## Date of Award

Spring 1993

## Document Type

Dissertation - Restricted

## Degree Name

Doctor of Philosophy (PhD)

## Department

Mechanical Engineering

## First Advisor

Nigro, N. J.

## Second Advisor

Elkouh, A. F.

## Third Advisor

Heinrich, S. M.

## Abstract

The primary objective of this research is to employ a modified Galerkin finite element procedure to analyze the steady state flow of a fluid contained between two concentric rotating spheres. The spheres are assumed to be rigid and the region in the cavity between the spheres is filled with an incompressible viscous Newtonian fluid. The inner sphere is constrained to rotate about a vertical axis due to a prescribed angular velocity while the outer sphere is fixed. The fluid problem, which is originally formulated in terms of the stream function and circumferential function variables, is reduced to second order form by introducing the vorticity variable. The system region is discretized with the use of finite elements. The fluid equations are reduced to a system of non-linear algebraic equations by employing a modification of the conventional Galerkin finite element procedure. The field variables are expanded ( over each element) in terms of products of cubic interpolation functions and element nodal coordinates. The nodal coordinates are selected so as to satisfy all of the boundary conditions. The finite element equations are linearized, assembled and then solved by employing a Newton-Raphson algorithm...