Numerical Solution and Stability Analysis of Transient MHD Duct Flow

This paper simulates the 2D transient magnetohydrodynamic (MHD) flow in a rectangular duct in terms of the velocity of the fluid and the induced magnetic field by using the radial basis function (RBF) approximation. The inhomogeneities in the Poisson’s type MHD equations are approximated using the polynomial functions (1+r) and the particular solution is found satisfying both the equations and the boundary conditions (no-slip and insulated walls). The Euler scheme is used for advancing the solution to steady-state with a time increment and a relaxation parameter which are determined for achieving stable solution. It is shown that, as Hartmann number increases, the fluid becomes stagnant at the center of the duct, the flow is flattened and boundary layers are developed on the Hartmann and side walls. These are the well-known characteristics of the MHD duct flow. The stability analysis is also carried in terms of the spectral radius of the coefficient matrix of the discretized coupled system. Stable solutions are obtained with RBF by using quite large time increment and suitable relaxation parameters on the expense of explicit Euler time-integration scheme used