Current Research Projects

1. Bozkaya, C. (coordinator) (01/2014-present). A numerical study on MHD mixed convection flow with a solid body, BAP-1, Department of Mathematics, Middle East Technical University. Project No: BAP-01-01-2014-002.

Completed Research Projects

2. Tezer-Sezgin, M. (coordinator), Bozkaya, C. (researcher), Turk, O. (scholar) (11/2011-present). Finite element and boundary element solutions of biomagnetic fluid flow through a stenosed artery, TUBITAK 1001 Project, 01.11.2011-01.11.2013, Department of Mathematics, Middle East Technical University, Project No: 111T269.

Abstract

This project will focus on the numerical solution of biomagnetic fluid flow and heat transfer through a stenosed artery under the influence of a spatially varying magnetic field. The most characteristic biomagnetic fluid is blood which behaves as a magnetic fluid due to the complex interaction of the intercellular protein, cell membrane and the hemoglobin, a form of iron oxides which are present in the mature red blood cells. A significant pathological condition (diseases such as stroke) results from the formation of clots in the blood vessels that may cause a partial or complete blood blockage. In the stenotic region, where the clot is formed, the flow passage narrows down, leading to significant changes in the flow pattern. The pressure distribution, the resistance of the flow, formation of vortices, and separation of the blood flow require careful studies on the flow pattern of biomagnetic fluid through stenotic contractions. A mathematical model of biomagnetic fluid dynamics (BFD) which considers blood as non-Newtonian fluid with varying viscosity and electrical conductivity in an irregularly stenosed artery will be given together with the heat transfer inside the blood. Both finite element method (FEM) and the boundaru element method (BEM) will be used for obtaining the flow pattern in the stenosed area. The advantages of both methods will be made use of. Boundary element method discretizes only the boundary of the problem domain (which will be suitable to discretize the variable boundaries in the stenosis), and results in considerably small systems to be solved compared to other domain discretization methods. Finite element method has the capacity of discritizing the stenosed region with very fine elements which suits the curved boundaries, and can easily adopts stabilizations to tackle with the nonlinearities present in the partial differential equations defining the above physical problem. Major changes in the flow pattern of BFD in a stenosis will be shown in terms of streamlines, vorticity contours, isotherms, and a comparison between the two method will be carried in terms of accuracy and stability.

Keywords:
FEM, BEM, DRBEM, Biomagnetic fluid flow (Blood flow), stenosis.

3. Bozkaya, C. (coordinator) and Tezer-Sezgin, M. (01/2012-1/2013). BEM solution of MHD flows in coupled ducts. BAP-1, 01.01.2012-31.12.2012, Department of Mathematics, Middle East Technical University. Project No: BAP-01-01-2012-002.

Abstract

Magnetohydrodynamic flows in coupled rectangular channels are numerically investigated under an external, horizontally applied magnetic field. The flows are driven by constant pressure gradients in the channels, which are separated with a thin partly insulating and partly conducting barrier. A direct boundary element formulation is utilized to solve these two-dimensional steady, convection-diffusion type coupled partial differential equations in terms of velocity and induced magnetic fields. The resulting system of linear equations is solved by reordering the unknown vector due to the insertion of the coupled boundary conditions along the conducting partition of the barrier. This study aims to examine the consequence of high values of Hartmann number on the velocity and induced magnetic fields. Further, the alteration in flow behavior due to the variations in the length of the conducting partition along the thin barrier and in the value of ratio of the pressure gradients of two channels is also analyzed.

Keywords:
Coupled rectangular ducts, MHD flow, BEM.

4. Tezer-Sezgin, M (coordinator). and Bozkaya, C. (researcher) (01/2011-12/2011). Magnetohydrodynamic flow in an electrodynamically conducting semi-infinite strip. BAP-1, Department of Mathematics, Middle East Technical University. Project No: BAP-01-01-2011-001.

Abstract

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 (BEM) solution has been obtained by using a fundamental solution which enables to threat the convection-diffusion type equations in coupled form with general wall conductivities. Constant elements are used for the discretization of the walls by keeping them as finite since the boundary integrals are restricted to these boundaries due to the regularity conditions at infinity. The solutions are presented in terms of equivelocity and induced magnetic field contours for several values of Hartmann number and conducting lengths. The effect of the parameters on the solution is visualized.

Keywords:
MHD flow, BEM, infinite channels, coupled PDE's, fundamental solution, boundary layer.