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

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Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Rocznik
Strony
785--803
Opis fizyczny
Bibliogr. 45 poz., wykr.
Twórcy
  • Department of Applied Mathematics, School of Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India
autor
  • Department of Applied Mathematics, School of Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India
autor
  • Department of Applied Mathematics, School of Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India
autor
  • Department of Applied Mathematics, School of Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India
autor
  • Department of Applied Mathematics, Rayalaseema University, Kurnool, Andhra Pradesh-518007, India
Bibliografia
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  • [26] Bhadauria B.S. and Kiran P. (2014): Weak non-linear oscillatory convection in a viscoelastic fluid saturated porous medium under gravity modulation. – Transp. Porous Med., vol.104, pp.451-467.
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  • [36] Bhadauria B.S., Hashim I. and Siddheshwar P.G. (2013): Effect of internal-heating on weakly non-linear stability analysis of Rayleigh-Benard convection under G-jitter. – Int. J. Nonlinear Mech., vol.54, pp.35-42.
  • [37] Bhadauria B.S, Hashim I. and Siddheshwar P.G. (2013): Study of heat transport in a porous medium under G-jitter and internal heating effects. – Transp. Porous Med., vol.96, pp.21-37.
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  • [39] Srivastava A., Bhadauria B.S., Siddheshwar P.G. and Hashim I. (2013): Heat transport in an anisotropic porous medium saturated with variable viscosity liquid under g-jitter and internal heating effects. – Transp. Porous Med., vol.99, pp.359-376.
  • [40] Altawallbeh A.A., Bhadauria B.S. and Hashim I. (2013): Linear and nonlinear double-diffusive convection in a saturated anisotropic porous layer with Soret effect and internal heat source. – Int. J. Heat Mass Transf., vol.59, pp.103-111.
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  • [45] Venezian G. (1969) Effect of modulation on the onset of thermal convection. – J. Fluid Mech., vol.35, pp.243-254.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-75b0ce0e-5010-479f-b384-4e9f12ca86c8
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