Effect of modulation on the onset of thermal convection in a viscoelastic fluid-saturated sparsely packed porous layer

1990 ◽  
Vol 68 (2) ◽  
pp. 214-221 ◽  
Author(s):  
N. Rudraiah ◽  
P. V. Radhadevi ◽  
P. N. Kaloni
Keyword(s):  
Porous Layer ◽  
Viscoelastic Fluid ◽  
Phase Modulation ◽  
Applied Field ◽  
Temperature Modulation ◽  
Elastic Parameters ◽  
Oldroyd Model ◽  
Maximum Range ◽  
Periodic Temperature ◽  
The Stability

The stability of a Boussinesq viscoelastic fluid-saturated horizontal porous layer, when the boundaries of the layer are subjected to periodic temperature modulation, is analyzed. The Darcy–Forchheimer–Brinkman–Oldroyd model is employed and only infinitesimal disturbances are considered. Three cases of the oscillating temperature field were examined: (a) symmetric, so that the wall temperatures are modulated in phase, (b) asymmetric, corresponding to out-of-phase modulation, and (c) only the bottom wall is modulated. Perturbation solution in powers of the amplitude of the applied field is obtained. The effect of the frequency of modulation on the stability is clearly shown. Possibilities of the occurrence of subcritical instabilities are also discussed. It is shown that an increase in the elastic parameters A1 and A2 has a stabilizing influence. An increase in the Prandtl number destabilizes the system for small values of the frequency but stabilizes the systems for large values of the frequency. It is shown that the system is most stable when the boundary temperatures are modulated out of phase. The maximum range of ε when subcritical instabilities exist is also determined.

Stability of a Horizontal Porous Layer with Timewise Periodic Boundary Conditions

1979 ◽  
Vol 101 (2) ◽  
pp. 244-248 ◽  
Author(s):  
B. Chhuon ◽  
J. P. Caltagirone
Keyword(s):  
Porous Layer ◽  
Periodic Boundary ◽  
Lower Boundary ◽  
Periodic Boundary Conditions ◽  
Temperature Oscillation ◽  
Linear Stability Theory ◽  
Onset Of Convection ◽  
Thermal Signal ◽  
Periodic Temperature ◽  
The Stability

The stability of a horizontal porous layer bounded by two impermeable planes is investigated. A time dependent periodic temperature profile is imposed on the lower boundary while the upper plane is kept at constant temperature. Starting from the preconvective temperature distribution, and using the linear stability theory, a criterion for the onset of convection is defined as a function of the perturbation wavenumber and of the amplitude and frequency of the temperature oscillation. Experimental work with a setup allowing both the amplitude and the frequency of the thermal signal to vary is done. Finally, the equations are also solved numerically and the results are compared to the previous ones. A synthesis of all results is included.

Effect of Modulation on the Onset of Convection in a Sparsely Packed Porous Layer

1990 ◽  
Vol 112 (3) ◽  
pp. 685-689 ◽  
Author(s):  
N. Rudraiah ◽  
M. S. Malashetty
Keyword(s):  
Porous Layer ◽  
Applied Field ◽  
Critical Rayleigh Number ◽  
Time Dependent ◽  
Brinkman Model ◽  
Onset Of Convection ◽  
Flow Limit ◽  
The Stability ◽  
Boussinesq Fluid ◽  
Degenerate Cases

The stability of a Boussinesq fluid-saturated horizontal porous layer heated from below is examined when the applied temperature gradient is the sum of a steady component and a time-dependent sinusoidal component. The Brinkman model is employed and only infinitesimal disturbances are considered. A perturbation solution as a function of the applied field is obtained. The critical Rayleigh number is obtained for several cases depending on the frequency of oscillations and it is found that it is possible to advance or delay the onset of convection by thermal modulation of the wall temperature. The Darcy limit and viscous flow limit are obtained as degenerate cases.

scholarly journals Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis of Rotation

1998 ◽  
Vol 4 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Peter Vadasz ◽  
Saneshan Govender
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Temperature Fields ◽  
Wave Number ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Wide Range ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
The Stability

The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.

scholarly journals Thermosolutal Instability in Compressible Viscoelastic Dusty Fluid through Porous Medium

2013 ◽  
Vol 18 (1) ◽  
pp. 99-112 ◽  
Author(s):  
P. Kumar ◽  
H. Mohan
Keyword(s):  
Porous Medium ◽  
Viscoelastic Fluid ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Linearized Stability ◽  
Medium Permeability ◽  
The Stability ◽  
Solute Gradient

