Steady finite-amplitude Rayleigh–Bénard convection of ethylene glycol–copper nanoliquid in a high-porosity medium made of 30% glass fiber-reinforced polycarbonate

2020 ◽  
Author(s):  
P. G. Siddheshwar ◽  
T. N. Sakshath
Keyword(s):  
Ethylene Glycol ◽  
Glass Fiber ◽  
Finite Amplitude ◽  
High Porosity ◽  
Fiber Reinforced ◽  
Bénard Convection ◽  
Glass Fiber Reinforced ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The effect of distant side-walls on the evolution and stability of finite-amplitude Rayleigh-Bénard convection

1981 ◽  
Vol 378 (1775) ◽  
pp. 539-566 ◽  
Keyword(s):  
Rayleigh Number ◽  
Prandtl Number ◽  
Finite Amplitude ◽  
Two Dimensional ◽  
Bénard Convection ◽  
Benard Convection ◽  
Side Walls ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

A recent study by Cross et al . (1980) has described a class of finite-amplitude phase-winding solutions of the problem of two-dimensional Rayleigh-Bénard convection in a shallow fluid layer of aspect ratio 2 L (≫ 1) confined laterally by rigid side-walls. These solutions arise at Rayleigh numbers R = R 0 + O ( L -1 ) where R 0 is the critical Rayleigh number for the corresponding infinite layer. Nonlinear solutions of constant phase exist for Rayleigh numbers R = R 0 + O ( L -2 ) but of these only the two that bifurcate at the lowest value of R are stable to two-dimensional linearized disturbances in this range (Daniels 1978). In the present paper one set of the class of phase-winding solutions is found to be stable to two-dimensional disturbances. For certain values of the Prandtl number of the fluid and for stress-free horizontal boundaries the results predict that to preserve stability there must be a continual readjustment of the roll pattern as the Rayleigh number is raised, with a corresponding increase in wavelength proportional to R - R 0 . These solutions also exhibit hysteresis as the Rayleigh number is raised and lowered. For other values of the Prandtl number the number of rolls remains unchanged as the Rayleigh number is raised, and the wavelength remains close to its critical value. It is proposed that the complete evolution of the flow pattern from a static state must take place on a number of different time scales of which t = O(( R - R 0 ) -1 ) and t = O(( R - R 0 ) -2 ) are the most significant. When t = O(( R - R 0 ) -1 ) the amplitude of convection rises from zero to its steady-state value, but the final lateral positioning of the rolls is only completed on the much longer time scale t = O(( R - R 0 ) -2 ).

scholarly journals Rayleigh-Benard convection in a viscoelastic fluid-filled high-porosity medium with nonuniform basic temperature gradient

2001 ◽  
Vol 25 (9) ◽  
pp. 609-619 ◽  
Author(s):  
Pradeep G. Siddheshwar ◽  
C. V. Sri Krishna
Keyword(s):  
Stability Analysis ◽  
Temperature Gradient ◽  
Viscoelastic Fluid ◽  
High Porosity ◽  
Rigid Boundary ◽  
Viscoelastic Problem ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The qualitative effect of nonuniform temperature gradient on the linear stability analysis of the Rayleigh-Benard convection problem in a Boussinesquian, viscoelastic fluid-filled, high-porosity medium is studied numerically using the single-term Galerkin technique. The eigenvalue is obtained for free-free, free-rigid, and rigid-rigid boundary combinations with isothermal temperature conditions. Thermodynamics and also the present stability analysis dictates the strain retardation time to be less than the stress relaxation time for convection to set in as oscillatory motions in a high-porosity medium. Furthermore, the analysis predicts the critical eigenvalue for the viscoelastic problem to be less than that of the corresponding Newtonian fluid problem.

The propagation of dislocations in Rayleigh-Bénard rolls and bimodal flow

1976 ◽  
Vol 75 (4) ◽  
pp. 715-720 ◽  
Author(s):  
J. A. Whitehead
Keyword(s):  
Prandtl Number ◽  
Finite Amplitude ◽  
Adjustment Mechanism ◽  
Bénard Convection ◽  
Benard Convection ◽  
Size Adjustment ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

When Rayleigh-Bénard convection is generated under random conditions, the finite amplitude rolls and bimodal flow are observed to possess randomly placed dislocations where the rolls fit together poorly. The dislocations move into the small wavelength convection, and hence provide a size-adjustment mechanism. It is observed that the dimensionless speed of the movement is smaller for larger Prandtl number fluid.

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