Abstract
The stability of steady convective flow in an inclined plane fluid layer bounded by ideally heat conducting solid planes is studied in the presence of a homogeneous longitudinal temperature gradient under unstable stratification conditions where the layer is inclined so that the temperature is higher in the lower part than in the upper part. It is shown that the inclination leads to the transition from critical perturbations to long-wavelength helical perturbations. Flow stability maps are given for the entire range of Prandtl numbers and inclination angles corresponding to unstable stratification.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. V. Birikh, “Thermocapillary Convection in a Horizontal Layer of Liquid,” Prkl. Mekh. Tekh. Fiz., No. 3, 69–72 (1966) [J. Appl. Mech. Tech. Phys. No. 3, 43–44 (1966)].
A. G. Kirdyashkin, “Thermogravitational and Thermocapillary Flows in a Horizontal Liquid Layer under the Conditions of a Horizontal Temperature Gradient,” Intern. J. Heat Mass Transfer.27 (8), 1205–1218 (1984).
G. Z. Gershuni, E. M. Zhukhovitskii, and A. A. Nepomnyashchii, Stability of Convective Flows (Nauka, Moscow, 1989)[in Russian].
V. K. Andreev and V. B. Bekezhanova, Stability of Non-Isothermal Liquids (Sib. Feder. Univ., Krasnoyarsk, 2010) [in Russian].
V. K. Andreev and V. B. Bekezhanova, “Stability of Non-Isothermal Fluids (Review),” Prkl. Mekh. Tekh. Fiz. 54 (2), 3–20 (2013) [Appl. Mech. Tech. Phys. 54 (2), 171–184 (2013)].
R. B. Sagitov and A. H. Sharifulin, “Long-Wave Instability of an Advective Flow in an Inclined Fluid Layer with Perfectly Heat-Conducting Boundaries,” Prkl. Mekh. Tekh. Fiz. 52 (6), 13–21 (2011) [Appl. Mech. Tech. Phys. 52 (6), 857–864 (2011)].
G. Z. Gershuni and E. M. Zhukhovitskii, Convective Stability of an Incompressible Fluid (Nauka, Moscow, 1972) [in Russian].
G. A. Ostroumov, Free Thermal Convection under the Conditions of the Internal Problem (Gostekhteoretizdat, Moscow, Leningrad, 1952) [in Russian].
N. I. Lobov, D. V. Lyubimov, and T. P. Lyubimova, Numerical Methods for Solving the Theory of Hydrodynamic Stability: a Textbook (Perm. Gos. Univ., Perm, 2004) [in Russian].
R. V. Birikh and R. N. Rudakov, “Use of the Orthogonalization Method in Stepwise Integration to Study the Stability of Convective Flows,” Uchen. Zap. Perm. Gos. Univ., No. 316, 149–158 (1974).
G. Z. ‘Gershuni, E. M. Zhukhovitskii, and V. M. Myznikov, “Stability of a Plane-Parallel Convective Flow of a Liquid in a Horizontal Layer,” Prkl. Mekh. Tekh. Fiz., No. 1, 95–100 (1974) [Appl. Mech. Tech. Phys. No.1, 78–82 (1974)].
G. Z. Gershuni, E. M. Zhukhovitskii, and V. M. Myznikov, “Stability of Plane-Parallel Convective Fluid Flow in a Horizontal Layer Relative to Spatial Perturbations,” Prkl. Mekh. Tekh. Fiz., No. 5, 145–147 (1974) [Appl. Mech. Tech. Phys., No. 5, 706–708 (1974)].
R. V. Birikh and T. N. Katanova, “Effect of High-Frequency Vibrations on the Stability of Advective Flow,” Izv.Ross. Akad. Nauk. Mekh. Zhidk. Gaza, No. 1, 16–22 (1998).
R. V. Birikh, “Convective Instability. Influence of Thin Permeable Partitions and High Frequency Vibrations,” Doctoral Dissertation (Perm, 1999).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © R.V. Sagitov, A.N. Sharifulin.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 58, No. 2, pp. 90–97, March–April, 2017.
Rights and permissions
About this article
Cite this article
Sagitov, R.V., Sharifulin, A.N. Stability of advective flow in an inclined plane fluid layer bounded by solid planes with a longitudinal temperature gradient. 1. Unstable stratification. J Appl Mech Tech Phy 58, 264–270 (2017). https://doi.org/10.1134/S0021894417020092
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894417020092