Solutions of the Momentum Equation for Laminar Flow through Concentric Ducts using Symmetry Methods

Abstract

Partial or ordinary di erential equations are used to solve problems in a variety of elds. The goal of achieving exact solutions of di erential equations is therefore of great importance and continues to attract great attention. The basic purpose of this thesis entitled "Solution of the Momentum Equation for Laminar Flow through Con- centric Ducts using Symmetry Method" is attempted to nd symmetries and the exact solutions of momentum equation. After that, we reduced partial di erential equation to ordinary di erential equations. Then we obtained exact solutions corresponding to these ordinary di erential equations. This thesis is divided into four chapters. The brief outlines of the research work pre- sented chapter wise in the thesis are as follows: In Chapter 1, is given the brief introduction of partial di erential equations and their solutions. Also we discussed preliminary material and relevant literature of Lie group of transformations. In Chapter 2, methods to solve partial di erential equations, Lie symmetries and in- variant solution of partial di erential equations are discussed. The core of the thesis is chapter 3. The symmetries and invariant solution of momen- tum equation are investigated. In Chapter 4, the thesis is concluded.