Interaction of a Conducting Fluid Stream with a Traveling Wave of Magnetic Field of Finite Extension

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Abstract
The ac induction MHD generator with a channel of rectangular cross section and a polyphase winding as a source of the traveling wave of magnetic field of any arbitrary but finite length is treated as a boundary value problem. The solutions obtained indicate that the appropriate parameter that could be treated as a figure of merit for the channel is Γ=4Ω/μσU2, where Ω is the ac frequency, U is the fluid velocity, and μ and σ refer to the fluid with their usual meaning. This parameter is inversely proportional to the magnetic Reynolds number with a characteristic length equal to the distance traveled by the stream in one period of the exciting alternating current. Expressions for the magnetic field, current density, power developed, power output, and Joule losses in the channel are developed as well as their approximations for both large and small Γ. A method to eliminate the electromagnetic end effects due to the finite length of the channel by an appropriate distribution of the exciting current in the polyphase winding is also developed. The feasibility of building fractional wavelength MHD generators then becomes apparent.

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