Energy-conserving model of hexagonal pattern in Rayleigh-Bénard convection

2022 ◽  
Author(s):  
Hiya Mondal ◽  
Alaka Das
Keyword(s):  
Wave Number ◽  
Onset Of Convection ◽  
Hexagonal Pattern ◽  
Available Energy ◽  
Bénard Convection ◽  
Benard Convection ◽  
Energy Conserving ◽  
Thermally Conducting ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract We have constructed an energy-conserving sixteen mode dynamical system to model hexagonal pattern in Rayleigh-Bénard convection of Boussinesq fluids with symmetric stress-free thermally conducting boundaries. The model shows stable roll pattern at the onset of convection. Hexagon is found to appear in the system via sausage and (or) stationary rhombus patterns. Both up and down hexagons arise periodically or chaotically with roll, sausage and rhombus patterns. Hexagonal patterns exist for all values of the Prandtl number, 1 ≤ Pr ≤ 5 explored here. However the pattern is more prominent for small Pr and k < kc , where k denotes the wave number. The plot of Nusselt number matches with previous theoretical result. In dissipationless limit, the total energy and the unavailable energy are constants though the kinetic energy, the potential energy and the available energy vary with time. The derived model does not diverge for large values of Rayleigh number Ra.

Randomly forced Rayleigh-Bénard convection

1980 ◽  
Vol 98 (2) ◽  
pp. 329-348 ◽  
Author(s):  
Bharat Jhaveri ◽  
G. M. Homsy
Keyword(s):  
Convective Transport ◽  
Time Intervals ◽  
Onset Of Convection ◽  
Nonlinear Convection ◽  
Bénard Convection ◽  
Benard Convection ◽  
Random Fluctuations ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

We consider the onset of Rayleigh–Bénard convection from random fluctuations arising within a fluid. In the specific case in which the fluctuations are thermodynamically determined, we reduce the problem to a random initial value problem for the Fourier modes. For the case of weak nonlinear convection, it is possible to truncate the number of modes and this truncated set is solved both by a Monte Carlo technique and by moment methods for various Rayleigh numbers. We find three stages in the evolution of ordered convection from random fluctuations which correspond to time intervals in which the fluctuations and the nonlinearity have different degrees of importance. It is shown that no simple moment truncation method will succeed and that the time for onset of convection is a mean over a distribution of times for which members of an ensemble exhibit appreciable convective transport.

Steady Finite-Amplitude Rayleigh–Bénard Convection in Nanoliquids Using a Two-Phase Model: Theoretical Answer to the Phenomenon of Enhanced Heat Transfer

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
P. G. Siddheshwar ◽  
C. Kanchana ◽  
Y. Kakimoto ◽  
A. Nakayama
Keyword(s):  
Thermophysical Properties ◽  
Phase Model ◽  
Engine Oil ◽  
Small Scale ◽  
Two Phase ◽  
Onset Of Convection ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Rayleigh–Bénard convection in liquids with nanoparticles is studied in the paper considering a two-phase model for nanoliquids with thermophysical properties determined from phenomenological laws and mixture theory. In the absence of nanoparticle-modified thermophysical properties as used in the paper, the problem is essentially binary liquid convection with Soret effect. The base liquids chosen for investigation are water, ethylene glycol, engine oil, and glycerine, and the nanoparticles chosen are copper, copper oxide, silver, alumina, and titania. Using data on these 20 nanoliquids, our theoretical model clearly explains advanced onset of convection in nanoliquids in comparison with that in the base liquid without nanoparticles. The paper sets to rest the tentativeness regarding the boundary condition to be chosen in the study of Rayleigh–Bénard convection in nanoliquids. The effect of thermophoresis is to destabilize the system and so is the effect of other parameters arising due to nanoparticles. However, Brownian motion effect does not have a say on onset of convection. In the case of nonlinear theory, the five-mode Lorenz model is derived under the assumptions of Boussinesq approximation and small-scale convective motions, and using it enhancement of heat transport due to the presence of nanoparticles is clearly explained for steady-state motions. Subcritical motion is shown to be possible in all 20 nanoliquids.

scholarly journals Thermal forcing and ‘classical’ and ‘ultimate’ regimes of Rayleigh–Bénard convection

2019 ◽  
Vol 868 ◽  
pp. 1-4 ◽  
Author(s):  
Charles R. Doering
Keyword(s):  
Heat Transport ◽  
Boundary Layers ◽  
Horizontal Layer ◽  
System Response ◽  
Thermal Forcing ◽  
Onset Of Convection ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The fundamental challenge to characterize and quantify thermal transport in the strongly nonlinear regime of Rayleigh–Bénard convection – the buoyancy-driven flow of a horizontal layer of fluid heated from below – has perplexed the fluid dynamics community for decades. Rayleigh proposed controlling the temperature of thermally conducting boundaries in order to study the onset of convection, in which case vertical heat transport gauges the system response. Conflicting experimental results for ostensibly similar set-ups have confounded efforts to discriminate between two competing theories for how boundary layers and interior flows interact to determine transport through the convecting layer asymptotically far beyond onset. In a conceptually new approach, Bouillaut, Lepot, Aumaître and Gallet (J. Fluid Mech., vol. 861, 2019, R5) devised a procedure to radiatively heat a portion of the fluid domain bypassing rigid conductive boundaries and allowing for dissociation of thermal and viscous boundary layers. Their experiments reveal a new level of complexity in the problem suggesting that heat transport scaling predictions of both theories may be realized depending on details of the thermal forcing.

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