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Periodic fluid transients in cylindrical ducts with transverse magnetic fields

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Summary

This paper treats periodic fluid transients in liquid metals contained in constant-area circular ducts with uniform, transverse, applied magnetic fields. The magnetic Reynolds and Mach numbers are assumed to be small, and the Reynolds number is assumed to be large. By the use of a complex coordinate transformation, closed-form solutions are obtained for the perfectly conducting duct. By the same technique, solutions in series of Mathieu functions are obtained for the fully insultating duct. A method for solving the dispersion relation for each case is outlined, and sample numerical results are presented.

Résumé

Cet article traite des ondes de compression périodiques dans un métal liquide contenu dans une conduite circulaire avec une section droite qui est constante et avec un champ magnétique transversal et uniforme que l'on applique. Ici on suppose que le nombre magnétique de Reynolds et le nombre de Mach sont petits et que le nombre de Reynolds est grand. A l'aide d'une transformation complexe des corrdonnées on obtient des solutions éxactes pour une conduite qui est parfaitement conductrice. Par le même technique on trouve les solutions pour la conduite parfaitement isolante dans une série de fonctions de Mathieu. Une méthode pour la solution de l'équation de dispersion est esquissée et des exemples de résultats numériques sont présentés.

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References

  1. John S. Walker,Periodic Fluid Transients in Rectangular Ducts with Transverse Magnetic Fields, Z. Angew. Math. Phys.25, 353–366 (1974).

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Authors and Affiliations

  1. Dept. of Theoretical and Applied Mechanics, University of Illinois, Urbana, Illinois, USA

    R. B. Myers & J. S. Walker

Authors
  1. R. B. Myers
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  2. J. S. Walker
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Myers, R.B., Walker, J.S. Periodic fluid transients in cylindrical ducts with transverse magnetic fields. Journal of Applied Mathematics and Physics (ZAMP) 29, 577–590 (1978). https://doi.org/10.1007/BF01601486

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  • DOI: https://doi.org/10.1007/BF01601486

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