Thermosolutal instability in a compressible Walters B’ viscoelastic fluid with suspended particles through a porous medium is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the Walters B’ viscoelastic fluid behaves like a Newtonian fluid and it is found that suspended particles and medium permeability have a destabilizing effect whereas the stable solute gradient and compressibility have a stabilizing effect on the system. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient and viscoelasticity are found to introduce oscillatory modes in the system which are non-existent in their absence.

scholarly journals Effect of Vadasz Number on Magnetoconvection in a Darcy Porous Layer with Concentration Based Internal Heating

2019 ◽  
pp. 1-13
Author(s):  
C. Israel-Cookey ◽  
L. Ebiwareme ◽  
E. Amos
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Internal Heat ◽  
Lewis Number ◽  
Mode Analysis ◽  
Internal Heating ◽  
Vadasz Number ◽  
The Stability ◽  
Solutal Rayleigh Number

In this research article, the effect of Vadasz number on magnetoconvection in a Darcy Porous Layer with concentration based internal heating is studied. The flow is governed by the Oberbeck-Boussineq model for Newtonian fluid. The stability analysis method based on the perturbation of infinitesimal amplitude is carried out using the normal mode analysis. The onset criterion for both the stationary and oscillatory convection on the stability of system is obtained. The analysis examines the effects of pertinent parameters on the stability of the system: magnetic field parameter, solutal Rayleigh number, Lewis number and Vadasz number. The result show that, internal heat parameter,  and Lewis number, , hastens the onset of instability in the system, whereas magnetic field, , Vadasz number,  and solutal Rayleigh number,  delay the onset of instability.

The Stability of a Two-Layer Inviscid Flow Between an Elastic Layer and a Rigid Boundary

1999 ◽  
Vol 66 (1) ◽  
pp. 197-203 ◽  
Author(s):  
P. J. Schall ◽  
J. P. McHugh
Keyword(s):  
Elastic Layer ◽  
Inviscid Flow ◽  
Elastic Parameters ◽  
Rigid Boundary ◽  
Two Fluids ◽  
Coating Flow ◽  
Fluid Layers ◽  
Mode 2 ◽  
Layer Flow ◽  
The Stability

The linear stability of two-layer flow over an infinite elastic substraw is considered. The problem is motivated by coating flow in a printing press. The flow is assumed to be inviscid and irrotational. Surface tension between the fluid layers is included, but gravity is neglected. The results show two unstable modes: one mode associated with the interface between the elastic layer and the fluid (mode 1), and the other concentrated on the interface between the two fluids (mode 2). The behavior of the unstable modes is examined while varying the elastic parameters, and it is found that mode 1 can be made stable, but mode 2 remains unstable at small wavenumber, similar to the classic Kelvin—Helmholtz mode.

scholarly journals Effect of Rotational Speed Modulation on the Weakly Nonlinear Heat Transfer in Walter-B Viscoelastic Fluid in the Highly Permeable Porous Medium

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1448
Author(s):  
Anand Kumar ◽  
Vinod K. Gupta ◽  
Neetu Meena ◽  
Ishak Hashim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Prandtl Number ◽  
Heat Transport ◽  
Viscoelastic Fluid ◽  
Rotational Speed ◽  
Weakly Nonlinear ◽  
Speed Modulation ◽  
The Stability ◽  
The Impact

In this article, a study on the stability of Walter-B viscoelastic fluid in the highly permeable porous medium under the rotational speed modulation is presented. The impact of rotational modulation on heat transport is performed through a weakly nonlinear analysis. A perturbation procedure based on the small amplitude of the perturbing parameter is used to study the combined effect of rotation and permeability on the stability through a porous medium. Rayleigh–Bénard convection with the Coriolis expression has been examined to explain the impact of rotation on the convective flow. The graphical result of different parameters like modified Prandtl number, Darcy number, Rayleigh number, and Taylor number on heat transfer have discussed. Furthermore, it is found that the modified Prandtl number decelerates the heat transport which may be due to the combined effect of elastic parameter and Taylor number.

Overstability of a Viscoelastic Fluid Layer Oscillating in a Vertical Periodic Motion and Heated From Below

1979 ◽  
Vol 46 (2) ◽  
pp. 454-456
Author(s):  
S. O. Onyegegbu
Keyword(s):  
Natural Frequency ◽  
Viscoelastic Fluid ◽  
Periodic Motion ◽  
Oscillation Frequency ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
The Stability ◽  
Oscillation Frequencies

This Note examines the effect of vertical periodic motion on the stability characteristics of a viscoelastic fluid layer in a classical Benard geometry. Numerical solutions show that a resonant type behavior which enhances stability occurs at oscillation frequencies near the convective natural frequency of the viscoelastic fluid, while the effect of the periodic motion vanishes as the oscillation frequency gets very large.

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