Solitary fluid transients in rectangular ducts with transverse magnetic fields

  • John S. Walker
Original Papers


This paper treats a fluid hammer wave which is propagating into a fully developed MHD duct flow and which is produced by suddenly closing a valve at some cross section of a rectangular, insulating duct with a uniform transverse, applied magnetic field. The Mach and magnetic Reynolds numbers are assumed to be small, while the Hartmann number is assumed to be large. For a small interaction parameter, the electromagnetic effects on the fluid hammer wave are small and consist of both dispersion and dissipation. The dispersion is cumulative and becomes larger for large time, while the dissipation remains small for all time.


Cet article traite de l'onde de choc produite par la fermeture subite d'une vanne et qui se propage dans un fluide conducteur d'electricité s'écoulant dans une conduite isolante de section rectangulaire à laquelle est appliqué un champ magnétique transversal et homogène. On admet que le nombre de Reynold magné tique et le nombre de Mach sont petits, alors que le nombre de Hartmann est grand. Pour des faibles valeurs du paramètre d'interaction, les effets électromagnétiques sur l'onde de choc sont petits et comprennent une dispersion et une dissipation. La dispersion est cummulative et augmente avec le temps, alors que la dissipation reste toujours petite.


Magnetic Field Reynolds Number Mathematical Method Interaction Parameter Large Time 
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  1. [1]
    J. S. Walker,Perturbation Solutions for Steady One-Dimensional Waterhammer Waves, J. Fluids Eng.97, 260–262 (1975).Google Scholar
  2. [2]
    F. J. Young andW. T. Rouleau,Pressure Surges in Magnetoviscous Flow, J. Basic Eng.87, 478–482 (1965).Google Scholar
  3. [3]
    John S. Walker,Periodic Fluid Transients in Rectangular Ducts with Transverse Magnetic Fields, Z. angew. Math. Phys.25, 353–366 (1974).Google Scholar
  4. [4]
    I. S. Gradshteyn andI. M. Ryzhik,Tables of Integrals, Series and Products, 4th Ed. in Translation, Academic Press, New York (1965).Google Scholar

Copyright information

© Birkhäuser-Verlag 1978

Authors and Affiliations

  • John S. Walker
    • 1
  1. 1.Dept. of Theoretical and Applied MechanicsUniversity of IllinoisUrbanaUSA

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