Unsteady Rotatory Oscillations of a Vertical Cylinder In Jeffery Fluid With Ion Slip Currents and Porous Medium

  • Authors

    • Nagaraju Gajjela Lebanese french university
    • podila Aparna VNR Vignana Jyothi Institute of Engineering and Technology, Kukatpally, Hyderabad
    2019-06-30
    https://doi.org/10.14419/ijet.v7i4.29314
  • Circular Cylinder, Ion-Slip, Jeffery Fluid, Magneto Hydrodynamic, Porous Medium.

  • Abstract

    The generated flow of a Jeffery fluid due to an infinite circular cylinder's rotatory oscillations is examined. Consideration is given to the effects of Magnetic field, Hall and Ion currents with porous medium. The governing partial differential equations ensuing from the linear momentum equations are determined analytically by the theory of Bessel’s functions. The velocity field, tangential drag force, torque and axial force acting on the cylinder are enumerated. The impacts different fluid parameters on transverse and axial velocities are investigated and presented in graph form. It is found that the longitudinal and polar velocity decreases with increasing Reynold number at a distance from the wall. The θ-component and z-component a velocity increase with a raise in Deborah number, also it increases with rising in Ion-slip parameter.

     

    Nomenclature

     

    Ρ:Fluid Density

    :Viscosity

    Σ:Electrical Conductivity

    ð‘˜0:Permeability of the Porous Medium

    T:Cauchy Stress Tensor

    I:Identity Tensor

    S:Extra Stress Tensor

    E:Rate of Strain

    :Jeffery Parameters

    Q0:Magnitude of Oscillations

    Î’0:Angle between the Directions of Transverse Oscillation with Base Vector

    J:Current Density

    B:Magnetic Field

    M:Magnetic Parameter

    Re:Reynolds Number

    Da:Darcy Number

    De:Debroah Number

    :Ion Slip Parameter

    :Hall Factor,

     

     

     

  • References

    1. [1] Stokes GG (1886), on the effect of rotation of cylinders and spheres about their own axes in increasing the logarithmic decrement of the arc of vibration (Mathematical and Philosophical Papers 5) Cambridge. Cambridge University Press, England, pp 207–214.

      [2] Casarella MJ & Laura PA (1969), Drag on oscillating rod with longitudinal and torsional motion. J. Hydronaut. 13, pp 180–183.https://doi.org/10.2514/3.62823.

      [3] Rao PM, Kuwahara K &Tsuboi K (1992), Computational study of unsteady viscous flow around a transversely and longitudinally oscillating circular cylinder in a uniform flow at high Reynolds number. Comput. Mech. 10, pp 414–428.https://doi.org/10.1007/BF00363996.

      [4] AkyildizFahir T (1998), Longitudinal and torsional oscillations of a rod in a viscoelastic fluid. Rheol. Acta 37, pp 508–511.https://doi.org/10.1007/s003970050137.

      [5] Calmelet-Eluhu C & Rosenhaus V (2001), Symmetries and solutions of a Micropolar fluid through a cylinder. Acta. Mech. 147, pp 59–72.https://doi.org/10.1007/BF01182352.

      [6] Owen D &RahamanK (2006), on the flow of an Oldroyd–B liquid through a straight circular tube performing longitudinal and torsional oscillations of different frequencies. Mathematica 14, pp 1–9.

      [7] Vieru D, Akhtar W, Fetecau C & Corina Fetecau (2007), Starting solutions for the oscillating motions of a Maxwell fluid in cylindrical domain. Meccanica 42, pp 573–583.https://doi.org/10.1007/s11012-007-9081-7.

      [8] Mehrdad Massoudi & Tran X.phouc (2008), on the motion of a second grade fluid due to longitudinal and torsional oscillations of a cylinder-A numerical study. Appl. Math. Comput.203, pp 471–481.https://doi.org/10.1016/j.amc.2008.05.133.

      [9] Ramana Murthy JV &NagarajuG (2009), Flow of a Couple stress fluid generated by a circular cylinder subject to longitudinal and torsional oscillations. Contemporary Engineering Sciences 2(10), pp 451–461.

      [10] Ramana Murthy JV, Nagaraju G & Muthu P (2010), Numerical solution of longitudinal and torsional oscillations of cylinder with suction in a couple stress fluid. Journal of Engg& Appl. Sci.5 (5), pp 51–63.

      [11] Ramana Murthy JV, Muthu P &NagarajuG (2010), Finite difference solution for mhd flow of couple stress fluid between two concentric rotating cylinders with porous lining. Int. J of Appl Math and Mech.6, pp 1–28.

