Autor:
Bhadauria, Beer Singh ; Singh, Manoj Kumar ; Singh, Ajay ; Singh, Brajesh Kumar ; Kiran, Palle
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Non-linear stability analysis ; complex Ginzburg-Landau equation ; gravity modulation ; internal heating ; bifurcations
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.
Wydawca:
Zielona Góra: Uniwersytet Zielonogórski
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Źródło:
IJAME, volume 21, number 4 (2016)