|M.Sc Student||Kosman Avraham|
|Subject||The Flow of a Line Sink Perpendicular to a Wall:|
An Exact Solution, Asymptotic Approximations and
a Description of the Flow
|Department||Department of Civil and Environmental Engineering||Supervisor||Professor Uri Shavit|
|Full Thesis text|
The flow of an infinite line sink in an unbounded domain is two dimensional and potential. The influence of adjacent walls on such a basic flow is a question of theoretical and practical importance. In this work we consider the flow driven by a half infinite line sink of uniform strength perpendicular to a plane wall. Analytical methods are used to develop an exact similarity solution, which involves the Gauss hypergeomteric functions and roots of transcendental equations. While the flow problem was previously solved numerically, the analytical form given here is new. In addition, the method of asymptotic expansions is used to derive asymptotic approximations for the flow in the two limiting cases of creeping flow and inviscid flow. In the latter, a boundary layer develops near the wall. We then examine in detail the velocity field, the pressure field and the resulting stresses on the wall. An emphasis is placed on a comparison between the resulting viscous flow and the two dimensional potential flow. Among several observations considered in the text, we mention the generation of axial velocity towards the wall and the decrease in pressure throughout the flow field, both become more dominant when the viscosity of the fluid is increased.