Prandtrs boundary layer concept, boundary layer equations, concept of similarity variable for analyzing the viscous flow problems, group theoretic approach of for finding invariant solution of an incompressible viscous fluid flows, arc discussed systematically. Using the similarity variable for some specific flow problems, a set of nonlinear ordinary differential equations, known as self similar equations arc derived. Analytical or closed-form solution as well as numerical solution of these nonlinear differential equations relating to particular class of flow problems arc obtained and the corresponding flow quantities are shown graphically and discussed physically. In general, matter is found to exist in four phases or states e.g. solid. liquid, gas and plasma (ionized gases). Out of these last three states of matter are termed as fluid. Fluid mechanics is the subject in which wc deal with the flow problems pertaining to one of these phases e.g. liquid. gas and plasma or combination, mainly of the first two or last two phases. Essentially, the fluid flow problems are of widely spread interest in various fields of engineering as well as in meteorology, oceanography and other subjects of physical sciences. We live in a world which is largely a fluid. Air, oceans, rivers and so on arc all fluids whose behaviour is mostly described using the principles of continuum hypothesis. The constitutive equations are framed using some assumptions based on the material behaviors of fluid and the flow conditions. lt's study 1s important to physicists or applied mathematicians whose main interest is in understanding the related physical phenomena. On the other hand fluid dynamical engineers worked out many problems of practical interest using empirical formula. Also an understanding of this subject helps us to explain a variety fascinating natural phenomena around us.