      [12] Ramana murthy JV, Nagaraju G & Muthu P(2012), Micropolar fluid flow generated by a circular cylinder subject to longitudinal and torsional oscillations with suction/injection. Tamkang Journal of Mathematics 43(3), pp 339–356.https://doi.org/10.5556/j.tkjm.43.2012.614.

      [13] Nagaraju G & Ramana Murthy JV (2013), Mhd flow of Longitudinal and Torsional oscillations of a circular cylinder with suction in a couple stress fluid. Int.J. of Applied Mechanics and Engineering 18(4), pp.1099–1114.https://doi.org/10.2478/ijame-2013-0069.

      [14] NagarajuG (2014), Unsteady MHD Micropolar Fluid Flow Generated Due to Longitudinal and Torsional Oscillations of Circular Cylinder. International Journal of Nonlinear Science.18 (1), pp.22-29.

      [15] Nagaraju G & Ramana Murthy JV (2014), unsteady flow of a micropolar fluid generated by a circular cylinder subject to longitudinal and torsional oscillations. Theoret.Appl.Mech. 41(1), pp.71-91.https://doi.org/10.2298/TAM1401071N.

      [16] Maqbool K, Shaheen S & Mann AB (2016), exact solution of cilia induced flow of a Jeffrey fluid in an inclined tube. Springer Plus 5, 1379. https://doi.org/10.1186/s40064-016-3021-8.

      [17] OdeluOjjela, Adigoppula Raju & Pravin Kashyap Kambhatla (2017), Influence of thermophoresis and induced magnetic field on chemically reacting mixed convective flow of Jeffrey fluid between porous parallel plates. Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2017.02.061.

      [18] Stanford Shateyi& Gerald T. Marewo (2018), Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction. Open Physics 16(1), pp 249–259.https://doi.org/10.1515/phys-2018-0036.

      [19] Ellahi R, Bhatti MM &IoanPop (2016), Effects of hall and ion slip on MHD peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct. International Journal of Numerical Methods for Heat & Fluid Flow 26(6), 1802 – 1820.https://doi.org/10.1108/HFF-02-2015-0045.

      [20] NagarajuGajjela, Anjanna Matta &KaladharK (2017), the effects of Soret and Dufour, chemical reaction, Hall and ion currents on magnetized micropolar flow through co-rotating cylinders. AIP Advances 7, 115201 (2017); https://doi.org/10.1063/1.4991442.

      [21] Sara I. Abdelsalam& Bhatti MM (2018), the study of non-Newtonian nanofluid with hall and ion slip effects on peristaltically induced motion in a non-uniform channel. RSC Adv.8, pp 7904–7915.https://doi.org/10.1039/C7RA13188G.

      [22] Imran Haider Qureshi, Nawaz M, & Shahzad A (2019), Numerical study of dispersion of nanoparticles in magnetohydrodynamic liquid with Hall and ion slip currents. AIP Advances 9, 025219, https://doi.org/10.1063/1.5084311.

      [23] Santhosh Nallapu&RadhakrishnamacharyaG (2014), Jeffrey Fluid Flow through Porous Medium in the Presence of Magnetic Field in Narrow Tubes. International Journal of Engineering Mathematics 2014, Article ID 713831, 8 pages. https://doi.org/10.1155/2014/713831.

      [24] Mohd Zin NA, Khan I &ShafieS (2017), Unsteady MHD free convection flow of rotating Jeffrey fluid embedded in a porous medium with ramped wall temperature. IOP Conf. Series: Journal of Physics: Conf. Series 890 (012043). https://doi.org/10.1088/1742-6596/890/1/012043.

      [25] Veera Krishna M, Bharathi K & Ali J. Chamkha(2018), Hall Effects On Mhd Peristaltic Flow Of Jeffrey Fluid Through Porous Medium In A Vertical Stratum. Interfacial Phenomena and Heat Transfer 6(3), 253–268.https://doi.org/10.1615/InterfacPhenomHeatTransfer.2019030215.

      [26] Eldabe NTM, Shaker MO &MahaSA (2018), Peristaltic Flow of MHD Jeffrey Fluid Through Porous Medium in a Vertical Channel with Heat and Mass Transfer with Radiation. Journal of Nanofluids 7(3), pp. 595-602.https://doi.org/10.1166/jon.2018.1466.

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  • How to Cite

    Gajjela, N., & Aparna, podila. (2019). Unsteady Rotatory Oscillations of a Vertical Cylinder In Jeffery Fluid With Ion Slip Currents and Porous Medium. International Journal of Engineering & Technology, 7(4), 6592-6596. https://doi.org/10.14419/ijet.v7i4.29314

    Received date: 2019-05-16

    Accepted date: 2019-06-03

    Published date: 2019-06-30