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Abstract
The hydrodynamic characteristics of a buoyancy-driven convection loop containing an electrically conducting fluid in a transverse magnetic field art investigated numerically using a two-dimensional spectral element numerical model. The lower portion of the loop is heated and the upper portion is cooled, both isothermally, while the middle portion is insulated. The study covers the range of Grashof number, Gr,from 103 to 105, Hartmann number, Ha, from 0 to 20, loop height-to-thickness ratio, L / D, from 5 to 26, and at Prandtl numbers Pr = 0·02 and Pr = 1. Results are presented for the velocity, temperature profiles, and heat transfer in terms of Hartmann number. Comparison is made with the analytical solutions of Ghaddar [1, 2], based on a parallel flow approximation, the numerical analysis compares well with the closed-form analytical solutions of the magnetohydrodynamic generator for the flow velocity and the induced current. The study also confirmed the existence of an optimal Hartmann number at which the induced electric current is maximized for all ranges of Prandtl numbers. The optimal Hartmann number found numerically for Pr = 0·02 is similar to the one predicted by the analytical I-D model of Ghaddar [1, 2].
Notes
Address correspondence to Nesreen Ghaddar, Department of Mechanical Engineering, Faculty of Engineering and Architecture, American University of Beirut, 850 Third Avenue, New York, NY 10022, USA E-mail: [email protected]