Canan Bozkaya

Finite element study of biomagnetic fluid flow in a symmetrically stenosed channel

The two-dimensional unsteady, laminar flow of a viscous, Newtonian, incompressible and electrically conducting biofluid in a channel with a stenosis, under the influence of a spatially varying magnetic field, is considered. The mathematical modeling of the problem results in a coupled nonlinear system of equations and is given in stream function-vorticity-temperature formulation for the numerical treatment. These equations together with their appropriate boundary conditions are solved iteratively using the finite element method for the spatial discretization, and an unconditionally stable backward difference scheme is employed for the time integration. The numerical results obtained are illustrated using streamlines, vorticity and temperature contours. The behavior of the biofluid along the thin channel is investigated for a symmetric stenosis of degrees 40% and 60%, with a magnetic source placed below the lower plate. The results indicate that the flow is appreciably affected by the presence of stenosis and the magnetic source in terms of vortices. The lengths of the vortices and the temperature increase with increase in the intensity of the magnetic field and the degree of the constriction.

Free surface wave interaction with an oscillating cylinder

Abstract The numerical solution of the special integral form of two-dimensional continuity and unsteady Navier–Stokes equations is used to investigate vortex states of a horizontal cylinder undergoing forced oscillations in free surface water wave. This study aims to examine the consequence of degree of submergence of the cylinder beneath free surface at Froude number 0.4. Calculations are carried out for a single set of oscillation parameters at a Reynolds number of R = 200 . Two new locked-on states of vortex formation are observed in the near wake region. The emphasis is on the transition between these states, which is characterized in terms of the lift force on the cylinder and the instantaneous patterns of vortex structures and pressure contours in the near wake.

DRBEM Solution of MHD Flow and Electric Potential in a Rectangular Pipe with a Moving Lid

We present the dual reciprocity boundary element method (DRBEM) solution of the system of equations which model magnetohydrodynamic (MHD) flow in a pipe with moving lid at low magnetic Reynolds number. The external magnetic field acts in the pipe-axis direction generating the electric potential. The solution is obtained in terms of stream function, vorticity and electric potential in the cross-section of the pipe, and the pipe axis velocity is also computed under a constant pressure gradient. It is found that fluid flow concentrates through the upper right corner forming boundary layers with the effect of moving lid and increased magnetic field intensity. Electric field behavior is changed accordingly with the insulated and conducting portions of the pipe walls. Fluid moves in the pipe-axis direction with an increasing rate of magnitude when Hartmann number increases. The boundary only nature of DRBEM provides the solution at a low computational expense.

DRBEM Simulation on Mixed Convection with Hydromagnetic Effect

The steady and laminar mixed convection flow of a viscous, incompressible, and electrically conducting fluid under the effect of an inclined magnetic field is numerically investigated. Specifically, the two-dimensional flow in a lid-driven cavity with a linearly heated wall is considered. The dual reciprocity boundary element method is used for solving the coupled nonlinear differential equations in terms of stream function, vorticity, and temperature. The study focuses on the effects of the physical parameters, such as Richardson and Hartmann numbers, on the flow field and the temperature distribution at different inclinations of the applied magnetic field. The streamlines and isotherms are used for the visualization of the flow and temperature fields. The code validations in terms of average Nusselt numbers show good agreement with the results given in the literature.

MHD flow in a rectangular duct with a perturbed boundary

Abstract The unsteady magnetohydrodynamic (MHD) flow of a viscous, incompressible and electrically conducting fluid in a rectangular duct with a perturbed boundary, is investigated. A small boundary perturbation e is applied on the upper wall of the duct which is encountered in the visualization of the blood flow in constricted arteries. The MHD equations which are coupled in the velocity and the induced magnetic field are solved with no-slip velocity conditions and by taking the side walls as insulated and the Hartmann walls as perfectly conducting. Both the domain boundary element method (DBEM) and the dual reciprocity boundary element method (DRBEM) are used in spatial discretization with a backward finite difference scheme for the time integration. These MHD equations are decoupled first into two transient convection–diffusion equations, and then into two modified Helmholtz equations by using suitable transformations. Then, the DBEM or DRBEM is used to transform these equations into equivalent integral equations by employing the fundamental solution of either steady-state convection–diffusion or modified Helmholtz equations. The DBEM and DRBEM results are presented and compared by equi-velocity and current lines at steady-state for several values of Hartmann number and the boundary perturbation parameter.

Magnetohydrodynamic pipe flow in annular-like domains

Abstract The magnetohydrodynamic (MHD) pipe flow in annular-like domains with electrically conducting walls is investigated using both the extended-domain-eigenfunction method (EDEM) and the boundary element method (BEM). EDEM aims to reformulate the original problem on an extended symmetric domain obtained by transforming the inner boundary to a smaller circle towards the centre of the pipe, so that an eigenfunction solution can be obtained theoretically. By collocating only the inner circular boundary, the solution is transformed back to the original inner wall, which can be regarded as a semi-theoretical solution. On the other hand, BEM is a boundary only nature technique which transforms the differential equation into a boundary integral equation using the fundamental solution of the differential equation. Calculations are carried out for increasing values of Hartmann number (M) in annular-like domains with several shapes of inner wall at various wall conductivities. It is observed that although the results obtained by EDEM and BEM are very compatible for small M, EDEM is computationally less expensive and faster in convergence compared to BEM. However, BEM gives more accurate results than EDEM for large M due to the accumulation of numerical errors close to inner boundary in EDEM.

Natural convection flow of a nanofluid in an enclosure under an inclined uniform magnetic field

In this study, the natural convection in a square enclosure filled with water-based aluminium oxide () under the influence of an externally applied inclined magnetic field is considered numerically. The flow is steady, two-dimensional and laminar; the nanoparticles and water are assumed to be in thermal equilibrium. The governing equations are solved in terms of stream function–vorticity–temperature using both the dual reciprocity boundary element method and the finite element method to see the influence of characteristic flow parameters, namely: solid volume fraction (), inclination angle (), Rayleigh (Ra) and Hartmann (Ha) numbers. Numerical simulations are performed for , , and the values of Rayleigh and Hartmann numbers up to and 300, respectively. The results show that the buoyancy-driven circulating flows undergo inversion of direction as Ra and Ha increase, and magnitudes of streamlines and vorticity contours increase as Ra increases, but decrease as Ha increases. The isotherms have a horizontal profile for high Ra values as a result of convective dominance over conduction. As Ha increases, effect of the convection on flow is reduced, thus the isotherms tend to have vertical profiles.

DRBEM Solution of the Double Diffusive Convective Flow

A numerical investigation of unsteady, two-dimensional double diffusive convection flow through a lid-driven square enclosure is carried on. The left and bottom walls of the enclosure are either uniformly or non-uniformly heated and concentrated, while the right vertical wall is maintained at a constant cold temperature. The top wall is insulated and it moves to the right with a constant velocity. The numerical solution of the coupled nonlinear differential equations is based on the use of dual reciprocity boundary element method (DRBEM) in spatial discretization and an unconditionally stable backward implicit finite difference scheme for the time integration. Due to the coupling and the nonlinearity, an iterative process is employed between the equations. The boundary only nature of the DRBEM and the use of the fundamental solution of Laplace equation make the solution process computationally easier and less expensive compared to other domain discretization methods. The study focuses on the effects of uniform and non-uniform heating and concentration of the walls for various values of physical parameters on the double-diffusive convection in terms of streamlines, isotherms and isoconcentration lines.