Unsteady laminar boundary layer studies through finite difference methods

Abstract

This thesis embodies a study of some problems in unsteady laminar compressible and incompressible boundary layer theory. The thesis is divided into five chapters. Each chapter contains a brief survey of the literature relevant to the problem considered and the contribution made by the author. The first chapter presents a brief introduction to the boundary layer theory and methods of solution of problems connected with it. The second chapter deals with unsteady compressible laminar flow with applied magnetic field while the remaining three chapters deal with incompressible flows. The second chapter consists mainly of two parts — the first dealing with semi?similar solution and the second self?similar solution. In both the cases, after reducing the governing equations to convenient form, using appropriate transformations, an implicit finite?difference scheme is employed to obtain the solution. The effects of various parameters on the hypersonic viscous flow on an electrically conducting gas with variable properties are dealt with. The third chapter deals with the variable viscosity effects on forced convection in unsteady three?dimensional stagnation?point water boundary layer. The viscosity and Prandtl number are assumed to vary inversely with temperature. Both semi?similar and self?similar solutions are obtained by finite?difference method. The fourth chapter deals with unsteady incompressible flow past a yawed cylinder. It consists of two parts — the semi?similar and self?similar solutions. The semi?similar solution is obtained using an implicit finite? difference scheme whereas to obtain the self?similar solution for large injection rates a quasilinearisation finite? difference scheme is used. In the last chapter non?similar solution for a two? dimensional unsteady incompressible laminar flow is studied with retarded free?stream velocity. An implicit finite? difference scheme is used to solve the partial differential equations with three variables. The books and original papers referred to in the text of the thesis are enlisted at the end of each chapter. Figures and Tables relevant to each chapter are presented at the end of the chapter. Papers based on the work in the thesis will be communicated for publication shortly.