Magnetohydrodynamic channel flow study

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Abstract
A finite‐difference study of a steady, incompressible, viscous, magnetohydrodynamic (MHD) channel flow which has direct application to dc electromagnetic pumps is presented. The study involves the numerical solution of the coupled Navier–Stokes and Maxwell equations at low magnetic Reynolds numbers. It is shown that the axial velocity profiles have a characteristic M shape as the fluid approaches and passes the electrode. The electric potential varies almost linearly from the channel centerline to the channel wall. The current shows a steep gradient near the electrodes. Comparison between the finite‐difference solution and a quasi‐one‐dimensional approach are presented. The two‐dimensional numerical calculations predict a larger pressure rise, a smaller net current, and a smaller pump efficiency than the quasi‐one‐dimensional model.

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