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Group theoretical and compatibility approaches to some nonlinear PDEs arising in the study of nonNewtonian fluid mechanicsAziz, Taha 06 May 2015 (has links)
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 nonNewtonian fluid mechanics by
employing group theoretic and compatibility approaches.
It is well known now that many manufacturing processes in industry involve
nonNewtonian fluids. Examples of such fluids include polymer solutions
and melts, paints, blood, ketchup, pharmaceuticals and many others. The
mathematical and physical behaviour of nonNewtonian 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 nonNewtonian fluids have been observed
experimentally such as the Weissenberg or rodclimbing effect, extrudate
swell or vortex growth in a contraction flow. Due to diverse physical
structure of nonNewtonian fluids, many constitutive equations have been
developed mainly under the classification of differential type, rate type and
integral type. Amongst the many nonNewtonian 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 nonNewtonian 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

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Group invariant solutions for the unsteady magnetohydrodynamic flow of a fourth grade fluid in a porous mediumCarrim, Abdul Hamid 18 July 2014 (has links)
The e ects of nonNewtonian 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 incompressible
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 higherorder nonlinear partial differential equations. A threedimensional Lie algebra is acquired for both uid ow problems.
In each case, the invariant solution corresponding to the nontravelling 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 approach.
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 nonNewtonian
fluid parameters.

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Mathematical and numerical modeling of coating flowsLivescu, Silviu. January 2006 (has links)
Thesis (Ph.D.)University of Delaware, 2006. / Principal faculty advisor: Romain Valéry Roy, Dept. of Mechanical Engineering. Includes bibliographical references.

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The effect of type and concentration of surfactant on stability and rheological properties of explosive emulsions /Tshilumbu, Nsenda Ngenda. January 2009 (has links)
Thesis (MTech (Chemical Engineering))Cape Peninsula University of Technology, 2009. / Includes bibliographical references (leaves 179194). Also available online.

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A global preconditioning method for the Euler equationsYildirim, B. Gazi. January 2003 (has links)
Thesis (M.S.)Mississippi State University. Department of Aerospace Engineering. / Title from title screen. Includes bibliographical references.

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Singular behaviour of NonNewtonian fluids /Mennad, Abed. January 1900 (has links)
Thesis (MTech (Mechanical Engineering))Peninsula Technikon, 1999. / Word processed copy. Summary in English. Includes bibliographical references (leaves 9599). Also available online.

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Influence of coil characteristics on heat transfer to Newtonian fluidsPrabhanjan, Devanahalli G. January 2000 (has links)
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 recirculate 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.s1 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 recirculation 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 underpredicted 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 SeiderTate 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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NonNewtonian conversion of emulsion liquid membranes in the extraction of lead and zinc from simulated wastewaterGilbert, Christopher Donald 12 1900 (has links)
No description available.

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Finite element simulation of nonNewtonian flow in the converging section of an extrusion die using a penalty function techniqueGhosh, Jayanto K. January 1989 (has links)
Thesis (Ph. D.)Ohio University, March, 1989. / Title from PDF t.p.

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Advanced analysis and design of polymer sheet extrusionWang, Qi, January 2007 (has links)
Thesis (Ph. D.)University of MissouriColumbia, 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 nontechnical 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.

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