DRBEM solutions of cauchy problem for the magnetohydrodynamic duct flow

Aydın, Cemre
In this thesis, the direct and inverse problems of the MHD flow in rectangular ducts are solved in terms of the velocity of the fluid and the induced magnetic field by using the Dual Reciprocity Boundary Element Method (DRBEM). The two-dimensional, steady flow of a viscous, incompressible, and electrically conducting fluid is considered under the effect of an externally applied mangetic field. The duct wall conditions for the MHD flow ranges from the no-slip to slip and insulated to perfectly conducting. In the DRBEM application, the fundamental solution of the Laplace equation is made use of transform the integral equations into boundary integral equations eliminating domain integral resulting from the inhomogeneity. The terms other than Laplacian are treated as inhomogeneity and they are approximated by using the radial basis functions which are related with the particular solution of the PDE through the Laplace operator. The boundary inverse and parameter identification problems are considered as the two types of inverse problems for the MHD duct flow. In the boundary type inverse formulation, the aim is to calculate the slip length on the slipping boundary and the conductivity constant on the variably conducting boundary. In the parameter identification, the parameter Hartmann number in the MHD flow equations is going to be redetermined for a preassigned velocity and induced magnetic field in the problem region. Since the inverse problems are ill-posed, the DRBEM is accompanied with three regularization techniques, namely, Tikhonov regularization, the direct-inverse iterations, and the well-posed iterations for obtaining the solution of the Cauchy MHD duct flow. The originality of this thesis lies in the construction and solution of the MHD duct flow problems as inverse problems.
Citation Formats
C. Aydın, “DRBEM solutions of cauchy problem for the magnetohydrodynamic duct flow,” Thesis (Ph.D.) -- Graduate School of Natural and Applied Sciences. Mathematics., Middle East Technical University, 2020.