Date

2014

Author

Türk, Önder

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In this thesis, solutions to steady and unsteady flow problems of incompressible viscous fluids are obtained numerically. In computational aspects, the primary focus is on the finite element analysis, however, spectral collocation and boundary element methods are also employed. The two-dimensional Navier-Stokes (N-S) equations in stream function-vorticity form are solved by using both finite element method (FEM) and Chebyshev spectral collocation method (CSCM). The accuracy of the FEM and CSCM methodologies is investigated by solving some benchmark fluid flow problems such as lid-driven cavity flow, and natural convection flow in enclosures. The natural convection flow problem is also considered under the effect of an externally applied magnetic field. The magnetohydrodynamic (MHD) system is coupled with the temperature effects through the gravitational force by means of the Boussinesq approximation. Different flow configurations with various boundary conditions are examined on both inclined and non-inclined enclosures, and the solutions are obtained by using FEM and CSCM for the case of small magnetic Reynolds number. The problem of unsteady, one-dimensional MHD flow and heat transfer between parallel plates, is solved with CSCM due to its simplicity in computations. For the time discretization, an implicit backward finite difference scheme is presented. The effect of the movement of the upper plate on the flow, and the convection action in terms of inflow/outflow through plates are examined. The MHD flow between parallel plates is extended to the case of dusty fluid by including differential equations for the dust particles. The Navier-slip conditions for both the fluid and dust particle velocities are introduced. The Hartmann number, viscosity parameter, and Navier-slip parameter influences on the flow and temperature are visualized in terms of graphics together with discussions. The biomagnetic fluid flow (blood flow) and heat transfer in channels between plates with various physical configurations are simulated. A blood model consistent with biomagnetic fluid dynamics (BFD), which includes the principles of MHD and ferrohydrodynamics (FHD), is considered. The fluid is assumed to be Newtonian, and both electrically conducting and nonconducting fluid flows are separately considered. The FEM and DRBEM applications are introduced for the steady biomagnetic fluid flow model where the fluid is considered as electrically non-conducting. The effects of the externally applied magnetic field on the flow and heat distribution are analyzed in details. FEM applications are also presented for the solution of biomagnetic fluid flow through channels between plates with differing constriction profiles. Alterations in the behaviors of the flow and temperature of the biomagnetic fluid due to the stenoses in the channel and location and intensity of the magnetic source are analyzed.

Subject Keywords

Magnetohydrodynamics., Finite element method., Fluid dynamics., Viscous flow.

URI

http://etd.lib.metu.edu.tr/upload/12616737/index.pdf
https://hdl.handle.net/11511/23234

Collections

Graduate School of Applied Mathematics, Thesis