Numerical studies of some laminar boundry layer flows using finite difference methods

Abstract

This thesis presents some investigations on certain problems in laminar incompressible and compressible boundary layers using finite?difference methods. It consists of an introductory chapter and three main 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 bears a brief introduction to the boundary layer theory together with different analytical and numerical methods which have been applied to solve various boundary layer problems. The second chapter deals with laminar compressible boundary layer flows over three?dimensional bodies with mass transfer. The heat and mass transfer for the unsteady laminar compressible asymmetric boundary?layer flow in the neighbourhood of a three?dimensional stagnation point (which includes both nodal and saddle points of attachment) for both cold and hot walls have been studied when the freestream velocity varies inversely as a linear function of time. The effect of the variation of the density–viscosity product across the boundary layer (variable gas properties) has been taken into account. The ordinary differential equations obtained have been solved numerically using an implicit finite?difference scheme. Further, the steady laminar compressible non?similar boundary layer flow of a gas with variable properties over a plane or a developable surface has been investigated between nodal and saddle points of attachment. Both cold and hot wall cases have been included in the analysis. An implicit finite?difference scheme is used to solve the partial differential equations governing the flow. The third chapter presents the study of three related problems concerned with unsteady laminar boundary layers over spinning bodies of revolution in forced flow. The unsteady laminar incompressible as well as compressible boundary layer flow over a class of bodies of revolution spinning arbitrarily with time about axes of symmetry in an otherwise undisturbed fluid has been investigated. Also, the unsteady axisymmetric laminar rotating compressible flow over the edge of a finite disk rotating arbitrarily with time has been studied. The effect of viscous dissipation has been included in the analysis. The effect of the variation of the density–viscosity product across the boundary layer in the case of compressible fluids has been taken into account. Further, both cold and hot wall temperature conditions have been considered. The partial differential equations governing the flow in each case have been transformed to semi?similar equations in dimensionless variables and the resulting equations involving similarity and time variables have been solved with the help of an implicit finite?difference scheme. In the last chapter, the unsteady laminar incompressible and compressible boundary layer flows over a longitudinal cylinder have been investigated when the freestream velocity, surface mass transfer and wall temperature vary arbitrarily with time. The effect of viscous dissipation has been included in the analysis. In the case of compressible boundary layer flow, the effect of the variation of the density–viscosity product across the boundary layer has been included in the analysis. Both cold and hot wall cases have been investigated. The partial differential equations governing both the problems have been transformed into dimensionless form using suitable transformations and the resulting non?similar equations involving three independent variables have been solved using an implicit finite?difference scheme. The books and original papers referred to in the text of the thesis are listed at the end of each chapter. Figures and Tables relevant to each chapter are presented at the end of the chapter. All symbols are defined as and when they arise but, for the sake of convenience, all the symbols are listed at the end of the thesis. Papers based on the work reported in the thesis will be communicated for publication shortly.