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Fluid Dynamics

, Volume 40, Issue 3, pp 349–358 | Cite as

Problem of Critical Convective Flows in Horizontal-Cylindrical Cavities

  • A. M. Pylaev
Article

Abstract

The results of an analysis of the linear perturbations of equilibrium of a viscous heat-conducting fluid or gas in cavities with simple geometric cross-sections are given. Both plane motions and motions periodic in the direction of the horizontal generator of the boundary surface are considered. Variants in which the acceleration of the mass force field can be both constant and periodically modulated are calculated. The solutions of the problem for the stream function (or the vertical velocity component) and the temperature are represented in the form of double or triple Fourier series. For the coefficients in the expansions an infinite system of equations which admits reduction is obtained. The results are found to be in good agreement with the known data.

Keywords

Boussinesq approximation modulations plane and three-dimensional perturbations infinite systems isolines 

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REFERENCES

  1. 1.
    M. R. Ukhovskii and V. I. Yudovich, “On steady-state convection equations,” Prikl. Mat. Mekh., 27, 295–300 (1963).Google Scholar
  2. 2.
    G. Z. Gershuni and E. M. Zhukhovitskii, Convective Stability of an Incompressible Fluid [in Russian], Nauka, Moscow (1972).Google Scholar
  3. 3.
    G. Z. Gershuni, E. M. Zhukhovitskii, and A. A. Nepomnyashchii, Stability of Convective Flows [in Russian], Nauka, Moscow (1989).Google Scholar
  4. 4.
    V. I. Polezhaev and V. V. Sazonov, “Mechanics of microgravity and gravity-sensitive systems,” in: Summaries Research Workshop Papers [in Russian], Institute for Problems in Mechanics of RAS, Moscow (1998).Google Scholar
  5. 5.
    B. David, “The planform and onset of convection with a temperature-dependent viscosity,” J. Fluid. Mech., 191, 247–288 (1988).Google Scholar
  6. 6.
    B. F. Edwards, “Crossed rolls at onset of convection in a rigid box,” J. Fluid. Mech., 181, 583–597 (1988).Google Scholar
  7. 7.
    E. Crespo del Arco, P. Bontoux, R. L. Sani, G. Hardin, and G. P. Extremet, “Steady and oscillatory convection in vertical cylinders heated from below. Numerical simulation of asymmetric flow regimes,” Adv. Space Res., 8, No.12, 281–292 (1988).CrossRefGoogle Scholar
  8. 8.
    W. Velte, “Stabilitatsverhalten und Verzweigung stationarer Losungen der Navier-Stokesschen Gleichungen,” Arch. Ration. Mech. Anal., 16, No.2, 97–125 (1964).CrossRefGoogle Scholar
  9. 9.
    G. Z. Gershuni, E. M. Zhukhovitskii, and E. L. Tarunin, “Numerical study of convection of a liquid heated from below,” Fluid Dynamics, 1, No.6, 58–62 (1966).CrossRefGoogle Scholar
  10. 10.
    U. H. Kurzweg, “Convective instability of hydromagnetic fluid within a rectangular cavity,” Intern. J. Heat Mass Transfer, 8, No.1, 35–41 (1965).CrossRefGoogle Scholar
  11. 11.
    E. M. Zhukhovitskii, “Application of the Galerkin method to a problem of stability of a nonuniformly heated fluid,” Prikl. Mat. Mekh., 18, 205–211 (1954).Google Scholar
  12. 12.
    M. Sherman, “Onset of thermal instability in a horizontal circular cylinder,” Phys. Fluids, 9, No.11, 2095 (1966).CrossRefGoogle Scholar
  13. 13.
    I. Catton, “Natural convection in horizontal circular layers,” Phys. Fluids, 9, No.12, 2521 (1966).CrossRefGoogle Scholar
  14. 14.
    G. Z. Gershuni and E. M. Zhukhovitskii, “Stability of equilibrium of a fluid in a horizontal cylinder heated from below,” Prikl. Mat. Mekh., 25, 1035–1040 (1961).Google Scholar
  15. 15.
    S. H. Davis, “Convection in a box: linear theory,” J. Fluid. Mech., 39, 465–478 (1967).Google Scholar
  16. 16.
    G. Z. Gershuni, E. M. Zhukhovitskii, and Yu. S. Yurkov, “Numerical determination of the limits of convective stability in a system with a periodically varying parameter,” Uchen. Zap. Perm. Univer., No. 248, Gidrodinamika, No. 3, 29–37 (1971).Google Scholar
  17. 17.
    L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis [in Russian], Gostekhizdat, Moscow, Leningrad (1950).Google Scholar

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© Springer Science+Business Media, Inc. 2005

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  • A. M. Pylaev

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