A study of boundary layer flow with no-slip and slip boundary conditions
Document Type Article
This thesis involves solving the two-dimensional boundary layer equations for axially symmetric fluid flow along a circular cylinder using the no-slip and slip boundary condition, and along a flat plate with the slip boundary condition. Initially, historical results in both areas are summarised. The research section of this thesis is concerned with extending these historical results. In the first research chapters, a Padé approximation and an Euler transformation are used to greatly extend the region of validity of the historical results. Following that is an investigation of the relaxation of the traditional no-slip boundary condition, which usually occurs when there is relative motion between a solid and a fluid. It is now known that, in certain circumstances, slip can occur, e.g. fluid flow in nano-tubes and flow in low density gases. Much of the recent literature in the general area of fluid flow problems is purely concerned with developing only computational techniques rather than using a blend of both the analytical and numerical/computational aspects of the problem. The approach taken in this thesis is to use a combination of both techniques. This involves using traditional perturbation theory to simplify the equations of motion and using computational techniques (with the aid of an advanced mathematical software engine) to obtain solutions; this is followed by an extension of the region of validity of the solutions via either a Padé approximation or an Euler transformation. A new successful method is thus developed. The approach used achieves successful results for the full axial and radial range without the need for exhaustive analytical or computational techniques.