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1

Chaotic convection of viscoelastic fluid in porous medium under G-jitter

Bhadauria B. S., Singh A., Singh M. K.

International Journal of Applied Mechanics and Engineering

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2019

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Vol. 24, no. 1

37--51

EN

The present article aims at investigating the effect of gravity modulation on chaotic convection of a viscoelastic fluid in porous media. For this, the problem is reduced into Lorenz system (non-autonomous) by employing the truncated Galerkin expansion method. The system shows transitions from periodic to chaotic behavior on increasing the scaled Rayleigh number R. The amplitude of modulation advances the chaotic nature in the system while the frequency of modulation has a tendency to delay the chaotic behavior which is in good agreement with the results due to [1]. The behavior of the scaled relaxation and retardation parameter on the system is also studied. The phase portrait and time domain diagrams of the Lorenz system for suitable parameter values have been used to analyze the system.

2

Stability analysis and internal heating effect on oscillatory convection in a viscoelastic fluid saturated porous medium under gravity modulation

Bhadauria B. S., Singh M. K., Singh A., Singh B. K., Kiran P.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 4

785--803

EN

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.

3

Effect of vertical vibrations on the onset of binary convection

Swamy M. S.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 3

899--910

EN

In the present work the linear stability analysis of double diffusive convection in a binary fluid layer is performed. The major intention of this study is to investigate the influence of time-periodic vertical vibrations on the onset threshold. A regular perturbation method is used to compute the critical Rayleigh number and wave number. A closed form expression for the shift in the critical Rayleigh number is calculated as a function of frequency of modulation, the solute Rayleigh number, Lewis number, and Prandtl number. These parameters are found to have a significant influence on the onset criterion; therefore the effective control of convection is achieved by proper tuning of these parameters. Vertical vibrations are found to enhance the stability of a binary fluid layer heated and salted from below. The results of this study are useful in the areas of crystal growth in micro-gravity conditions and also in material processing industries where vertical vibrations are involved.

4

Three - dimensional MHD free - convection flow past an infinite vertical porous plate with gravity modulation

Saini B. S., Rajvanshi S. C.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 4

1093-1107

EN

In the present study, the effect of a fluctuating gravitational field on a three - dimensional MHD free - convection flow past a vertical porous plate with transversally varying suction velocity is investigated. A constant heat flux is prescribed on the plate. It is assumed that the gravity modulation is given by […]. The transformed equations are solved by the perturbation technique. The effect of various physical parameters on the fluid velocity and temperature are computed numerically and discussed through graphs.