scholarly journals Effect of Rotational Modulation on Rayleigh – B´enard Convection in a Couple Stress Liquid

2020 ◽  
Vol 18 (3) ◽  
pp. 1-12
Author(s):  
S Pranesh ◽  
Sangeetha George K
Keyword(s):  
Rayleigh Number ◽  
Couple Stress ◽  
Horizontal Layer ◽  
External Control ◽  
Regular Perturbation ◽  
Onset Of Convection ◽  
Rotational Modulation ◽  
Steady Rotation ◽  
The Stability ◽  
Internal Convection

The Rayleigh-B´enard convection in a couple stress liquid with rotational modulation is studied using the linear analysis based on normal mode technique. The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady rotation, a time-periodic sinusoidal perturbation is applied. The expression for Rayleigh number and correction Rayleigh number are obtained using regular perturbation method. The expression for correction Rayleigh number is obtained as a function of frequency of modulation, Taylor number, Couple Stress parameter and Prandtl number. It is observed that rotational modulation leads to delay in onset of convection. Rotation modulation is an example of external control of internal convection.

scholarly journals Effect of Gravity Modulation on Single Component Convection in a Couple Stress Fluid with Maxwell-Cattaneo Law

2018 ◽  
Vol 7 (4.10) ◽  
pp. 657
Author(s):  
Maria Thomas ◽  
Sangeetha George K
Keyword(s):  
Heat Conduction ◽  
Couple Stress ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Couple Stress Fluid ◽  
Gravity Modulation ◽  
Inertial Effects ◽  
Regular Perturbation ◽  
Onset Of Convection ◽  
Perturbed State

The outset of convection in a thin layer of couple stress fluid is analyzed using the linear stability analysis when the fluid is heated from below. In order to assimilate the inertial effects Maxwell-Cattaneo law is used in lieu of the classical Fourier's heat conduction law. The normal mode analysis is used to arrive at the eigenvalues of the perturbed state and a regular perturbation method to find the analytical solutions. The effect of Cattaneo number, couple stress parameter and Prandtl number is discussed and it is concluded that gravity modulation can delay or advance the onset of convection.  

Stability and Convection in Impulsively Heated Porous Layers

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
M. J. Kohl ◽  
M. Kristoffersen ◽  
F. A. Kulacki
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Heated Surface ◽  
Critical Rayleigh Number ◽  
Axisymmetric Flow ◽  
Temperature Fluctuations ◽  
Lower Surface ◽  
Onset Of Convection ◽  
Upward Moving ◽  
The Stability

Experiments are reported on initial instability, turbulence, and overall heat transfer in a porous medium heated from below. The porous medium comprises either water or a water-glycerin solution and randomly stacked glass spheres in an insulated cylinder of height:diameter ratio of 1.9. Heating is with a constant flux lower surface and a constant temperature upper surface, and the stability criterion is determined for a step heat input. The critical Rayleigh number for the onset of convection is obtained in terms of a length scale normalized to the thermal penetration depth as Rac=83/(1.08η−0.08η2) for 0.02<η<0.18. Steady convection in terms of the Nusselt and Rayleigh numbers is Nu=0.047Ra0.91Pr0.11(μ/μ0)0.72 for 100<Ra<5000. Time-averaged temperatures suggest the existence of a unicellular axisymmetric flow dominated by upflow over the central region of the heated surface. When turbulence is present, the magnitude and frequency of temperature fluctuations increase weakly with increasing Rayleigh number. Analysis of temperature fluctuations in the fluid provides an estimate of the speed of the upward moving thermals, which decreases with distance from the heated surface.

The instability of a layer of fluid heated below and subject to Coriolis forces

1953 ◽  
Vol 217 (1130) ◽  
pp. 306-327 ◽  
Keyword(s):  
Coriolis Force ◽  
Thermal Instability ◽  
Horizontal Layer ◽  
Onset Of Convection ◽  
Dimensional Parameter ◽  
Coriolis Forces ◽  
Effective Gravity ◽  
The Stability ◽  
Bounding Surfaces ◽  
Rayleigh Numbers

