Group Invariant Methods of Some Multidimensional Fluid Flows with Heat Transfer Analysis

Abstract

In this thesis,a multidimensional fluid flows with heat transfer by using the Lie group approach is investigated. In the first chapter, a brief introduction and background of symmetries,Navier-Stokes equations for the fluid flow, energy equations, boundary layer equations, and some basic definitions of flow and heat characteristics are given. Chapter one also has three pages of historical notes. In chapter two,two different cases are studied. In case (i), the invariants for MHD non-Newtonian fluid flow with heat transfer in the presence of source/sink effects is investigated. In case (ii), the system of ordinary differential equations by using the group theoretic method to analyze the MHD non-Newtonian fluid flow with thermal radiation effects is studied. In particular, for both cases an invariant and find the analytic solutions after considering the stretching sheet phenomenon has been opted. In chapter three, thenon-Newtonian unsteady flow with viscous dissipation effects are studied. After finding the invariants, an analytic solution for the governing system of differential equations is calculated. An unsteady stretching sheet case is considered to observe the flow characteristics. In chapter four, two cases namely; (i) the stagnation point flow phenomenon in the presence of thermal radiation effects are taken into account. The governing equations are simplified through group a theoretic method. For a particular invariant we consider the flat plate case to observe the flow characteristics.In case (ii) the similarity analysis of MHD Hall current effects on free convective non- Newtonian flow with heat transfer phenomenon is presented.By considering flat plate case the governing system of ordinary differential equations are solved by numerical technique to observe the flow behavior. In chapter five, the non-Newtonian flow with heat and mass transfer over the stretching walls in the presence of source/sink effects are analyzed by using Lie group method. The influence of different physical parameters on velocity, temperature and concentration profiles are presented through graphs and tables. In chapter six, the Lie group analysis of MHD non-Newtonian flow with heat transfer over a stretching rotating surface is reported. Flow characteristics are also investigated through graphs and tables. viii Chapters seven summarize the presented study and suggest some future work.