Convective instabilities in a viscoelastic-fluid-saturated porous medium with throughflow

Shivakumara, I. S.; Sureshkumar, S.

doi:10.1088/1742-2132/4/1/012

Cited by 40 publications

(31 citation statements)

References 23 publications

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“…This reduces the effective thickness of the stratified layer, while the characteristic temperature difference across the layer remains constant. Thus, one would expect that the critical Rayleigh number increases with the increase in P e. Shivakumara and Sureshkumar [40] pointed out that the reason for the opposite effect may be due to the distortion of steady-state basic temperature distribution from linear to nonlinear because of throughflow. A measure of throughflow is given by the basic state temperature, and this can be interpreted as a rate of energy transfer into the disturbance by interaction of the perturbation convective motion with the basic temperature gradient.…”

Section: Resultsmentioning

confidence: 99%

“…They found that irrespective of the nature of boundaries, a small amount of throughflow in either of its direction destabilizes the system, a result which is in contrast to the single component system. Shivakumara and Sureshkumar [40] used the linear study to investigate the convective instability in a horizontal porous medium with viscoelastic fluid of Oldroyd-B type in the presence of vertical throughflow. They found that the effect of throughflow is to suppress the oscillatory convection independent of its direction when the velocity boundary conditions are of 1288 P. KIRAN the same type.…”

Section: Introductionmentioning

confidence: 99%

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Throughflow and g-jitter effects on binary fluid saturated porous medium

Kiran

2015

Appl. Math. Mech.-Engl. Ed.

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A non-autonomous complex Ginzburg-Landau equation (CGLE) for the finite amplitude of convection is derived, and a method is presented here to determine the amplitude of this convection with a weakly nonlinear thermal instability for an oscillatory mode under throughflow and gravity modulation. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature, and solutal fields are treated by a perturbation expansion in powers of the amplitude of the applied gravity field. Throughflow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The Nusselt and Sherwood numbers are obtained numerically to present the results of heat and mass transfer. It is found that throughflow and gravity modulation can be used alternately to heat and mass transfer. Further, oscillatory flow, rather than stationary flow, enhances heat and mass transfer.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Throughflow and g-jitter effects on binary fluid saturated porous medium

Kiran

2015

Appl. Math. Mech.-Engl. Ed.

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“…Shivakumara et al (2006) and Malashetty et al (2006a,b) have discussed, respectively, the effect of local thermal nonequilibrium on the onset of convection in a sparsely and densely packed Oldroyd-B viscoelastic fluid-saturated porous medium. Shivakumara and Sureshkumar (2007) have used linear stability theory to investigate convective instability in a horizontal porous layer saturated with viscoelastic fluid of Oldroyd-B type in the presence of vertical throughflow, and these authors have also extended their previous work to include the effect of quadratic drag in the presence of an additional diffusing component (Shivakumara and Sureshkumar 2008). Thermal stability of a viscoelastic Walters B liquid saturating a porous anisotropic horizontal layer in the presence of a chemical reaction has been discussed by Postelnicu (2007).…”

Section: Introductionmentioning

confidence: 99%

Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

et al. 2010

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The linear stability of Walters B viscoelastic fluid-saturated horizontal porous layer is examined theoretically when the walls of the porous layer are subjected to time-periodic temperature modulation. Three types of boundary temperature modulations are considered namely, symmetric, asymmetric, and only the lower wall temperature is modulated while the upper wall is held at constant temperature. A regular perturbation method based on small amplitude of applied temperature field is used to compute the critical values of Rayleigh number and the corresponding wave number. The shift in critical Rayleigh number is calculated as a function of modulation frequency, viscoelastic parameter, and Prandtl number. The effect of all three types of modulations is found to be destabilizing as compared to the unmodulated system. This result is in contrast to the system with other types of fluids. Besides, the influence of physical parameters on the control of convective instability of the system is discussed.

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“…The literature on the study of the effect of vertical throughflow on convective instability in a porous medium is much less widespread, although recent studies include Shivakumara and Suma [12], Shivakumara and Khalili [13], Shivakumara and Sureshkumar [14], Nield and Kuznetsov [15], Hill et al [16] and Harfash and Hill [17].…”

Section: Introductionmentioning

confidence: 99%

Magnetic field and throughflow effects on double-diffusive convection in internally heated anisotropic porous media

Harfash

Alshara

2015

Korean J. Chem. Eng.

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A model for double-diffusive convection in an anisotropic porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source and subjected to a vertical magnetic field and variable gravity effect. The validity of both the linear instability and global nonlinear stability thresholds are tested using three dimensional simulation. Our results show that the linear theory produce a good prediction on the onset of instability in the steady state throughflow. It is known that as R c increases the onset of convection is more likely to be via oscillatory convection as opposed to steady convection, and the three dimensional simulation results show that as R c increases, the actual threshold moving toward the nonlinear stability threshold and the behaviour of the perturbation of the solutions becomes more oscillated.

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Convective instabilities in a viscoelastic-fluid-saturated porous medium with throughflow

Cited by 40 publications

References 23 publications

Throughflow and g-jitter effects on binary fluid saturated porous medium

Throughflow and g-jitter effects on binary fluid saturated porous medium

Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

Magnetic field and throughflow effects on double-diffusive convection in internally heated anisotropic porous media

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