Parameter Identification in MHD Duct Flow Cauchy Problem using the DRBEM

Abstract

In this study, the Hartmann number (Ha) is identified through the inverse formulation of Cauchy problem for magnetohydrodynamic (MHD) flow in a duct with insulated but no-slip or variably slipping walls. The solutions for direct and inverse problems are obtained using the dual reciprocity boundary element method (DRBEM), and Tikhonov regularization with L-curve method is used for solving ill-conditioned linear system of equations resulted from the inverse problem. The velocity and the induced magnetic field profiles are simulated from the direct solution depicting the well-known MHD characteristics. The Hartmann number is reconstructed from the inverse problem with an accuracy of 10−4 to 10−6. The DRBEM provides overdetermined information needed in the inverse MHD flow problem since it gives both the solution and its normal derivatives on the boundary points.