Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



On the motion past thin airfoils of incompressible fluids with conductivity tensor

Author: L. Dragos
Journal: Quart. Appl. Math. 28 (1970), 313-325
DOI: https://doi.org/10.1090/qam/99788
MathSciNet review: QAM99788
Full-text PDF

Abstract | References | Additional Information

Abstract: This note is a study of the problem of the steady motion of an inviscid incompressible fluid past thin airfoils, the Hall effect being taken into account. The case of crossed fields (one of the most important in aerodynamics) is studied in detail. The results for the cases of aligned fields and Alfvén motion are also given. The general solution is represented by a continuous superposition of plane waves. The boundary conditions determine the solution by means of a Fredholm-type integral equation which may be solved with the aid of the method of successive approximations. If the parameter of the magneto-hydrodynamic interaction $ \left( S \right)$ is equal to zero, one obtains the known solution of classical aerodynamics. The equation is solved explicitly for Alfvén motion.

References [Enhancements On Off] (What's this?)

  • [1] W. R. Sears and E. L. Resler, Jr., Magneto-hydrodynamic flow past bodies, Advances in Appl. Mech., vol. 8, Academic Press, New York, 1964, pp. 1-68
  • [2] L. Dragos, Magnetodynamics of fluids, Publ. House Romanian Academy of Science, Bucharest, 1969
  • [3] J. Y. T. Tang and H. Seebass, The effect of tensor conductivity on continuum magnetodynamic flows, Quart. Appl. Math. 26, 311-320 (1968)
  • [4] L. Dragos, L'effet Hall dans l'écoulement des fluides en présence des profils minces, C. R. Acad. Sci. Paris Ser. A-B 267, A579 (1968)
  • [5] L. Dragos, L'effet Hall dans l'écoulement des fluides compressibles en présence des profils minces, C. R. Acad. Sci. Paris Ser. A-B 269 (1969)
  • [6] L. Dragos, Hall effect on the motion of viscous fluids past the flat plate, Rev. Roumaine Math. Pures Appl. 15 (1970), 683–692. MR 0270622
  • [7] Lazăr Dragos, Theory of thin airfoils in magnetohydrodynamics, Arch. Rational Mech. Anal. 13 (1963), 262–278. MR 0157582, https://doi.org/10.1007/BF01262696
  • [8] I. M. Gel'fand and G. E. Šilov, Genralized functions. I: Operations on them, Fizmatgiz, Moscow, 1958; English transl., Academic Press, New York, 1964
  • [9] Caius Jacob, Introduction mathématique à la mécanique des fluides, Préface de Henri Villat, Éditions de l’Académie de la République Populaire Roumaine, Bucharesst; Gauthier-Villars, Paris, 1959 (French). MR 0114422
  • [10] N. I. Mushelišvili, Singular integral equations, OGIZ, Moscow, 1946; English transl., Noordhoff, Groningen, 1953
  • [11] W. R. Sears and E. L. Resler, Theory of thin airfoils in fluids of high electrical conductivity, J. Fluid Mech. 5 (1959), 257–273. MR 0101742, https://doi.org/10.1017/S0022112059000180
  • [12] Keith Stewartson, Magneto-fluid dynamics of thin bodies in oblique fields. II, Z. Angew. Math. Phys. 13 (1962), 242–255 (English, with German summary). MR 0143440, https://doi.org/10.1007/BF01601086
  • [13] Lazăr Dragos, La théorie de l’aile mince en magnétohydrodynamique. II, C. R. Acad. Sci. Paris 255 (1962), 1289–1290 (French). MR 0143448

Additional Information

DOI: https://doi.org/10.1090/qam/99788
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society