#### Date of Award

1994

#### Degree Type

Dissertation

#### Degree Name

Ph.D.

#### Department

Mathematics and Statistics

#### First Advisor

Chandna, O. P.

#### Keywords

Mathematics.

#### Rights

CC BY-NC-ND 4.0

#### Abstract

In this dissertation, we have investigated analytically various flow problems of subclasses of viscoelastic (non-Newtonian) fluids of differential type of complexity 2 and 3. Both steady and unsteady fluid flows are considered, and in some cases, the fluids are electrically conducting. Exact solutions of the equations of the steady, plane, isochoric motion of a second grade fluid and an electrically conducting second grade fluid are obtained employing the von Mises transformations. In the latter case, we explore the possibility of obtaining solutions for fluids of infinite and finite electrical conductivities. We investigate if these fluids can flow along a given family of curves. If this answer is determined in the affirmative, we proceed to obtain the exact integral of the flow along the given family of curves. Next, we obtain inverse solutions of the equations of the steady, plane flow of an incompressible second grade fluid by assuming a certain form of the stream function in one case, and in another by assuming certain forms of the vorticity function. The exact solutions of these flows are determined. An attempt is made to investigate the possibility of an incompressible, electrically conducting third grade fluid of infinite and finite magnetic Reynolds numbers admitting a von Karman-type solution for the equations of a steady, plane flow between two parallel plates, one of which is porous. The lower plate is being stretched by two equal and opposite forces so that the origin is fixed. We find that electrically conducting third grade fluid flow under the aforementioned circumstances is impossible. Approximate solutions, employing the perturbation method, are obtained for the flow of an electrically conducting second grade fluid of infinite magnetic Reynolds number. Finally, exact solutions are obtained for the equations of an unsteady, plane, isochoric motion of an electrically conducting second grade fluid. Inverse method is employed for which the vorticity distribution is proportional to the stream function perturbed by a uniform stream. The cases when the electrically conducting fluid has finite and infinite electrical conductivities are studied.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1994 .O38. Source: Dissertation Abstracts International, Volume: 56-01, Section: B, page: 0281. Adviser: Om P. Chandna. Thesis (Ph.D.)--University of Windsor (Canada), 1994.

#### Recommended Citation

Oku-Ukpong, Edima Okon., "Solutions of non-Newtonian flow problems." (1994). *Electronic Theses and Dissertations*. 3516.

http://scholar.uwindsor.ca/etd/3516