Analysis of fluid flow in the entrance region of a duct with an eccentric annular cross-section

The purpose of this dissertation is to analyze the velocity development of laminar incompressible flow in the entrance region of a straight duct with an unchanging eccentric annular cross-section. A linearized version of the governing equations is solved under the assumptions that the velocity is zero on the duct wall and that the initial velocity profile is uniform across the cross-section. The analysis leads to a two-dimensional eigenvalue value problem which is then posed in the appropriate Hilbert space. Galerkin's method is shown to converge for, and then applied to, this eigenvalue problem.