A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2015. / This thesis is primarily concerned with the analysis of some nonlinear problems arising in the study of non-Newtonian fluid mechanics by employing group theoretic and compatibility approaches. It is well known now that many manufacturing processes in industry involve non-Newtonian fluids. Examples of such fluids include polymer solutions and melts, paints, blood, ketchup, pharmaceuticals and many others. The mathematical and physical behaviour of non-Newtonian fluids is intermediate between that of purely viscous fluid and that of a perfectly elastic solid. These fluids cannot be described by the classical Navier–Stokes theory. Striking manifestations of non-Newtonian fluids have been observed experimentally such as the Weissenberg or rod-climbing effect, extrudate swell or vortex growth in a contraction flow. Due to diverse physical structure of non-Newtonian fluids, many constitutive equations have been developed mainly under the classification of differential type, rate type and integral type. Amongst the many non-Newtonian fluid models, the fluids of differential type have received much attention in order to explain features such as normal stress effects, rod climbing, shear thinning and shear thickening. Most physical phenomena dealing with the study of non-Newtonian fluids are modelled in the form of nonlinear partial differential equations (PDEs). It is easier to solve a linear problem due to its extensive study as well due to

The e ects of non-Newtonian uids are investigated by means of two appropri- ate models studying a third and fourth grade uid respectively. The geometry of both these models is described by the unsteady unidirectional ow of an in-compressible uid over an in nite at rigid plate within a porous medium. The uid is electrically conducting in the presence of a uniform applied magnetic eld that occurs in the normal direction to the ow. The classical Lie symmetry approach is undertaken in order to construct group invariant solutions to the governing higher-order non-linear partial dif-ferential equations. A three-dimensional Lie algebra is acquired for both uid ow problems. In each case, the invariant solution corresponding to the non-travelling wave type is considered to be the most signi cant solution for the uid ow model under investigation since it directly incorporates the magnetic eld term. A numerical solution to the governing partial di erential equation is produced and a comparison is made with the results obtained from the analytical ap-proach. Finally, a graphical analysis is carried out with the purpose of observing the e ects of the emerging physical parameters. In particular, a study is carried out to examine the in uences of the magnetic eld parameter and the non-Newtonian fluid parameters.

Thesis (Ph.D.)--University of Delaware, 2006. / Principal faculty advisor: Romain Valéry Roy, Dept. of Mechanical Engineering. Includes bibliographical references.

Thesis (MTech (Chemical Engineering))--Cape Peninsula University of Technology, 2009. / Includes bibliographical references (leaves 179-194). Also available online.

Thesis (M.S.)--Mississippi State University. Department of Aerospace Engineering. / Title from title screen. Includes bibliographical references.

Thesis (MTech (Mechanical Engineering))--Peninsula Technikon, 1999. / Word processed copy. Summary in English. Includes bibliographical references (leaves 95-99). Also available online.

A water bath thermal Processor was designed and built to study the influence of helical coil characteristics on heat transfer to Newtonian fluids like water and base oil with three different viscosities. The system consisted of a thermally insulated water bath, an electric heater, pump to re-circulate water in the bath and for pumping the processing fluid through the coil, copper helical coils and a storage tank for the processing fluid. / Comparative study has shown that the outer and total heat transfer coefficients were significantly lower in natural than in forced convection water bath. However, inner heat transfer coefficient was not significantly affected. Flow rate as low as 0.001 m.s-1 in the water bath improved the outer and total heat transfer coefficients by 35 and 22% respectively. One could expect a higher rate with an increase in water re-circulation rate inside the water bath. Percent rise in heat transfer was limited to seven with respect to inner heat transfer. With the Pearson correlation, it was possible to express total heat transfer rate directly in terms of outer and inner rates. Significant interactions were observed between variables and constants. / Experiments with 2 pitch cases were conducted with water to water heat transfer using coils to determine the Nusselt number correlation for natural convection. Characteristic lengths were changed in the models. The Nusselt number was under-predicted by 25 to 37% for water bath temperatures of 75° and 95°C respectively. Flow rate inside the coil had slight effect on Nusselt number due to change in the temperature gradient along the length of the coil. / Studies conducted with three base oils have shown significant difference in viscosity after heating the oil for several turns. Each fluid was heated in a distinct flow regime. The observed Nusselt number inside the coil for low Reynolds number was as high as an order of magnitude than the predicted values calculated by Seider-Tate relation for laminar flow. Vorticies formed associated with the eddy structure could very well be the cause for this kind of rise in the value. / Preliminary study conducted has shown a higher rise in temperature of processing fluid in case of helical coil compared to that of a straight tube. Larger the diameter of the tube better was the heat transfer. An elevated bath temperature had higher heat transfer.

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Thesis (Ph. D.)--Ohio University, March, 1989. / Title from PDF t.p.

Thesis (Ph. D.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on March 3, 2008) Vita. Includes bibliographical references.