Browsing by Author "Pekmen, Bengisen"

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Citation - WoS: 15
Citation - Scopus: 18
Differential Quadrature Solution of Hyperbolic Telegraph Equation
(Hindawi Publishing Corporation, 2012) Pekmen, B.; Tezer-Sezgin, M.; Mathematics
Differential quadrature method (DQM) is proposed for the numerical solution of one- and two-space dimensional hyperbolic telegraph equation subject to appropriate initial and boundary conditions. Both polynomial-based differential quadrature (PDQ) and Fourier-based differential quadrature (FDQ) are used in space directions while PDQ is made use of in time direction. Numerical solution is obtained by using Gauss-Chebyshev-Lobatto grid points in space intervals and equally spaced and/or GCL grid points for the time interval. DQM in time direction gives the solution directly at a required time level or steady state without the need of iteration. DQM also has the advantage of giving quite good accuracy with considerably small number of discretization points both in space and time direction.
Citation - WoS: 38
Citation - Scopus: 40
Differential Quadrature Solution of Nonlinear Klein-Gordon and Sine-Gordon Equations
(Elsevier Science Bv, 2012) Pekmen, B.; Tezer-Sezgin, M.; Mathematics
Differential quadrature method (DQM) is proposed to solve the one-dimensional quadratic and cubic Klein-Gordon equations, and two-dimensional sine-Gordon equation. We apply DQM in space direction and also blockwise in time direction. Initial and derivative boundary conditions are also approximated by DQM. DQM provides one to obtain numerical results with very good accuracy using considerably small number of grid points. Numerical solutions are obtained by using Gauss-Chebyshev-Lobatto (GCL) grid points in space intervals, and GCL grid points in each equally divided time blocks. (C) 2012 Elsevier B.V. All rights reserved.
Citation - WoS: 7
Citation - Scopus: 12
Drbem Solution of Free Convection in Porous Enclosures Under the Effect of a Magnetic Field
(Pergamon-elsevier Science Ltd, 2013) Pekmen, B.; Tezer-Sezgin, M.; Mathematics
The dual reciprocity boundary element method (DRBEM) is applied for solving steady free convection in special shape enclosures filled with a fluid saturated porous medium under the effect of a magnetic field. The left and right walls are maintained at constant or different temperatures while the top and bottom walls are kept adiabatic. The effect of the external magnetic field on the flow and temperature behavior is visualized with different Rayleigh numbers Ra, Hartmann numbers Ha and inclination angle phi. The boundary only nature of DRBEM results in considerably small computational cost in obtaining numerical solution. The results are in good qualitative agreement with the available numerical results in the literature. It is found that the increase in the strength of the magnetic field causes the suppression on the motion of the fluid which points to the conductive heat transfer. (C) 2012 Elsevier Ltd. All rights reserved.
Citation - WoS: 4
Citation - Scopus: 5
Drbem Solution of Incompressible Mhd Flow With Magnetic Potential
(Tech Science Press, 2013) Pekmen, B.; Tezer-Sezgin, M.; Mathematics; Mathematics
The dual reciprocity boundary element method (DRBEM) formulation is presented for solving incompressible magnetohydrodynamic (MHD) flow equations. The combination of Navier-Stokes equations of fluid dynamics and Maxwell's equations of electromagnetics through Ohm's law is considered in terms of stream function, vorticity and magnetic potential in 2D. The velocity field and the induced magnetic field can be determined through the relations with stream function and magnetic potential, respectively. The numerical results are visualized for several values of Reynolds (Re), Hartmann (Ha) and magnetic Reynolds number (Rem) in a lid-driven cavity, and in a channel with a square cylinder. The well-known characteristics of the fluid flow and MHD flow are exhibited. These are the shift of the core region of the flow and the development of the main vortex in the vorticity through the center of the cavity as Re increases. An increase in Ha causes Hartmann layers for the flow at the bottom and top walls. Higher values of Rem result in circulation of the magnetic potential at the center of the cavity. An increase in Re causes symmetric vortices behind the cylinder to elongate through the channel, and an increase in Hartmann number suppresses this elongation.
Citation - WoS: 3
Citation - Scopus: 3
Drbem Solution of Mhd Flow With Magnetic Induction and Heat Transfer
(Tech Science Press, 2015) Pekmen, B.; Tezer-Sezgin, M.; Mathematics; Mathematics
This study proposes the dual reciprocity boundary element (DRBEM) solution for full magnetohydrodynamics (MHD) equations in a lid-driven square cavity. MHD equations are coupled with the heat transfer equation by means of the Boussinesq approximation. Induced magnetic field is also taken into consideration. The governing equations in terms of stream function, temperature, induced magnetic field components, and vorticity are solved employing DRBEM in space together with the implicit backward Euler formula for the time derivatives. The use of DRBEM with linear boundary elements which is a boundary discretization method enables one to obtain small sized linear systems. This makes the whole procedure computationally efficient and cheap. The results are depicted with respect to varying physical parameters such as Prandt1 (0.005 <= Pr <= 1), Reynolds (100 <= Re <= 2500), magnetic Reynolds (1 <= Rein <= 100), Hartmann (10 <= Ha <= 100) and Rayleigh (10 <= Ra <= 10(6)) numbers for discussing the effect of each parameter on the flow and temperature behaviors of the fluid. It is found that an increase in Ha slows down the fluid motion and heat transfer becomes conductive. Centered square blockage causes secondary flows on its left and light even for small Re. Strong temperature gradients occur around the blockage and near the moving lid for increasing values of Ra.
