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
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/17646 |
| Date | 06 May 2015 |
| Creators | Aziz, Taha |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf, application/pdf |
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