Abstract
The equations for two‐dimensional Hartmann flow through ducts of rectangular cross section are solved numerically by the Peaceman–Rachford alternating direction implicit method for boundary conditions appropriate to those encountered in a Faraday magnetohydrodynamic generator. Cross‐stream variation in fluid electrical condictivity as well as variable conductivity of the electrode walls are considered and quantities such as velocity distribution, current streamline distribution, volume flow rate, and conversion efficiency are obtained for a range of Hartmann numbers up to M=100. Results show that decreasing the electrical conductivity in a continuous manner from a high value near the walls to a minimum along the duct axis leads to a high velocity region near the duct axis, a result differing from the essential slug flow character found for Hartmann flows of constant conductivity fluids at high M. The known one‐dimensional Hartmann flow solutions are found to give excellent agreement with the two‐dimensional results for constant conductivity fluids whenever the product of the duct aspect ratio and the square root of the Hartmann number is greater than about ten.
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