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Existence and stability of solutions to the equations of fibre suspension flows
Includes bibliographical references.
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2014
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| _version_ | 1867613237843853312 |
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| access_status_str | Open Access |
| author | Munganga, Justin Manango Wazute |
| author2 | Reddy, B Daya |
| author_browse | Munganga, Justin Manango Wazute Reddy, B Daya |
| author_facet | Reddy, B Daya Munganga, Justin Manango Wazute |
| author_sort | Munganga, Justin Manango Wazute |
| collection | Thesis |
| description | Includes bibliographical references. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/9728 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:57.328Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/9728 Existence and stability of solutions to the equations of fibre suspension flows Munganga, Justin Manango Wazute Reddy, B Daya Mathematical Sciences Includes bibliographical references. A popular approach to formulating the initial-boundary value problem for fibre suspension flows is that in which fibre orientation is accounted for in an averaged sense, through the introduction of a second-order orientation tensor A. This variable, together with the velocity and pressure, then constitutes the set of unknown variables for the problem. The governing equations are balance of linear momentum, the incompressibility condition, an evolution equation for A, and a constitutive equation for the stress. The evolution equation contains a fourth-order orientation tensor A, and it is necessary to approximate A as a function of A, through a closure relation. The purpose of this these is to examine the well-posedness of the equations governing fibre fibre suspension flows, for various closure relations. It has previously been shown by GP Galdi and BD Reddy that, for the linear closure, the problem is wellposed provided that the particle number, a material constant, is less than a critical value. The work by Galdi and Reddy made of a model in which rotary diffusivity is a function of the flow. This thesis re-examines these issues in two different ways. First, the second law of thermodynamics is used to establish the constraints that the constitutive equations have to satisfy in order to be compatible with this law. This investigation is carried out for a variety of closure rules. The second contribution of the thesis concerns the existence and uniqueness of solutions to the governing equations, for the linear and quadratic closures; for a model in which the rotary diffusivity is treated as a constant, local and global existence of solutions are established, for sufficiently small data, and in the case of the linear closure, for admissible values of the particle number. The existence theory uses a Schauder fixed point approach. 2014-11-19T06:46:32Z 2014-11-19T06:46:32Z 1999 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/9728 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematical Sciences Munganga, Justin Manango Wazute Existence and stability of solutions to the equations of fibre suspension flows |
| thesis_degree_str | Doctoral |
| title | Existence and stability of solutions to the equations of fibre suspension flows |
| title_full | Existence and stability of solutions to the equations of fibre suspension flows |
| title_fullStr | Existence and stability of solutions to the equations of fibre suspension flows |
| title_full_unstemmed | Existence and stability of solutions to the equations of fibre suspension flows |
| title_short | Existence and stability of solutions to the equations of fibre suspension flows |
| title_sort | existence and stability of solutions to the equations of fibre suspension flows |
| topic | Mathematical Sciences |
| url | http://hdl.handle.net/11427/9728 |
| work_keys_str_mv | AT mungangajustinmanangowazute existenceandstabilityofsolutionstotheequationsoffibresuspensionflows |