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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. V. Getling, Rayleigh—Bénard convection (Editorial URSS, Moscow, 1999) [in Russian].
K. Stork and U. Möller, “Convection in boxes: experiments,” J. Fluid Mech. 54(4), 599–611 (1972).
S. H. Davis, “Convection in a box: linear theory,” J. Fluid Mech. 30(3), 465–478 (1967).
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).
E. Bodenschatz, W. Pesch, and G. Ahlers, “Recent developments in Rayleigh-Bénard convection,” Annu. Rev. Fluid Mech. 32, 709–778 (2000).
J. G. Symons and M. K. Peck, “Natural convection heat transfer through inclined longitudinal slots,” J. Heat Transfer 106(4), 824–829 (1984).
K. R. Kirchartz and J. H. Oertel, “Three-dimensional thermal cellular convection in rectangular boxes,” J. Fluid Mech. 192, 249–286 (1988).
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).
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).
G. Z. Gershuni, E. M. Zhukhovitskii, and A. A. Nepomniashchii, Stability of convective flows (Nauka, Moscow, 1989) [in Russian].
F. Drazin, Introduction to hydrodynamic stability (Cambridge Univ. Press, Cambridge, 2002).
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).
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).
S. Chandrasekhar, Hydrodynamic and hydromagnetic stability (Dover Publ., New York, 1961).
Author information
Authors and Affiliations
Corresponding author
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
About this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462819010117