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

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Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Rocznik
Strony
37--51
Opis fizyczny
Bibliogr. 31 poz., wykr.
Twórcy
  • Department of Mathematics, School of Physical and Decisions Sciences Babasaheb Bhimrao Ambedkar University, Lucknow-226025, INDIA
autor
  • Department of Humanities and Applied Sciences, School of Management Sciences Gosainganj, Lucknow-226501, INDIA
autor
  • Department of Mathematics and Statistics, Banasthli Vidyapith Rajasthan- 304022, INDIA
Bibliografia
  • [1] Bhadauria B.S. and Kiran P. (2015): Chaotic and oscillatory magneto-convection in a binary viscoelastic fluid under G-jitter. Int. J. Heat Mass Transf., vol.84, pp.610-624.
  • [2] Ingham D.B. and Pop I. (2005): Transport Phenomena in Porous Media. 1st Edn., vol.3, Elsevier, Oxford.
  • [3] Nield D.A. and Bejan A. (2006): Convection in Porous Media. 3rd Edn. New York: Springer.
  • [4] Vafai K. (2000): Handbook of Porous Media. New York: Marcel Dekker.
  • [5] Gresho P.M. and Sani R. (1970): The effects of gravity modulation on the stability of a heated fluid layer. J. Fluid Mech., vol.40, pp.783-806.
  • [6] Govender S. (2005): Weak non-linear analysis of convection in a gravity modulated porous layer. Transp. Porous Media, vol.60, pp.33-42.
  • [7] Malashetty M.S. and Padmavathi V. (1997): Effect of gravity modulation on the onset of convection in a fluid and porous layer. Int. J. Engg. Science, vol.35, pp.829-839.
  • [8] Malashetty M.S. and Swamy M. (2011): Effect of gravity modulation on the onset of thermal convection In rotating fluid and porous layer. Phys Fluids, vol.23, No.6, pp.064108.
  • [9] Rees D.A.S. and Pop I. (2000): The effect of G-jitter on vertical free convection boundary-layer flow in porous media. Int. Comm. Heat Mass Transfer, vol.27, No.3, pp.424.
  • [10] Siddhavaram V.K. and Homsy G.M. (2006): The effects of gravity modulation on fluid mixing Part 1. Harmonic modulation. J. Fluid Mech., vol.562, pp.445-475.
  • [11] Saravanan S. and Sivakumar T. (2011): Thermo vibrational instability in a fluid saturated anisotropic porous medium. ASME, J. Heat Transfer, vol.133, No.5, 051601, doi:10.1115/1.4003013.
  • [12] Green T. (1968) III: Oscillating convection in an elasticoviscous liquid. Phys. Fluids, vol.11, 1410.
  • [13] Vest C.M. and Arpaci V.S. (1969): Overstability of a viscoelastic fluid layer heated from below. J. Fluid Mech., vol.36, pp.613-623.
  • [14] Bhatia P.K. and Steiner J.M. (1972): Convective instability in a rotating viscoelastic fluid layer. ZAMM 52, pp.321-327.
  • [15] Kim M.C., Lee S.B., Kim S. and Chung B.J. (2003): Thermal instability of viscoelastic fluids in porous media. Int. J. Heat Mass Transfer, vol.46, pp.5065-5072.
  • [16] Malashetty M.S. and Kulkarni S. (2009): The convective instability of Maxwell fluid-saturated porous layer using a thermal non-equilibrium model. J. Non Newton Fluid Mech., vol.162, No.1-3, pp.29-37.
  • [17] Wang S. and Tan W. (2011): Stability analysis of Soret-driven double-diffusive convection of Maxwell fluid in a porous medium. Int. J. Heat Fluid Flow, vol.32, No.1, pp.88-94.
  • [18] Bhadauria B.S. and Kiran P. (2014): Weak non-linear oscillatory convection in a viscoelastic fluid saturated porous medium under gravity modulation. Transp. Porous Media, vol.104, pp.451-467.
  • [19] Bhadauria B.S. and Kiran P. (2014): Weak non-linear oscillatory convection in a viscoelastic fluid layer under gravity modulation. Int. J. Non-Linear Mech., vol.65, pp.133-140.
  • [20] Bhadauria B.S. and Kiran P. (2014): Weakly non-linear oscillatory convection in a viscoelastic fluid saturating porous medium under temperature modulation. Int. J. Heat Mass Transfer, vol.77, pp.843-851.
  • [21] Poincaré J.H. (1890): Sur le probléme des trois corps et les équations de la dynamique. Acta Mathematica, vol.13, pp.01-279.
  • [22] Lorenz E.N. (1963): Deterministic non-periodic flow. J. Atmos Sci., vol.20, pp.130-141.
  • [23] Sparrow C. (1982): The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. New York: Springer-Verlag.
  • [24] Vadasz P. and Olek S. (1998): Transition and chaos for free convection in a rotating porous layer. Int. J. Heat Mass Transfer, vol.41, No.11, pp.1417-1435.
  • [25] Vadasz P. and Olek S. (1999): Weak turbulence and chaos for low Prandtl number gravity driven convection In porous media. Transp. Porous Media, vol.37, No.1, pp.69-91.
  • [26] Vadasz P. and Olek S. (1999): Computational recovery of the homoclinic orbit in porous media convection. Int. J. Non-Linear Mech., vol.34, No.6, pp.89-93.
  • [27] Vadasz P. and Olek S. (2000): Route to chaos for moderate Prandtl number convection in a porous layer heated from below. Transp. Porous Med., vol.41, No.2, pp.211-239.
  • [28] Vadasz P. and Olek S. (2000): Convergence and accuracy of Adomian’s decomposition method for the solution of Lorenz equations. Int. J. Heat Mass Transfer, vol.43, No.10, pp.1715-1734.
  • [29] Vadasz et al. (2014): Chaotic and Periodic natural convection for moderate and high Prandtl numbers in a porous layer subject to vibrations. Transp. Porous Media, vol.103, pp.279-294.
  • [30] Bhadauria B.S. and Kiran P. (2015): Chaotic convection in a porous medium under temperature modulation. Transp. Porous Media, vol.107, pp.745-763.
  • [31] Sheu L.-J., Tam L.-M., Chen J.-H., Chen H.-K., Lin K.-T. and Kang Y. (2008): Chaotic convection of viscoelastic fluid in porous media. Chaos, Solitons and Fractals, vol.37, No.1, pp.113-124.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c2d2b6a1-d25a-47dd-bb45-8383fdb89a0f
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