Abstract:
The stability of the state of rest of a heated infinite horizontal layer of a viscous heat-conducting fluid (the Rayleigh–Benard problem) is considered. The equation of state for the fluid takes into account the nonmonotonic temperature and pressure dependence of water density. Instability of the mechanical equilibrium with respect to small monotonic perturbations is studied. The effect of the problem parameters on the Rayleigh numbers and their corresponding critical motions is investigated numerically using linear theory. Numerical investigation of the spectral problem is based on the Godunov–Abramov orthogonalization method. The calculation results are compared with the well-known results for the limiting case where the density is considered a quadratic function of temperature and does not depend on pressure.
Citation:
A. N. Ermolenko, “Rayleigh–Benard problem for an anomalous fluid”, Prikl. Mekh. Tekh. Fiz., 48:2 (2007), 27–38; J. Appl. Mech. Tech. Phys., 48:2 (2007), 166–175
This publication is cited in the following 5 articles:
Aymen Benbeghila, Riadh Ouzani, Ammar Benderradji, Zineddine Alloui, Sofiane Khelladi, “Linear stability of Rayleigh-Bénard-Poiseuille flow of water near 4°C in a channel bounded by slip walls”, International Communications in Heat and Mass Transfer, 160 (2025), 108370
Vladimir Kossov, Olga Fedorenko, Dauren Zhakebayev, Venera Mukamedenkyzy, Dyusembek Kulzhanov, “Convective mass transfer of a binary gas mixture in an inclined channel”, Z Angew Math Mech, 102:1 (2022)
V. N. Kosov, O. V. Fedorenko, M. K. Asembaeva, V. Mukamedenkyzy, “Changing Diffusion–Convection Modes in Ternary Mixtures with a Diluent Gas”, Theor Found Chem Eng, 54:2 (2020), 289
E. A. Lukashev, E. V. Radkevich, N. N. Yakovlev, O. A. Vasil'eva, “Introduction to the generalized theory of non-equilibrium Cahn-Hilliard phase transitions
(Thermodynamic problems in continuum mechanics)”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 221:3 (2017), 437–472
E. A. Lukashev, E. V. Radkevich, N. N. Yakovlev, O. A. Vasil′teva, AIP Conference Proceedings, 1910, 2017, 020017