Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the one-dimensional flow of a conducting gas in crossed fields

Author: Erling Dahlberg
Journal: Quart. Appl. Math. 19 (1961), 177-193
MSC: Primary 76.34
DOI: https://doi.org/10.1090/qam/134613
MathSciNet review: 134613
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Abstract: The equations governing the quasi-one-dimensional steady flow of a conducting perfect gas in crossed, transverse electric and magnetic fields are treated under the assumptions that the electric conductivity is a scalar, that the wall drag is small and that the magnetic field due to the currents in the gas is negligible. The equations are normalized and different flow situations are illustrated by means of phase diagrams (drawn for a gas of constant specific heats, $ \gamma = 1.33$). The possibility of a smooth transition from supersonic to subsonic motion is pointed out and the phenomena of standing shock fronts and choking are surveyed for constant-area, small-friction, power-yielding flow. The appendix contains some general remarks on the system of non-linear differential equations: $ x' = P\left( {x,y} \right)/R\left( {x,y} \right)$; $ y' = Q(x,y)/R(x,y)$.

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DOI: https://doi.org/10.1090/qam/134613
Article copyright: © Copyright 1961 American Mathematical Society

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