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
This study presents the numerical solutions of regularly perturbed magnetohydrodynamic (MHD) flow equations of an electrically conducting, incompressible fluid in a long channel of rectangular cross-section (duct). The steady, laminar, fully-developed MHD flow equations are coupled in terms of the velocity V (x, y) and the induced magnetic field B(x, y) in the duct region. If the applied magnetic field is very weak for a fluid with small electrical conductivity but high viscosity coefficient, it is possible to have a Hartmann number which is much less than one, that's why it can be treated as a perturbation parameter and the MHD duct flow problem becomes regularly perturbed. The dual reciprocity boundary element method (DRBEM) is used to discretize the regularly perturbed and coupled MHD flow equations with the fundamental solution of Laplace equation to convert them into boundary integral equations. Numerical results are simulated for the boundary conditions such as no-slip and insulated or no-slip and electrically perfectly/variably conducting walls to show the physical effects of the wall conductivity on the behavior of the fluid velocity and the induced magnetic field. It is seen that, when the conductivity parameter rises, the profiles of the velocity stay the same but slightly decrease in magnitudes whereas the induced magnetic field profiles become to be perpendicular to the side walls. Moreover, we see that the regular perturbation technique for small Hartmann number not only captures the expected behavior of the rectangular MHD duct flow problem but also coincides with the exact solutions when available.