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.

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