Skip to main content
Log in

On the Orientation of Convective Rolls in an Inclined Rectangular Channel

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

An analysis of the linear stability of convective flow in a channel of rectangular cross-section inclined to the horizon is presented. The behavior of three-dimensional monotonic disturbances is considered for different values of the channel width and fluid properties. The main flow is obtained in an analytical form. Two angles of inclination, at which the convective roll changes, are determined. A strong dependence of the smaller inclination angle on the channel width and its weak dependence on the medium characteristics and a weak dependence of the greater inclination angle on the channel width are established.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. V. Getling, Rayleigh—Bénard convection (Editorial URSS, Moscow, 1999) [in Russian].

    MATH  Google Scholar 

  2. K. Stork and U. Möller, “Convection in boxes: experiments,” J. Fluid Mech. 54(4), 599–611 (1972).

    Article  ADS  Google Scholar 

  3. S. H. Davis, “Convection in a box: linear theory,” J. Fluid Mech. 30(3), 465–478 (1967).

    Article  ADS  MATH  Google Scholar 

  4. J. De Graaf and E. Van Der Held, “The relation between the heat transfer and the convection phenomena in enclosed plane air layers,” Appl. Sci. Res. 3(6), 393–409. (1953).

    Article  Google Scholar 

  5. E. Bodenschatz, W. Pesch, and G. Ahlers, “Recent developments in Rayleigh-Bénard convection,” Annu. Rev. Fluid Mech. 32, 709–778 (2000).

    Article  ADS  MATH  Google Scholar 

  6. J. G. Symons and M. K. Peck, “Natural convection heat transfer through inclined longitudinal slots,” J. Heat Transfer 106(4), 824–829 (1984).

    Article  Google Scholar 

  7. K. R. Kirchartz and J. H. Oertel, “Three-dimensional thermal cellular convection in rectangular boxes,” J. Fluid Mech. 192, 249–286 (1988).

    Article  ADS  Google Scholar 

  8. R. V. Birikh, G. Z. Gershuni, E. M. Zhukhovitskii, and R. N. Rudakov, “Hydrodynamic and thermal instabilities of steady convective motion,” Prikl. Mat. Mekh. 32(2), 256–263 (1968).

    Google Scholar 

  9. G. Z. Gershuni and E. M. Zhukhovitskii, “Stability of the plane-parallel convective motion with respect to spatial disturbances,” Prikl. Mat. Mekh. 33(5), 855–860 (1969).

    Google Scholar 

  10. G. Z. Gershuni, E. M. Zhukhovitskii, and A. A. Nepomniashchii, Stability of convective flows (Nauka, Moscow, 1989) [in Russian].

    Google Scholar 

  11. F. Drazin, Introduction to hydrodynamic stability (Cambridge Univ. Press, Cambridge, 2002).

    Book  MATH  Google Scholar 

  12. S. A. Korpela, “A study on the effect of prandtl number on the stability of the conduction regime of natural con-vection in an inclined slot,” Int. J. Heat Mass Transfer 17(2), 215–222 (1974).

    Article  Google Scholar 

  13. D. Pivovarov, “The solution of problems of the stability of three-dimensional convective flows in a closed rectangular cavity by the collocation method,” J. Appl. Math. Mech. 78(2), 137–143 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  14. S. Chandrasekhar, Hydrodynamic and hydromagnetic stability (Dover Publ., New York, 1961).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. E. Pivovarov.

Additional information

Russian Text © The Author(s), 2019, published in Izvestiya RAN. Mekhanika Zhidkosti i Gaza, 2019, No. 2, pp. 31–37.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pivovarov, D.E. On the Orientation of Convective Rolls in an Inclined Rectangular Channel. Fluid Dyn 54, 177–183 (2019). https://doi.org/10.1134/S0015462819010117

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462819010117

Keywords

Navigation