Akademik Veri Yönetim Sistemi
11th International Conference on Mathematical Modeling in Physical Sciences, IC-MSQUARE 2022, Virtual, Online, Sırbistan, 5 - 08 Eylül 2022, cilt.2872
In this study, the unsteady Magnetohydrodynamics (MHD) slip flow in a square cavity subjected to a uniform horizontal magnetic field is investigated. The coupled, time-dependent MHD equations, with the slipping velocity and the insulated wall conditions, are discretized by the dual reciprocity boundary element method (DRBEM). The resultant algebraic equations, containing both the velocity and the induced magnetic field unknowns and their normal derivatives, are rearranged. The time is discretized by the explicit Euler method. The numerical stability analysis is carried out through the spectral radius of the final coefficient matrix. The choices of the relaxation parameters and the time steps for the problem constants are discussed. The steady-state flow behaviors for various slip lengths, Hartmann (Ha), Reynolds (Re), and magnetic Reynolds (Rm) numbers combinations are presented. It is found that, for fixed Ha, Rm, relaxation parameters, and time step, the spectral radius of the coefficient matrix increases as Re or slip length advances. Large time steps and the relaxation parameters close to one give numerically stable results. The slip on the walls accelerates the flow, thickens the side layers, and shrinks the Hartmann layers. Increasing Ha decelerates the flow. The DRBEM is capable of giving numerically stable results for the MHD slip flow problem with a less computational cost due to its boundary-only discretization nature.