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Article Citation - WoS: 8Citation - Scopus: 12Drbem Solution of Free Convection in Porous Enclosures Under the Effect of a Magnetic Field(Pergamon-elsevier Science Ltd, 2013) Pekmen, B.; Tezer-Sezgin, M.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.Article Citation - WoS: 43Citation - Scopus: 48Mhd Flow and Heat Transfer in a Lid-Driven Porous Enclosure(Pergamon-elsevier Science Ltd, 2014) Pekmen, B.; Tezer-Sezgin, M.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.Article Citation - WoS: 13Citation - Scopus: 13Numerical Solution of Buoyancy Mhd Flow With Magnetic Potential(Pergamon-elsevier Science Ltd, 2014) Pekmen, B.; Tezer-Sezgin, M.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.
