An Application of the Extended Kantorovich Method to Mhd Duct Flow

摘要

The extended Kantorovich method developed by A.D. Kerr and recently applied to the solution of a clamped plate by A.D. Kerr and H. Alexander, is used in the present paper to analyze the steady flow of a viscous, electrically conducting fluid through a perfectly insulated rectangular duct under a uniform, arbitrarily oriented, externally applied magnetic field. It is shown that the generated solution is independent of the choice of initial function, and that the convergence of the iterative procedure is very rapid. The obtained solution exhibits good correlation with the exact solution for small values of the Hartmann number. The inaccuracy at high Hartmann numbers is shown to be a result of a shortcoming in the method as it is presently applied. (Author)