Existence and stability of solutions to the equations of fibre suspension flows

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dc.contributor.advisorReddy, B Dayaen_ZA
dc.contributor.authorMunganga, Justin Manango Wazuteen_ZA
dc.date.accessioned2014-11-19T06:46:32Z
dc.date.available2014-11-19T06:46:32Z
dc.date.issued1999en_ZA
dc.descriptionIncludes bibliographical references.en_ZA
dc.description.abstractA 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.en_ZA
dc.identifier.apacitationMunganga, J. M. W. (1999). <i>Existence and stability of solutions to the equations of fibre suspension flows</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/9728en_ZA
dc.identifier.chicagocitationMunganga, Justin Manango Wazute. <i>"Existence and stability of solutions to the equations of fibre suspension flows."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1999. http://hdl.handle.net/11427/9728en_ZA
dc.identifier.citationMunganga, J. 1999. Existence and stability of solutions to the equations of fibre suspension flows. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Munganga, Justin Manango Wazute AB - 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. DA - 1999 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1999 T1 - Existence and stability of solutions to the equations of fibre suspension flows TI - Existence and stability of solutions to the equations of fibre suspension flows UR - http://hdl.handle.net/11427/9728 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/9728
dc.identifier.vancouvercitationMunganga JMW. Existence and stability of solutions to the equations of fibre suspension flows. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1999 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/9728en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematical Sciencesen_ZA
dc.titleExistence and stability of solutions to the equations of fibre suspension flowsen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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