Numerical Study of Boundary Layer Flow with Variable Properties

Abstract

dominated by viscosity and creating the majority of drag experienced by the boundary body and one outside the boundary layer, where viscosity can be neglected without significant effects on the so lution. This allows a closed-form so lution for the tlow in both areas, a significant simplification of the full Navier-Stokes equations. The majority of the heat / transfer to and from a body also takes place within the boundary layer. again allowing the equations to be simplified in the Dow fie ld outside the boundary layer. The pressure distribution throughout the boundary layer in the direction nonnal to the surface (such as an airfoil) remains constant throughout the boundary layer, and is the same as on the surface itself. The fie ld of boundary layer flow in the presence of stagnation point flow over surface and the several combinations of additional effects on the stretching problems are important in many practical appli cations, such as polymer sheet or fi lament extrusion from a dye or long thread between feed roll or wind -up roll, glass fiber and paper production, drawing of plastic films, liquid films in condensation process. Due to the high applicability of this problem in such industrial phenomena, it has attracted many researchers and one of the pioneering studies has been done by Sakiadis. Numerous investigations have been conducted on the magnetohydrodynamic (MI-ID) flows and heat transfer. The stud y of MHD boundary layer flow on a continuous stretching sheet has got considerable attention during the last few decades due to its numerous applications. The study of heat transfer and flow field is necessary for determining the quali ty of the fi nal products of such processes. Both the kinematics of stretching and the simultaneous heating or cooling during such processes has a decisive influence on the qua li ty of the final products. A broad review of the prevailing literature reveals that much commitment is absorbed to the fluid flow having phase slip solution. Heat transfer phenomena for flow of two dimensional viscous fluids after using MHD, variable thelmal conductivity, heat generation/absorption, slip conditions is not being v addressed comprehensively along with numerical solutions. Consideration of convective surface adds further complexities in the modelling. Specially, applications of numerical techniques for justification of the obtained approximate solutions of such type of highly nonlinear models are not addressed in deta il. We intend to discuss such issues in this thesis. In the view of above mentioned discussion, this thesis is structured in the fo llowing forms: Chapter 1 is devoted to introduction and literature survey. Chapter 2 deals with the phase slip solution of boundary layer magnetic modulated flow. We numerically investi gate Taylor-Couette tlow in a wide-gap configuration. The fluid is taken to be electrically conducting. As the Reynolds number measuring the rotation rate is increased, the initial onset of vortices invo lves phase sli p events. Subsequent bifurcations lead to a variety of other so lutions, including ones both symmetric and asymmetric about the mid-plane. For even larger Reynolds number a different type of phase slip arises, in which vortices form at the outer edges of the pattern and drift inward, disappearing abruptly at a certain point. These so lutions can also be symmetric or asymmetric about the mid-plane, and co-exist at the same Reynolds number "Published in Acta Mech. Chapter 3 deals with free convcction boundary layer flow over a stretching flat plate with variable thermal conductivity and radiation. This work addresscs the behavior of viscous fluid over a stretching Oat plate with variable thermal conductivity. The cffects of radiation are also encountered. Thermal conductivity is considered as a linear func tion of temperature. Approximate solutions through Homotopy Analysis Method (HAM) are obtained. The effects of different physical parameters on velocity and temperature fields are shown through tables and graphs. Numerical solution by using Runge-Kutta-Fehlberg method is computed for comparison which shows good agreement with the HAM solution "Published in International Journal of Pure and App licd Mathcmatics. Chapter 4 deals with Stagnation poiht Dow over a stretching cylinder with variable thermal conductivity and slip condition. In this chapter we will discuss the behavior of viscous fluid near stagnation point over a stretching cylinder with variable thermal conductivity. The effects of slip conditions are also encountered in this work. Thermal conductivity is considered as a linear function of temperature. Numerical solutions of momentum and energy equations obtained through Homotopy Analysis Method (HAM) and shooting method are compared through tables. The effects of vari ation in physical parameters upon velocity and temperature field are also presented graphically. Skin friction and local NusseIt number are computed for further analysis "Accepted in International Journal of Pure and Applied Mathematics" . Chapter 5 deals MI-':ID Stagnation point over a stretching cylinder with variable thermal conductivity. This chapter addrcsses the behavior of viscous fluid near stagnation point over a stretching cylinder with variabl e thermal conductivity. The effects of heat generation/absorption are also encountered. Here thermal conductivity is considered as a linear function of temperature. Numerical solution obtained through Shooting method in conjunction with Runge-Kutta-Fehlberg method is compared with solution computed by HAM. The effect of variation in different physical parameters on velocity and temperature fi elds are shown graphi call y. Skin friction and Nusselt number are computed at the surface of cylinder to examine the behavior of Ouid flow on boundary "Submitted in Int. J. Fluid Mechanics" .