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Title: Conditional and unconditional nonlinear stability in fluid dynamics
Author: Budu, Paula
Awarding Body: Durham University
Current Institution: Durham University
Date of Award: 2002
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In this thesis we examine some of the interesting aspects of stability for some convection problems. Specifically, the first part of the thesis deals with the Bénard problem for various Non-Newtonian fluids, whereas the second part develops a stability analysis for convection in a porous medium. The work on stability for viscoelastic fluids includes nonlinear stability analyses for the second grade fluid, the generalised second grade fluid, the fluid of dipolar type and the fluid of third grade. It is worth remarking that throughout the work the viscosity is supposed to be any given function of temperature, with the first derivative bounded above by a positive constant. The connection between the two parts of the thesis is made through the method used to approach the nonlinear stability analysis, namely the energy method. It is shown in the introductory chapter how this method works and what are its advantages over the linear analysis. Nonlinear stability results established in both Part I and Part II are the best one can get for the considered physical situations. Different choices of energy have been considered in order to achieve conditional or unconditional nonlinear stability results.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Viscoelastic fluids; Porous media Applied mathematics Fluid mechanics