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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Nonlinear Throughflow Effects on Thermally Modulated Rotating Porous Medium

Journal of Applied Nonlinear Dynamics 6(1) (2017) 27--44 | DOI:10.5890/JAND.2017.03.003

Palle Kiran$^{1}$, B.S. Bhadauria$^{2}$, Y Narasimhulu$^{1}$

$^{1}$ Department of Mathematics, Rayalaseema University, Kurnool 518002, AP, India

$^{2}$ Department of Mathematics, Institute of Science, BHU, Varanasi 221005, India

2Department of Applied Mathematics, School for Physical Sciences, BBAU, Lucknow 226025, UP, India

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Abstract

The effect of throughflow and temperature modulation on a rotating porous medium is investigated. The generalized Darcy model is used for the momentum equation. Heat transfer analysis is based on weakly nonlinear thermal instability. It is computed numerically in terms of the Nusselt number, which is governed by a non-autonomous complex Ginzburg-Landau equation. Both concepts, rotation and throughflow are used as an external mechanism to regulate heat transfer. The effect of amplitude and frequency of modulation on heat transport is discussed and presented graphically. The effect of throughflow has duel by nature on heat transfer, the outflow enhances and inflow diminishes the heat transfer. It is found that, high rotational rates promotes heat transfer than low rotational rates. Further, the effect of modulation on mean Nusselt number depends on both the phase difference and frequency rather than on only the choice of the frequency of small amplitude modulation.

Acknowledgments

One of the author PK is grateful to the Department of Atomic Energy, Government of India, for providing him financial assistance in the form of NBHM-Post-Doctoral Fellowship (Lett. No: 2/40(27)/2015/R&DII/9470).

