Thermal instability in a Hele-Shaw cell with nanofluid saturated porous medium under throughflow and gravity modulation

2021 ◽  
Author(s):  
B S Bhadauria ◽  
Awanish Kumar
Keyword(s):  
Porous Medium ◽  
Thermal Instability ◽  
Saturated Porous Medium ◽  
Gravity Modulation ◽  
Hele Shaw Cell

Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell

1969 ◽  
Vol 39 (3) ◽  
pp. 477-495 ◽  
Author(s):  
R. A. Wooding
Keyword(s):  
Porous Medium ◽  
Numerical Solutions ◽  
Hyperbolic Equations ◽  
Saturated Porous Medium ◽  
Mean Amplitude ◽  
Wave Number ◽  
Two Fluids ◽  
Averaged Equations ◽  
The Mean ◽  
Hele Shaw Cell

Waves at an unstable horizontal interface between two fluids moving vertically through a saturated porous medium are observed to grow rapidly to become fingers (i.e. the amplitude greatly exceeds the wavelength). For a diffusing interface, in experiments using a Hele-Shaw cell, the mean amplitude taken over many fingers grows approximately as (time)2, followed by a transition to a growth proportional to time. Correspondingly, the mean wave-number decreases approximately as (time)−½. Because of the rapid increase in amplitude, longitudinal dispersion ultimately becomes negligible relative to wave growth. To represent the observed quantities at large time, the transport equation is suitably weighted and averaged over the horizontal plane. Hyperbolic equations result, and the ascending and descending zones containing the fronts of the fingers are replaced by discontinuities. These averaged equations form an unclosed set, but closure is achieved by assuming a law for the mean wave-number based on similarity. It is found that the mean amplitude is fairly insensitive to changes in wave-number. Numerical solutions of the averaged equations give more detailed information about the growth behaviour, in excellent agreement with the similarity results and with the Hele-Shaw experiments.

Gravity Modulation of Thermal Instability in a Viscoelastic Fluid Saturated Anisotropic Porous Medium

2012 ◽  
Vol 67 (1-2) ◽  
pp. 1-9 ◽  
Author(s):  
Beer S. Bhadauria ◽  
Atul K. Srivastava ◽  
Nirmal C. Sacheti ◽  
Pallath Chandran
Keyword(s):  
Porous Medium ◽  
Gravity Field ◽  
Viscoelastic Fluid ◽  
Thermal Instability ◽  
Time Dependent ◽  
Periodic Part ◽  
Gravity Modulation ◽  
Dependent Part ◽  
Anisotropic Porous Medium ◽  
The Stability

The present paper deals with a thermal instability problem in a viscoelastic fluid saturating an anisotropic porous medium under gravity modulation. To find the gravity modulation effect, the gravity field is considered in two parts: a constant part and an externally imposed time-dependent periodic part. The time-dependent part of the gravity field, which can be realized by shaking the fluid, has been represented by a sinusoidal function. Using Hill’s equation and the Floquet theory, the convective threshold has been obtained. It is found that gravity modulation can significantly affect the stability limits of the system. Further, we find that there is a competition between the synchronous and subharmonic modes of convection at the onset of instability. Effects of various parameters on the onset of instability have also been discussed.

scholarly journals Stability Analysis and Internal Heating Effect on Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium Under Gravity Modulation

2016 ◽  
Vol 21 (4) ◽  
pp. 785-803 ◽  
Author(s):  
B.S. Bhadauria ◽  
M.K. Singh ◽  
A. Singh ◽  
B.K. Singh ◽  
P. Kiran
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Viscoelastic Fluid ◽  
Saturated Porous Medium ◽  
Landau Equation ◽  
Power Series Expansion ◽  
Gravity Modulation ◽  
Internal Heating ◽  
Onset Of Convection ◽  
Fluid Saturated Porous Medium

Abstract In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.

Magnetofluidconvection in a Rotating Porous Layer Under Modulated Temperature on the Boundaries

2006 ◽  
Vol 129 (7) ◽  
pp. 835-843 ◽  
Author(s):  
B. S. Bhadauria
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Prandtl Number ◽  
Thermal Instability ◽  
Fluid Layer ◽  
Saturated Porous Medium ◽  
Critical Rayleigh Number ◽  
Temperature Modulation ◽  
Brinkman Model ◽  
Vertical Magnetic Field

Thermal instability in an electrically conducting fluid saturated porous medium, confined between two horizontal walls, has been investigated in the presence of an applied vertical magnetic field and rotation, using the Brinkman model. The temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent oscillatory part. Only infinitesimal disturbances are considered. The combined effect of permeability, rotation, vertical magnetic field, and temperature modulation has been investigated using Galerkin’s method and Floquet theory. The value of the critical Rayleigh number is calculated as function of amplitude and frequency of modulation, Chandrasekhar number, Taylor number, porous parameter, Prandtl number, and magnetic Prandtl number. It is found that rotation, magnetic field, and porous medium all have a stabilizing influence on the onset of thermal instability. Further, it is also found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation of the walls’ temperature. In addition the results corresponding to the Brinkman model and Darcy model have been compared for neutral instability.

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