scholarly journals Triply resonant penetrative convection

2012 ◽  
Vol 468 (2148) ◽  
pp. 3804-3823 ◽  
Author(s):  
B. Straughan
Keyword(s):  
Rayleigh Number ◽  
Sharp Increase ◽  
Viscous Incompressible Fluid ◽  
Penetrative Convection ◽  
Density Maximum ◽  
Convection Model ◽  
Source Sink ◽  
Unconditional Nonlinear Stability ◽  
Vertical Height ◽  
Active Temperature

A thermal convection model is considered that consists of a layer of viscous incompressible fluid contained between two horizontal planes. Gravity is acting vertically downward, and the fluid has a density maximum in the active temperature range. A heat source/sink that varies with vertical height is imposed. It is shown that in this situation there are three possible (different) sub-layers that may induce convective overturning instability. The possibility of resonance between the motion in these layers is investigated. A region is discovered where a very sharp increase in Rayleigh number is observed. In addition to a linearized instability analysis, two global (unconditional) nonlinear stability thresholds are derived.

Nonlinear Rayleigh–Bénard Convection With Variable Heat Source

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
P. G. Siddheshwar ◽  
P. Stephen Titus
Keyword(s):  
Rayleigh Number ◽  
Heat Source ◽  
Critical Point ◽  
Classical Analysis ◽  
Lorenz Model ◽  
Ginzburg Landau ◽  
Variable Heat ◽  
Source Sink ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Linear and nonlinear Rayleigh–Bénard convections with variable heat source (sink) are studied analytically using the Fourier series. The strength of the heat source is characterized by an internal Rayleigh number, RI, whose effect is to decrease the critical external Rayleigh number. Linear theory involving an autonomous system (linearized Lorenz model) further reveals that the critical point at pre-onset can only be a saddle point. In the postonset nonlinear study, analysis of the generalized Lorenz model leads us to two other critical points that take over from the critical point of the pre-onset regime. Classical analysis of the Lorenz model points to the possibility of chaos. The effect of RI is shown to delay or advance the appearance of chaos depending on whether RI is negative or positive. This aspect is also reflected in its effect on the Nusselt number. The Lyapunov exponents provide useful information on the closing in and opening out of the trajectories of the solution of the Lorenz model in the cases of heat sink and heat source, respectively. The Ginzburg-Landau models for the problem are obtained via the 3-mode and 5-mode Lorenz models of the paper.

Numerical Simulation of Natural Convection of Water Near Its Density Maximum Around a Cylinder Inside a Concentric Triangular Enclosure

2012 ◽  
Author(s):  
Yu-Peng Hu ◽  
You-Rong Li ◽  
Chun-Mei Wu
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Inclination Angle ◽  
Temperature Fields ◽  
Density Inversion ◽  
Density Maximum ◽  
Triangular Enclosure ◽  
Density Inversion Parameter ◽  
Boussinesq Fluid

In this paper, a series of numerical simulations for natural convection of water near its maximum-density around a cylinder inside a concentric triangular enclosure were conducted using finite volume method. The effects of the density inversion parameter, the aspect ratio, the Rayleigh number and the inclination angle on natural convection were discussed. Furthermore, the flow and temperature fields, the local and average Nusselt numbers at different parameters were obtained and analyzed. The results show that the flow pattern and temperature distribution are unique for various density inversion parameters and inclination angles. The density inversion parameter, the aspect ratio, the Rayleigh number all have significant effects on the overall heat transfer rates, except for the inclination angle. The present results can also contribute further information on the natural convection of non-Boussinesq fluid in enclosures.

Non-linear Rayleigh-Benard Magnetoconvection in Temperature-sensitive Newtonian Liquids with Variable Heat Source

2021 ◽  
Vol 88 (1-2) ◽  
pp. 08
Author(s):  
A. S. Aruna ◽  
V. Ramachandramurthy ◽  
N. Kavitha
Keyword(s):  
Rayleigh Number ◽  
Heat Source ◽  
Variable Viscosity ◽  
Critical Rayleigh Number ◽  
Lorenz Model ◽  
Onset Of Convection ◽  
Variable Heat ◽  
Non Linear ◽  
Source Sink ◽  
Rayleigh Benard

The present paper aims at weak non-linear stability analysis followed by linear analysis of nite-amplitude Rayleigh-Benard magneto convection problem in an electrically conducting Newtonian liquid with heat source/sink. It is shown that the internal Rayleigh number, ther- morheological parameter, and the Chandrasekhar number in uence the onset of convection. The generalized Lorenz model derived for the prob- lem is essentially the classical Lorenz model but with some coecient depending on the variable heat source (sink), viscosity, and the applied magnetic eld. The result of the parameters' in uence on the critical Rayleigh number explains their in uence on the Nusselt number. It is found that an increasing strength of the magnetic eld is to stabilize the system and diminishes heat transport whereas the heat source and variable viscosity in-tandem to work system unstable and enhances heat transfer.

Effect of inclination angle on bioconvection in porous square cavity containing gyrotactic microorganisms and nanofluid

2021 ◽  
pp. 095440622110556
Author(s):  
Chandra Shekar Balla ◽  
Jamuna Bodduna ◽  
SVHN Krishna Kumari ◽  
Ahmed M. Rashad
Keyword(s):  
Rayleigh Number ◽  
Inclination Angle ◽  
Momentum Equation ◽  
Darcy Law ◽  
Square Cavity ◽  
Gyrotactic Microorganisms ◽  
Number Formula ◽  
Vertical Walls ◽  
Current Article ◽  
Source Sink

The current article investigates the effect of inclination angle on thermo-bioconvection within the porous-square shaped cavity filled with gyrotactic type microorganisms and nanofluid. The Darcy law with Boussinesq estimation is used for the momentum equation in porous media. The transformed governing equations are solved by Galerkin’s method of finite elements. The effect of inclination angle in the square cavity is interpreted by varying the angle from [Formula: see text] to [Formula: see text]. The effect of inclination on different quantities, for instance, Rayleigh number, bioconvective Rayleigh number, Peclet number, Brownian motion, heat source/sink, and ratio of buoyancy, is discussed. Further, the mean quantities of Nusselt number [Formula: see text], Sherwood number [Formula: see text], and density number [Formula: see text] are analyzed at vertical walls. A quantitative outcome of the study is that the maximum values of [Formula: see text], [Formula: see text], and [Formula: see text] are found for the angle [Formula: see text] and [Formula: see text].

POROUS PENETRATIVE CONVECTION WITH A SALT FIELD AND INTERNAL HEAT SOURCE

1992 ◽  
Vol 02 (04) ◽  
pp. 407-421
Author(s):  
LORNA RICHARDSON
Keyword(s):  
Porous Medium ◽  
Temperature Gradient ◽  
Heat Source ◽  
Nonlinear Stability ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Penetrative Convection ◽  
Weighted Energy ◽  
The Stability ◽  
Unconditional Nonlinear Stability

We investigate the stability of convection in a porous medium containing a heat source in which a destabilizing salt field and stabilizing temperature gradient are present. Both conditional and unconditional nonlinear stability thresholds are calculated and we note that RaE(conditional)>RaE(unconditional). The unconditional nonlinear analysis requires the use of a “weighted” energy.

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