#### Date of Award

1993

#### Degree Type

Dissertation

#### Degree Name

Ph.D.

#### Department

Mathematics and Statistics

#### First Advisor

Chandna, O. P.

#### Keywords

Applied Mechanics.

#### Rights

CC BY-NC-ND 4.0

#### Abstract

This dissertation is devoted to (i) an analytical investigation of steady plane magnetohydrodynamic (MHD) fluid flows and (ii) a numerical study of a viscoelastic second grade fluid flow. In the analytical study, we pose and answer the following two questions for steady plane flow: (a) Given a family of plane curves l(x,y) = constant, can a viscous fluid of constant viscosity flow along these curves? (b) Given a family of streamlines in a viscous fluid flow of constant viscosity, what is the exact integral or exact solution of the flow defined by the given streamline pattern? To answer these two questions, we develop a new approach using different curvilinear coordinate systems depending upon the problem under consideration. This approach has been used to recover some existing exact solutions and yield several new exact solutions of infinitely conducting MHD aligned, finitely conducting MHD aligned, infinitely conducting MHD orthogonal, infinitely conducting MHD variably-inclined and non-MHD fluid flows. In the case of MHD aligned fluid flow, some boundary value problems have been considered. We also show that the Hamel's problem for infinitely conducting MHD aligned fluid flow has more solutions than the four well-known solutions of the ordinary viscous fluid flow. A study of confluent flows for MHD transverse-aligned flow is also carried out in this part of the analytical investigation. A fluid flow is defined to be confluent if two physically important families of curves coincide in the physical plane. In the numerical part of this dissertation, we study the oblique flow of a viscoelastic second grade fluid impinging on a flat porous wall with suction or blowing on the wall. The behaviour of the fluid near the wall is investigated for various magnitudes of suction and blowing. We also investigate the effects of elasticity on this fluid flow.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1993 .L337. Source: Dissertation Abstracts International, Volume: 54-09, Section: B, page: 4765. Adviser: O. P. Chandna. Thesis (Ph.D.)--University of Windsor (Canada), 1993.

#### Recommended Citation

Labropulu, Fotini., "Some exact solutions of steady plane Newtonian, non-Newtonian and MHD fluid flows." (1993). *Electronic Theses and Dissertations*. 3527.

http://scholar.uwindsor.ca/etd/3527