Mathematical Modeling and Theoretical Analysis of Fluid Flow with Heat Transfer over a Stretching/Shrinking Sheet

Abstract

The study about heat transfer and boundary layer flow over a stretching sheet gotten consideration from numerous analysts due to its significance in many engineering and industrial applications, such as, paper generation, glass-fiber generation, solidification of fluid gems, petroleum generation, extraordinary oils, suspension arrangements, wire drawing, ceaseless cooling and fibers turning, fabricating plastic films and extraction of polymer sheet. In the view of above applications, theocratical analysis is carried out for the flow of Carreau fluid over a stretching/shriking sheet. The problems are formulated under the effects of various parameters with suitable transformations. The obtained boundary layers equations are transformed from PDEs to ODEs with the given boundary conditions. Thesis are divided into 7 chapters. Chapter one deals with fundamental preliminaries that will make this thesis understandable for readers. Literature review is also a part of this chapter. Chapter two deal with the investigation of MHD mixed convection Carreau fluid flow over a nonlinear stretching/ shrinking permeable sheet near a stagnation point. Homotopy Analysis Method (HAM) is utilized to find the solution of the system of nonlinear problem. Qualitative comparison of the HAM and BVP4C numerical routine are presented. The influences of different parameters such as Weissenberg number We2, Magnetic parameter M2, Suction and Injection parameter s, Stretching or Shrinking parameter B, Mixed convection parameter A, Nonlinear parameter m and Lewis number Le on concentration, velocity and temperature distributions are studied graphically and analyzed. Chapter three concerned with the study of magnetohydrodynamic (MHD) boundary layer flow of Carreau fluid with variable thermal conductivity and viscosity over stretching/shrinking sheet. The viscosity and thermal conductivity is considered to vary linearly with temperature. Analysis are made analytically by HAM. Numerical solutions of the problem is also obtained by BVP4C numerical routine, which agrees well with analytical solution. The influence of natural parameters, such as the Prandtl number, Weissenberg number, Lewis number, Magnetic parameter, Suction parameter, Stretching/ Shrinking parameter and the heat flux constants are shown in several plats and in tabulated results. The purpose of chapter four is to examine an unsteady motion of Carreau fluid produced by stretching/ shrinking sheet with a magnetic field applied normal to the sheet. The governing momentum and the energy equation admit a self similarity solution. Results are discussed in terms of Weissenberg number, Unsteadiness parameter, Stretching/ Shrinking parameter, Power law index, Prandtl number, Blowing and Magnetic parameter. The aim of chapter five is to study the MHD Carreau fluid slip flow together with viscous dissipation and heat transfer by taking the impact of thermal radiation over a stretching sheet embedded in a porous medium with variable thickness and variable thermal conductivity. Thermal conductivity of the liquid is expected to differ straightly with temperature. The effects of various parameters such as magnetic parameter M2, Weissenberg number We2, porosity parameter D,power law index n, wall thickness parameter α, power index parameter m, thermal conductivity parameter ε, slip parameter λ ,radiation parameter R and Prandtl number Pr on velocity and temperature profiles are studied graphically and analyzed. The focus of chapter six is to study of Carreau fluid flow over sheet stretching in the xy-plane. For this purpose equations are modeled from the set of Naiver-Stoke equations combine with heat and mass transport taking into account the effects of thermophoresis and Brownian motion. From similarity transformations non-dimensional parameters of our interest such as Weissenberg number We2, Magnetic parameter M2, Suction parameter S, Stretching parameters B,A, power law index n, thermophoresis parameter Nt, Prandtl number Pr, Lewis number Le, Brownian motion parameter Nb and Biot numbers B1,B2 are introduced. The effects of these parameters are analyzed with the help of graphs.