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

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.


A numerical solution of the steady MHD flow through infinite strips with BEM
Bozkaya, Canan; Tezer, Münevver (2012-04-01)
The magnetohydrodynamic (MHD) flow of an incompressible, viscous, electrically conducting fluid in infinite channels in the presence of a magnetic field is investigated. The fluid is driven either by a pressure gradient or by the currents produced by electrodes placed parallel in the middle of the walls. The applied magnetic field is perpendicular to the infinite walls which are combined from conducting and insulated parts. A boundary element method (BEM) solution has been obtained by using a fundamental so...
The dual reciprocity boundary element method solution of fluid flow problems
Gümgüm, Sevin; Tezer, Münevver; Department of Scientific Computing (2010)
In this thesis, the two-dimensional, transient, laminar flow of viscous and incompressible fluids is solved by using the dual reciprocity boundary element method (DRBEM). Natural convection and mixed convection flows are also solved with the addition of energy equation. Solutions of natural convection flow of nanofluids and micropolar fluids in enclosures are obtained for highly large values of Rayleigh number. The fundamental solution of Laplace equation is used for obtaining boundary element method (BEM) ...
A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations
Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01)
In this paper we provide an error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible Navier-Stokes equations. Optimal continuous in time error estimates of the velocity are derived. The analysis is completed with some error estimates for two fully discrete schemes, which are first and second order in time, respectively.
The dual reciprocity boundary element solution of helmholtz-type equations in fluid dynamics
Alsoy Akgün, Nagehan; Tezer Sezgin, Münevver; Department of Mathematics (2013)
In this thesis, the two-dimensional, unsteady, laminar and incompressible fluid flow problems governed by partial differential equations are solved by using dual reciprocity boundary element method (DRBEM). First, the governing equations are transformed to the inhomogeneous modified Helmholtz equations, and then the fundamental solution of modified Helmholtz equation is used for obtaining boundary element method (BEM) formulation. Thus, all the terms in the equation except the modified Helmholtz operator ar...
A numerical study on magneto-hydrodynamic mixed convection flow
Bozkaya, Canan (2014-01-01)
This paper, describes a study conducted to numerically investigate the two-dimensional, steady, laminar, magneto-hydrodynamic mixed convection flow and heat transfer characteristics in a lid-driven enclosure beneath an externally applied magnetic field. A solid square block is placed inside the cavity. The governing equations in the form of a stream function-vorticity-temperature formulation are solved numerically using the dual reciprocity boundary element method with constant elements. Treatment of nonlin...
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.