A Qualitative Analysis of the Similarity Boundary Layer Equations : Asymptotic Behaviour, Convex-Concave and Oscillatory Solutions of the Non-autonomous Differential Equations

This book is concerned primarily with an especially simple class of exact solutions of the boundary layer equations. Similar flows exist only in certain flows in which the velocity and enthalpy profiles at different positions on the body have a similar shape. The similarity technique essentially consists of converting the partial differential equations to ordinary differential equations. The reduction of the system to a set of ordinary differential equations can be achieved by transforming the dependent and independent variables to suitable non-dimensional dependent and independent variables called the similarity variables with the aid of transformations known as similarity transformations. Qualitative properties of solutions of differential equations assume importance in the absence of closed form solutions. In case the solutions are not expressible in terms of usual known functions, an analysis of the equations is necessary to find the facets of the solutions.