Effects of a Magnetic Field on Natural Convection in a Toroidal Channel

[+] Author and Article Information
Paul Concus

Lawrence Radiation Laboratory, University of California, Berkeley, Calif.

J. Appl. Mech 29(3), 559-567 (Sep 01, 1962) (9 pages) doi:10.1115/1.3640604 History: Received May 15, 1961; Online September 16, 2011


The problem of the natural convection of an electrically and thermally conducting fluid within a long, narrow, vertical toroidial channel centered in a large block of an electrically and thermally conducting solid is analyzed. A uniform horizontal magnetic field is applied to the fluid, and the bottom of the solid block is maintained at a higher fixed temperature than the top. The laminar, steady-state, single-cell convective motion of the fluid is considered and an approximate solution is found for the heat-transfer rate between the bottom and top surfaces of the block in the limiting cases of small and large Hartmann number. A numerical example is given for liquid sodium in which the application of a magnetic field of a few hundred gauss is shown to reduce the rate of heat transfer significantly.

Copyright © 1962 by ASME
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