This paper is devoted to examining the stability of a horizontal layer of fluid heated below, subject to an effective gravity ( g ) acting (approximately) in the direction of the vertical and the Coriolis force resulting from a rotation of angular velocity Ω about a direction making an angle ϑ with the vertical. It is shown that the effect of the Coriolis force is to inhibit the onset of convection, the extent of the inhibition depending on the value of the non-dimensional parameter T = 4 d 4 Ω 2 cos 2 ϑ/ v 2 , where d denotes the depth of the layer and v is the kinematic viscosity. Tables of the critical Rayleigh numbers ( R c ) for the onset of convection are provided for the three cases ( a ) both bounding surfaces free, ( b ) both bounding surfaces rigid and ( c ) one bounding surface free and the other rigid. In all three cases R c →constant x T 2/3 as T →∞ ; the corresponding dependence of the critical temperature gradient (— β c ) for the onset of convection, on v and d , is gαβ c = constant x ĸ (Ω 4 cos 4 ϑ/ d 4 v ) 1/2 ( ĸ is the coefficient of thermometric conductivity and α is the coefficient of volume expansion). The question whether thermal instability can set in as oscillations of increasing amplitude (i.e. as 'overstability’) is examined for case ( a ), and it is shown that if ĸ/v <1.478, this possibility does not arise; but if ĸ/v >1.478, over-stability is the first type of instability to arise for all T greater than a certain determinate value. It further appears that these latter possibilities should be considered in meteorological and astrophysical applications of the theory.

The Onset of Convection in a Layer of Cellular Porous Material: Effect of Temperature-Dependent Conductivity Arising From Radiative Transfer

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
D. A. Nield ◽  
A. V. Kuznetsov
Keyword(s):  
Rayleigh Number ◽  
Porous Material ◽  
Effective Conductivity ◽  
Critical Rayleigh Number ◽  
Horizontal Layer ◽  
Wave Number ◽  
Effect Of Temperature ◽  
Onset Of Convection ◽  
Cellular Foams ◽  
Variation Parameter

The onset of convection in a horizontal layer of a cellular porous material heated from below is investigated. The problem is formulated as a combined conductive-convective-radiative problem in which radiative heat transfer is treated as a diffusion process. The problem is relevant to cellular foams formed from plastics, ceramics, and metals. It is shown that the variation of conductivity with temperature above that of the cold boundary leads to an increase in the critical Rayleigh number (based on the conductivity of the fluid at that boundary temperature) and an increase in the critical wave number. On the other hand, the critical Rayleigh number based on the conductivity at the mean temperature decreases with increase in the thermal variation parameter if the radiative contribution to the effective conductivity is sufficiently large compared with the nonradiative component.

scholarly journals Rayleigh-Bénard convection in an elastico-viscous Walters’ (model B’) nanofluid layer

2015 ◽  
Vol 63 (1) ◽  
pp. 235-244 ◽  
Author(s):  
G.C. Rana ◽  
R. Chand
Keyword(s):  
Fluid Model ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Lewis Number ◽  
Horizontal Layer ◽  
Linear Stability Theory ◽  
Mode Analysis ◽  
Physical Parameters ◽  
Onset Of Convection ◽  
The Stability

Abstract In this study, the onset of convection in an elastico-viscous Walters’ (model B’) nanofluid horizontal layer heated from below is considered. The Walters’ (model B’) fluid model is employed to describe the rheological behavior of the nanofluid. By applying the linear stability theory and a normal mode analysis method, the dispersion relation has been derived. For the case of stationary convection, it is observed that the Walters’ (model B’) elastico-viscous nanofluid behaves like an ordinary Newtonian nanofluid. The effects of the various physical parameters of the system, namely, the concentration Rayleigh number, Prandtl number, capacity ratio, Lewis number and kinematics visco-elasticity coefficient on the stability of the system has been numerically investigated. In addition, sufficient conditions for the non-existence of oscillatory convection are also derived.

The thermohaline Rayleigh-Jeffreys problem

1967 ◽  
Vol 29 (3) ◽  
pp. 545-558 ◽  
Author(s):  
D. A. Nield
Keyword(s):  
Rayleigh Number ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Stability Boundary ◽  
Boundary Curve ◽  
Solute Concentration ◽  
Horizontal Layer ◽  
Wave Number ◽  
Convection Cell ◽  
Onset Of Convection

The onset of convection induced by thermal and solute concentration gradients, in a horizontal layer of a viscous fluid, is studied by means of linear stability analysis. A Fourier series method is used to obtain the eigenvalue equation, which involves a thermal Rayleigh numberRand an analogous solute Rayleigh numberS, for a general set of boundary conditions. Numerical solutions are obtained for selected cases. Both oscillatory and monotonic instability are considered, but only the latter is treated in detail. The former can occur when a strongly stabilizing solvent gradient is opposed by a destablizing thermal gradient. When the same boundary equations are required to be satisfied by the temperature and concentration perturbations, the monotonic stability boundary curve in the (R, S)-plane is a straight line. Otherwise this curve is concave towards the origin. For certain combinations of boundary conditions the critical value ofRdoes not depend onS(for some range ofS) or vice versa. This situation pertains when the critical horizontal wave-number is zero.A general discussion of the possibility and significance of convection at ‘zero’ wave-number (single convection cell) is presented in an appendix.

