Chaotic convection in an Oldroyd viscoelastic fluid in saturated porous medium with feedback control

2020 ◽  
Vol 30 (7) ◽  
pp. 073109 ◽  
Author(s):  
M. N. Mahmud ◽  
Z. Siri ◽  
J. A. Vélez ◽  
L. M. Pérez ◽  
D. Laroze
Keyword(s):  
Porous Medium ◽  
Feedback Control ◽  
Viscoelastic Fluid ◽  
Saturated Porous Medium ◽  
Chaotic Convection

scholarly journals Chaotic Convection in a Viscoelastic Fluid Saturated Porous Medium with a Heat Source

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
B. S. Bhadauria
Keyword(s):  
Heat Source ◽  
Viscoelastic Fluid ◽  
Saturated Porous Medium ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Momentum Equation ◽  
Darcy Law ◽  
Chaotic Convection ◽  
Saturated Porous Layer ◽  
Truncated Fourier Series

Chaotic convection in a viscoelastic fluid saturated porous layer, heated from below, is studied by using Oldroyd’s type constituting relation and in the presence of an internal heat source. A modified Darcy law is used in the momentum equation, and a heat source term has been considered in energy equation. An autonomous system of fourth-order differential equations has been deduced by using a truncated Fourier series. Effect of internal heat generation on chaotic convection has been investigated. The asymptotic behavior can be stationary, periodic, or chaotic, depending upon the flow parameters. Construction of four-scroll, or “two-butterfly,” and chaotic attractor has been examined.

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.

scholarly journals Weakly Nonlinear Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium with Throughflow and Temperature Modulation

2018 ◽  
Vol 23 (3) ◽  
pp. 635-653 ◽  
Author(s):  
P. Kiran ◽  
Y. Narasimhulu ◽  
S.H. Manjula
Keyword(s):  
Porous Medium ◽  
Heat Transport ◽  
Viscoelastic Fluid ◽  
Saturated Porous Medium ◽  
Landau Equation ◽  
Oscillatory Mode ◽  
Stationary Mode ◽  
Temperature Modulation ◽  
Through Flow ◽  
Fluid Saturated Porous Medium

Abstract The effect of vertical throughfow and temperature modulation on a viscoelastic fluid saturated porous medium has been investigated. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small and the disturbances are expanded in terms of power series of amplitude of convection. A weak nonlinear stability analysis has been performed for the oscillatory mode of convection, and heat transport in terms of the Nusselt number, which is governed by the non autonomous complex Ginzburg- Landau equation, is calculated. The effect of vertical through flow is found to stabilize the system irrespective of the direction of through flow in the case of permeable boundary conditions. The time relaxation has a destabilizing effect, while the time retardation parameter has a stabilizing effect on the system. The effects of amplitude and frequency of modulation on heat transport have been analyzed and depicted graphically. The study shows that the heat transport can be controlled effectively by a mechanism that is external to the system. Further, it is also found that heat transfer is more in oscillatory mode of convection rather than in stationary mode of convection.

scholarly journals Oscillatory motion of an electrically conducting viscoelastic fluid over a stretching sheet in a saturated porous medium with suction/blowing

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
K. Rajagopal ◽  
P. H. Veena ◽  
V. K. Pravin
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Porous Media ◽  
Skin Friction ◽  
Viscoelastic Fluid ◽  
Stretching Sheet ◽  
Saturated Porous Medium ◽  
Oscillatory Motion ◽  
Power Series Method ◽  
Viscoelastic Parameter

The effect of an oscillatory motion of a viscoelastic fluid over an infinite stretching sheet through porous media in the presence of magnetic field with applied suction has been studied. The surface absorbs the fluid in a porous medium in the presence of magnetic field and the velocity oscillates depending on the stretching rate(b). Analytical expressions for the velocity and the coefficient of skin friction have been studied, first by the perturbation method and then by power series method. The effect of viscoelastic parameterk1, porous parameterk2, magnetic parameter Mn, and the vertical distancexin the presence of suction/blowing on the velocity and the flow characteristics are discussed. The velocity of the viscoelastic fluid is found to decrease in the presence of magnetic field and porous media, as compared to the study of viscous fluid. It is also found that the effect of unsteadiness in the wall velocity and skin friction are found to be appreciable in the presence of suction/blowing parameter.

Feedback Control of Chaos in Porous Medium under G-jitter Effects

2018 ◽  
Vol 10 (1) ◽  
Author(s):  
Ajay Singh ◽  
B.S. Bhadauria ◽  
Prashant Kumar Gangwar
Keyword(s):  
Porous Medium ◽  
Feedback Control ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Expansion Method ◽  
Gravity Modulation ◽  
Control Of Chaos ◽  
Chaotic Convection ◽  
Chaotic Nature ◽  
Energy Equations

In the present paper, we studied feedback control of chaotic convection in porous medium under gravity modulation. A non-autonomous system having three differential equations is obtained by employing the truncated Galerkin expansion method in to the modulated momentum and energy equations, called as Lorenz system in the literature. The parameter R demonstrates either periodic or chaotic behavior of the system as increasing R. It is also found that the influence of amplitude of modulation is to advance the chaotic nature in the system whereas the feedback control and frequency of modulation parameters have tendency to delay the chaotic behavior.

Feedback Control of Chaos in Porous Medium under G-jitter Effects

2018 ◽  
Vol 10 (01) ◽  
pp. 25-32
Author(s):  
Ajay Singh ◽  
B. S. Bhadauria ◽  
Prashant Kumar Gangwar
Keyword(s):  
Porous Medium ◽  
Feedback Control ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Expansion Method ◽  
Gravity Modulation ◽  
Control Of Chaos ◽  
Chaotic Convection ◽  
Chaotic Nature ◽  
Energy Equations

In the present paper, we studied feedback control of chaotic convection in porous medium under gravity modulation. A non-autonomous system having three differential equations is obtained by employing the truncated Galerkin expansion method in to the modulated momentum and energy equations, called as Lorenz system in the literature. The parameter R demonstrates either periodic or chaotic behavior of the system as increasing R. It is also found that the influence of amplitude of modulation is to advance the chaotic nature in the system whereas the feedback control and frequency of modulation parameters have tendency to delay the chaotic behavior.

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