Citation - WoS: 3
Citation - Scopus: 6
Drbem Solution of Natural Convective Heat Transfer With a Non-Darcy Model in a Porous Medium
(Springer, 2015) Pekmen, B.; Tezer-Sezgin, M.; Mathematics
This study presents the dual reciprocity boundary element (DRBEM) solution of Brinkman-Forchheimer-extended Darcy model in a porous medium containing an incompressible, viscous fluid. The governing dimensionless equations are solved in terms of stream function, vorticity and temperature. The problem geometry is a unit square cavity with either partially heated top and bottom walls or hot steps at the middle of these walls. DRBEM provides one to obtain the expected behavior of the flow in considerably small computational cost due to the discretization of only the boundary, and to compute the space derivatives in convective terms as well as unknown vorticity boundary conditions using coordinate matrix constructed by radial basis functions. The Backward-Euler time integration scheme is utilized for the time derivatives. The decrease in Darcy number suppresses heat transfer while heat transfer increases for larger values of porosity, and the natural convection is pronounced with the increase in Rayleigh number.
Citation - WoS: 43
Citation - Scopus: 48
Mhd Flow and Heat Transfer in a Lid-Driven Porous Enclosure
(Pergamon-elsevier Science Ltd, 2014) Pekmen, B.; Tezer-Sezgin, M.; Mathematics
The mixed convection flow in a lid-driven square cavity filled with a porous medium under the effect of a magnetic field is studied numerically using the dual reciprocity boundary element method (DRBEM) with Houbolt time integration scheme. Induced magnetic field is also taken into consideration in terms of magnetic potential in solving magnetohydrodynamic (MHD) flow and temperature equations. Effects of the characteristic dimensionless parameters as Darcy (Da), Magnetic Reynolds (Rem), Grashof (Gr) and Hartmann (Ha) numbers, on the flow and heat transfer in the cavity are investigated at the final steady-state. It is found that the decrease in the permeability of porous medium and the increase in the intensity of the applied magnetic field cause the fluid to flow slowly. The convective heat transfer is reduced with an increase in Hartmann number. Magnetic potential circulates throughout the cavity with high magnetic permeability of the fluid. The combination of DRBEM with the Houbolt scheme has the advantage of using considerably small number of boundary elements and large time increments which results in small computational cost for solving the mixed convection MHD flow in a porous cavity. (C) 2013 Elsevier Ltd. All rights reserved.
Citation - WoS: 12
Citation - Scopus: 13
Numerical Solution of Buoyancy Mhd Flow With Magnetic Potential
(Pergamon-elsevier Science Ltd, 2014) Pekmen, B.; Tezer-Sezgin, M.; Mathematics
In this study, dual reciprocity boundary element method (DRBEM) is applied for solving the unsteady flow of a viscous, incompressible, electrically conducting fluid in channels under the effect of an externally applied magnetic field and buoyancy force. Magnetohydrodynamics (MHD) equations are coupled with the energy equation due to the heat transfer by means of the Boussinessq approximation. Then, the 20 non-dimensional full MHD equations in terms of stream function, temperature, magnetic potential, current density and vorticity are solved by using DRBEM with implicit backward Euler time integration scheme. Numerical results are obtained utilizing linear boundary elements and linear radial basis functions approximation for the inhomogeneities, in a double lid-driven staggered cavity and in a channel with backward facing step. The results are given for several values of problem parameters as Reynolds number (Re), magnetic Reynolds number (Rem), Hartmann number (Ha) and Rayleigh number (Ra). With the increase in Rem, both magnetic potential and current density circulate near the abrupt changes of the walls. The increase in Ha suppresses this perturbation, and forces the magnetic potential lines to be in the direction of the applied magnetic field. The boundary layer formation through the walls emerge in the flow and current density for larger values of Ha. (C) 2013 Elsevier Ltd. All rights reserved.
Citation - Scopus: 0
Steady mixed convection in a heated lid-driven square cavity filled with a fluid-saturated porous medium
(Springer Verlag, 2015) Pekmen,B.; Tezer-Sezgin,M.; Mathematics
Steady mixed convection flow in a porous square cavity with moving side walls is studied numerically using the dual reciprocity boundary element method (DRBEM). The equations governing the two-dimensional, steady, laminar mixed convection flow of an incompressible fluid are solved for various values of parameters as Darcy (Da), Grashof (Gr), and Prandtl (Pr) numbers. The results are given in terms of vorticity contours, streamlines and isotherms. Further, average Nusselt number variations with respect to the problem parameters are also presented. The fluid flows slowly as Da decreases since the permeability of the medium decreases, and the increase in Grashof number causes the flow to pass to the natural convective behavior. DRBEM has the advantage of using considerably small number of grid points due to the boundary only nature of the method. This provides the numerical procedure computationally cheap and efficient. © Springer International Publishing Switzerland 2015.
Citation - Scopus: 2
Steady Mixed Convection in a Heated Lid-Driven Square Cavity Filled With a Fluid-Saturated Porous Medium
(Springer Verlag, 2015) Pekmen,B.; Pekmen, Bengisen; Tezer-Sezgin,M.; Pekmen, Bengisen; Mathematics; Mathematics
Steady mixed convection flow in a porous square cavity with moving side walls is studied numerically using the dual reciprocity boundary element method (DRBEM). The equations governing the two-dimensional, steady, laminar mixed convection flow of an incompressible fluid are solved for various values of parameters as Darcy (Da), Grashof (Gr), and Prandtl (Pr) numbers. The results are given in terms of vorticity contours, streamlines and isotherms. Further, average Nusselt number variations with respect to the problem parameters are also presented. The fluid flows slowly as Da decreases since the permeability of the medium decreases, and the increase in Grashof number causes the flow to pass to the natural convective behavior. DRBEM has the advantage of using considerably small number of grid points due to the boundary only nature of the method. This provides the numerical procedure computationally cheap and efficient. © Springer International Publishing Switzerland 2015.