A Numerical approach for the solutions of fluid dynamics problems in the presence of magnetic field

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2018
Oğlakkaya, Fatma Sidre
This thesis is conducted to investigate numerically the two-dimensional steady or unsteady, laminar flow of viscous, incompressible and electrically conducting fluids in complex geometries subject to either uniform inclined magnetic field or nodal magnetic sources. Specifically, the hydromagnetic natural/mixed convection of either conventional fluid or water-based nanofluid flow and the heat transfer are considered in irregular enclosures with wavy walls. The equations governing the steady magnetohydrodynamic (MHD) convection flow, which are obtained from the Navier-Stokes, the energy equations of fluid dynamics and the electromagnetic equations of the magnetohydrodynamics discretized by using the dual reciprocity boundary element method (DRBEM). The DRBEM uses the fundamental solution of the Laplace equation and treats all the other terms in the equations as non-homogeneity which is approximated by radial basis functions. On the other hand, for the unsteady MHD convection flow and heat transfer problems the DRBEM in space is combined with a two-level integration scheme in time; and the numerical stability analysis is further performed in terms of time increment, time relaxation parameters and the several physical controlling parameters. The proposed numerical technique is first applied for the steady/unsteady mixed convection flow in a lid-driven cavity with a wall involving flat, semi-rectangular, semi-circular or sinusoidal heaters with Joule heating effect in the presence of inclined magnetic field. Later, the numerical simulation of the MHD natural convection flow not only in an inclined semi-circular annulus enclosure but also in a semi-annulus enclosure with a sinusoidal wavy inner wall filled with a water-based nanofluid is studied under the influence of a uniform inclined magnetic field. Finally, the effects of the nodal magnetic sources and the complex geometry of the computational domain on the ferrofluid flow and the heat transfer are investigated in annulus enclosures with different types of sinusoidal inner walls determined by using different number of undulation. The results obtained for all problems under consideration are visualized in terms of streamlines, isotherms and average Nusselt number for various combinations of physical controlling parameters, namely Hartmann number, Rayleigh number, Joule heating parameter, inclination angle of the externally applied magnetic field, number of undulation determining the shape of the wavy wall and the solid volume fraction. It is well-observed that the strength of the magnetic field and incorporating nanoparticles to conventional fluids can be used to control the fluid flow and the heat transfer enhancement in irregular enclosures with wavy walls.

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Citation Formats
F. S. Oğlakkaya, “A Numerical approach for the solutions of fluid dynamics problems in the presence of magnetic field,” Ph.D. - Doctoral Program, Middle East Technical University, 2018.