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dc.creatorAlshehri, Nada
dc.descriptionA Thesis Submitted in Partial Fulfillment of the Requirements for Degree of MASTER OF SCIENCE in The Graduate Mathematics Program in Applied and Computational Mathematics from Texas A&M University - Corpus Christi.
dc.descriptionFlow past a circular cylinder or a sphere embedded in a porous medium is investigated mathematically by treating porous matrix as an incompressible fluid. Closed form analytic solutions for the fourth order scalar boundary-value problems for Ψ (r, θ) - known as the Stokes stream function - are obtained by using Navier-slip conditions. Our exact results for Ψ (r, θ) capture flow fields prevailing in the vicinity of a cylinder/sphere suspended in a uniform or a shear flow field. All the physical quantities computed from our solutions depend on two key parameters, namely, δ (the effective permeability) and ζ (slip coefficient). Flow separation and velocity overshoot behavior are found for certain values of δ and ζ. The force acting on the cylinder/sphere is calculated in each case. It is observed that the presence of slip decreases the force on the boundary. Our results show that in the limit δ -> 0, there is no solution to the two-dimensional boundary-value problem, confirming the familiar Stokes paradox
dc.descriptionMathematics and Statistics
dc.descriptionCollege of Science and Engineering
dc.rightsThis material is made available for use in research, teaching, and private study, pursuant to U.S. Copyright law. The user assumes full responsibility for any use of the materials, including but not limited to, infringement of copyright and publication rights of reproduced materials. Any materials used should be fully credited with its source. All rights are reserved and retained regardless of current or future development or laws that may apply to fair use standards. Permission for publication of this material, in part or in full, must be secured with the author and/or publisher.
dc.subjectApplications of PDEs
dc.subjectporous media
dc.subjectfluid dynamics
dc.subjectslip flows past a cylinder
dc.subjectslip flows past a sphere
dc.subjectflows past a solid inclusions
dc.subjectBrinkman model
dc.subjectNavier-slip conditions
dc.subjectStokes paradox.
dc.titleMathematical results for slipping flows past a cylinder or a sphere embedded in a porous medium

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