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Numerical simulation of side‐heated free convection loop placed in transverse magnetic field; the induced electric current

Nesreen K. Ghaddar (American University of Beirut, Faculty of Engineering and Architecture, Beirut, Lebanon)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 1 November 1998

322

Abstract

The hydrodynamic characteristic of a buoyancy‐driven convection loop containing an electrically‐conducting fluid in a transverse magnetic field is numerically investigated using a two‐dimensional spectral element numerical model. One side of the loop is heated isothermally, the other side is cooled isothermally and the top and bottom sections are insulated. The study covers ranges of Grashof number, Gr, from 103 to 105, the Hartmann number, Ha, from 0 to 20, loop height to thickness ratio, L/d, from 10 to 20 and at Prandtl numbers of Pr = 0.02 and Pr = 1. Results are presented for the velocity, temperature profiles and heat transfer in terms of Hartmann number. At high Hartmann numbers the velocity gradient in the core of the flow decreases outside the Hartmann layer in the vicinity of the walls normal to the magnetic field. Comparison is made with the analytical solution of Ghaddar (1997), based on a parallel flow approximation and its range of validity is delineated. The numerical analysis compares well with the closed form analytical solution of the magnetohydrodynamic generator for the flow velocity and the induced current. This study reveals the existence of an optimal Hartmann number at which the induced electric current is maximised 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 1‐D model.

Keywords

Citation

Ghaddar, N.K. (1998), "Numerical simulation of side‐heated free convection loop placed in transverse magnetic field; the induced electric current", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 8 No. 7, pp. 814-840. https://doi.org/10.1108/09615539810226139

Publisher

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MCB UP Ltd

Copyright © 1998, MCB UP Limited

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