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Some Applications of Extremum Principles to Magnetohydrodynamic Pipe Flow
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 336, No. 1605 (Jan. 22, 1974), pp. 211-222
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/78500
Page Count: 12
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This paper is concerned with the application of extremum principles to the laminar flow of a conducting fluid along a pipe with conducting walls. The extremum principles provide upper and lower bounds to the mass-flow rate Q. While these may supply numerical bounds for Q their main application lies in the construction of asymptotic series at large Hartmann numbers. The most important result is a formula for the leading coefficient in the asymptotic series for Q for a wide class of pipe sections with thick conducting walls. A number of examples are given. A particular example is the square channel with thin conducting walls and it is shown how the 'thin wall' approximation can be derived from the extremum principles.
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences © 1974 Royal Society