References

  1. [1]  Suthar, Om.P., Bhadauria, B.S., and Khan, A. (2009), Modulated centrifugal convection in a rotating vertical porous layer distant from the axis of rotation, Transport in Porous Media, 79(2), 255-264.
  2. [2]  Suthar, Om.P., Bhadauria, B.S., and Khan, A. (2011), Rotating Brinkman Lapwood Convection with Modulation, Transport in Porous Media, 88, 369-383.
  3. [3]  Donnelly, R.J. (1964), Experiments on the stability of viscous flow between rotating cylinders III: enhancement of hydrodynamic stability by modulation, Proc. R. Soc. Lond. Ser, 281A, 130-139.
  4. [4]  Horton, C.W. and Rogers, F.T. (1945), Convection currents in a porous medium, J. Appl. Physics, 16, 367-370.
  5. [5]  Lapwood, E.R. (1948), Convection of a fluid in a Porous medium, Proc. Camb. Philos. Soc, 44, 508-521.
  6. [6]  Venezian, G. (1969), Effect of modulation on the onset of thermal convection, J. Fluid Mech, 35, 243-254.
  7. [7]  Finucane, R.G. and Kelly, R.E. (1976), Onset of instability in a fluid layer heated sinusoidally from below, Int. J. Heat Mass Transf, 19, 71-85.
  8. [8]  Gresho, PM. and Sani, R.L. (1970), The effect of gravity modulation on the stability of a heated fluid layer, J. Fluid Mech, 40, 783-806.
  9. [9]  Bhadauria, B.S. and Kiran, P. (2014), Effect of rotational speed modulation on heat transport in a fluid layer with temperature dependent viscosity and internal heat source, Ain Shams Eng J, 5, 1287-1297.
  10. [10]  Davis, S. (1976), The stability of time-periodic flows, Annual Review of Fluid Mech, 8, 57-74.
  11. [11]  Jones, M.C. and Persichetti, J.M. (1986), Convective instability in packed beds with throughflow, AIChE J, 32, 1555-1557.
  12. [12]  Nield, D.A. (1987), Convective instability in porous media with throughflow, AIChE J, 33, 1222-1224.
  13. [13]  Kiran, P, Bhadauria, B.S, and Narasimhulu, Y. (2016), Nonlinear throughflow effects on vibrational rotating porous medium, Computational Mathematics and Modeling Accepted.
  14. [14]  Shivakumara, I.S. (1997), Effects of throughflow on convection in porous media, Proc. 7th Asian Congr. Fluid Mech, 2, 557-560.
  15. [15]  Shivakumara, I.S. and Sureshkumar, S. (2007), Convective instabilities in a viscoelastic-fluid-saturated porous medium with throughflow, J. Geophys. Eng, 4, 104-115.
  16. [16]  Wooding, R.A. (1960), Rayleigh instability of a thermal boundary layer in a flow through a porous medium at large Reynolds number or Peclet number, J. Fluid Mech, 9, 183-192.
  17. [17]  Sutton, F.M. (1970), Onset of convection in a porous channel with net throughflow, Phys. of Fluids, 13, 1931-1934.
  18. [18]  Kiran, P. and Bhadauria, B.S. (2015), Nonlinear throughow effects on thermally modulated porous medium, Ain Shams Eng J, 7, 473-482.
  19. [19]  Malkus, W.V.R. and Veronis, G. (1958), Amplitude cellular convection, J of Fluid Mech, 4, 225.
  20. [20]  Kiran, P. (2016), Throughflow and gravity modulation effects on heat transport in a porous medium, J of Applied Fluid Mech, 9, 1105-1113.
  21. [21]  Bhadauria, B.S. and Kiran, P. (2013), Heat transport in an anisotropic porousmedium saturated with variable viscosity liquid under temperature modulation, Transport in Porous Media, 100, 279-295.
  22. [22]  Bhadauria, B.S. Siddheshwar, P.G. Kumar, J., and Suthar, Om.P. (2012), Weakly nonlinear stability analysis of temperature/gravity modulated stationary Rayleigh-Bénard convection in a rotating porous medium, Transport in Porous Media, 92, 633-647.
  23. [23]  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 Transf, 46, 5065.
  24. [24]  Bhadauria, B.S. and Kiran, P. (2015), Chaotic and oscillatory magneto-convection in a binary viscoelastic fluid under G-jitter, Int.J of Heat and Mass Transf, 84, 610-624.
  25. [25]  Vadasz, J.J., Meyer, J.P., and Govender, S. (2014), Chaotic and Periodic Natural Convection for Moderate and High Prandtl Numbers in a Porous Layer subject to Vibrations, Transport in Porous Media, 103, 279-294.
  26. [26]  Shivakumara, I.S. (1999), Boundary and inertia effects on convection in a porous media with throughflow, Acta Mechanica, 137, 151-165.
  27. [27]  Kiran, P. (2015), Throughflow and g-jitter effects on binary fluid saturated porous medium, Applied Math Mech, 36, 1285-1304.
  28. [28]  Kiran, P. (2016), Throughflow and non-uniform heating effects on double diffusive oscillatory convection in a porous medium, Ain Shams Eng J, 7, 453-462.
  29. [29]  Kiran, P. and Narasimhulu Y (2016) Weakly nonlinear oscillatory convection in an electrically conducting fluid layer under gravity modulation, Int J Applied and Compu Maths. Accepted.
  30. [30]  Kiran, P. (2015),Weak nonlinear oscillatory convection in a nonuniform heating porous medium with throughflow, Int J of Eng Math Model, 2, 63-78.
  31. [31]  Kiran, P. (2016), Nonlinear througflow and internal heating effects on vibrating porous medium, Alexandria Engg J, http://dx.doi.org/10.1016/j.aej.2016.01.012.
  32. [32]  Kumar, A. and Bhadauria, B.S. (2011), Thermal instability in a rotating anisotropic porous layer saturated by a viscoelastic fluid, Int. J of Non linear Mech, 46, 47-56.
  33. [33]  Kumar, A. and Bhadauria, B.S. (2011), Non-Linear Two Dimensional Double Diffusive Convection in a Rotating Porous Layer Saturated by a Viscoelastic Fluid. Transport in Porous Media, 87, 229-250
  34. [34]  Bhadauria, B.S. (2007), Fluid convection in a rotating porous layer under modulated temperature on the boundaries, Transport in Porous Media, 67(2), 297-315.
  35. [35]  Bhadauria, B.S. (2007), Magnetofluidconvection in a rotating porous layer under modulated temperature on the boundaries, ASME J. Heat Transf, 129, 835-843.
  36. [36]  Bhadauria, B.S. (2007), Double diffusive convection in a rotating porous layer with modulated temperature on the boundaries, J. Porous Media, 10(6), 569-584.
  37. [37]  Malashetty, M.S. and Mahantesh, S. (2007), Combined effect of thermal modulation and rotation on the onset of stationary convection in a porous layer, Transport in Porous Media, 69, 313-330.
  38. [38]  Vanishree, R.K. and Siddheshwar, P.G. (2010), Effect of rotation on thermal convection in an anisotropic porous medium with temperature-dependent viscosity, Transport in Porous Media, 81, 73-87.
  39. [39]  Kiran, P. and Bhadauria, B.S. (2016), Weakly nonlinear oscillatory convection in a rotating fluid layer under temperature modulation, ASME,J of Heat Transf, 138(5), 051702.
  40. [40]  Bhadauria, B.S. and Kiran, P. (2014),Weakly nonlinear oscillatory convection in a viscoelastic fluid saturating porous medium under temperature modulation, Int. J. Heat Mass Transf, 77 843-851.
  41. [41]  Bhadauria, B.S. Kiran, P. (2014), Heat and mass transfer for oscillatory convection in a binary viscoelastic fluid layer subjected to temperature modulation at the boundaries, Int. Communi in Heat and Mass Transf, 58, 166-175.
  42. [42]  Kiran, P. and Bhadauria, B.S. (2015), Chaotic Convection in a Porous Medium Under Temperature Modulation, Transport in Porous Media, 107(3), 745-763.

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