scholarly journals Thermosolutal Natural Convection in Partially Porous Domains

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Dominique Gobin ◽  
Benoît Goyeau
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Heat And Mass Transfer ◽  
Fluid Layer ◽  
Horizontal Layer ◽  
Clear Fluid ◽  
Onset Of Convection ◽  
The Stability ◽  
Double Diffusive

In many industrial processes or natural phenomena, coupled heat and mass transfer and fluid flow take place in configurations combining a clear fluid and a porous medium. Since the pioneering work by Beavers and Joseph (1967), the modeling of such systems has been a controversial issue, essentially due to the description of the interface between the fluid and the porous domains. The validity of the so-called one-domain approach—more intuitive and numerically simpler to implement—compared to a two-domain description where the interface is explicitly accounted for, is now clearly assessed. This paper reports recent developments and the current state of the art on this topic, concerning the numerical simulation of such flows as well as the stability studies. The continuity of the conservation equations between a fluid and a porous medium are examined and the conditions for a correct handling of the discontinuity of the macroscopic properties are analyzed. A particular class of problems dealing with thermal and double diffusive natural convection mechanisms in partially porous enclosures is presented, and it is shown that this configuration exhibits specific features in terms of the heat and mass transfer characteristics, depending on the properties of the porous domain. Concerning the stability analysis in a horizontal layer where a fluid layer lies on top of a porous medium, it is shown that the onset of convection is strongly influenced by the presence of the porous medium. The case of double diffusive convection is presented in detail.

On the Effect of Mechanical and Thermal Anisotropy on the Stability of Gravity Driven Convection in Rotating Porous Media

2005 ◽  
Author(s):  
Saneshan Govender ◽  
Peter Vadasz
Keyword(s):  
Rayleigh Number ◽  
Critical Rayleigh Number ◽  
Equation Model ◽  
Linear Stability Theory ◽  
Mechanical Anisotropy ◽  
Onset Of Convection ◽  
Thermal Anisotropy ◽  
Gravity Driven ◽  
The Stability ◽  
Rayleigh Benard

We investigate Rayleigh-Benard convection in a porous layer subjected to gravitational and Coriolis body forces, when the fluid and solid phases are not in local thermodynamic equilibrium. The Darcy model (extended to include Coriolis effects and anisotropic permeability) is used to describe the flow whilst the two-equation model is used for the energy equation (for the solid and fluid phases separately). The linear stability theory is used to evaluate the critical Rayleigh number for the onset of convection and the effect of both thermal and mechanical anisotropy on the critical Rayleigh number is discussed.

Finite Amplitude Convection in a Rotating Porous Medium

1987 ◽  
Vol 42 (1) ◽  
pp. 13-20
Author(s):  
B. S. Dandapat
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Interstitial Fluid ◽  
Saturated Porous Medium ◽  
Critical Rayleigh Number ◽  
Vertical Axis ◽  
Horizontal Layer ◽  
Finite Amplitude ◽  
Linear Stability Theory ◽  
Onset Of Convection

The onset of convection in a horizontal layer of a saturated porous medium heated from below and rotating about a vertical axis with uniform angular velocity is investigated. It is shown that when S ∈ σ >1, overstability cannot occur, where ε is the porosity, σ the Prandtl number and S is related to the heat capacities of the solid and the interstitial fluid. It is also shown that for small values of the rotation parameter T1, finite amplitude motion with subcritical values of Rayleigh number R (i.e. R < Re, where Re is the critical Rayleigh number according to linear stability theory) is possible. For large values of T1, overstability is the preferred mode.

Classical cellular convection with a spatial heat source

1968 ◽  
Vol 32 (2) ◽  
pp. 399-411 ◽  
Author(s):  
Pauline M. Watson
Keyword(s):  
Rayleigh Number ◽  
Aspect Ratio ◽  
Heat Source ◽  
Viscous Fluid ◽  
Heat Loss ◽  
Critical Rayleigh Number ◽  
Horizontal Layer ◽  
Stable Layer ◽  
Constant Rate ◽  
The Stability

This paper considers the problem of the stability of an infinite horizontal layer of a viscous fluid which loses heat throughout its volume at a constant rate. The variation of the critical Rayleigh number, Rt, and the cell aspect ratio, a, with the rate of heat loss, is calculated with two sets of boundary conditions corresponding to two free and two rigid boundaries. In both cases we find that, as the rate of heat loss increases, Rt decreases, showing that the layer becomes more unstable, and a increases, showing that the cells become narrower. We also consider the possibility that a double layer of cells is formed for large values of the rate of heat loss, by the stable layer at the top, and find that this does not occur while the temperature of the upper surface of the layer is less than that of the lower.

Sign in / Sign up

Export Citation Format

Share Document