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Combine Impacts of Electrokinetic Variable Viscosity and Partial Slip on Peristaltic MHD Flow Through a Micro-channel

  • R. E. Abo-Elkhair
  • Kh. S. Mekheimer
  • A. M. A. MoawadEmail author
Research Paper

Abstract

This article addresses the impacts of external electric field and thickness of the electric double layer (EDL) on peristaltic pumping of a fluid with variable viscosity through a micro-channel. Low Reynolds number and long wavelength assumptions have been used. The flow is measured in the wave frame of reference moving with a uniform velocity C. The systematic results are obtained for the velocity and pressure gradient distribution. Poisson Boltzmann equation has been solved to obtain the (electrical double layer) EDL potential distribution. The pressure rise data are extracted numerically. The diagrammatic sketch effect of various observing parameters on pressure rise, frictionless force, and axial velocity are drawing manually. The extension and contraction phenomenon of the whole bolus is also displayed in the end. It is recorded that the axial velocity deserves to provide the main characteristics of flow behavior in the micro-channel for micro-fluidic applications. Electrical and magnetic fields offer an excellent mode for regulating flows, and such a result is important at the time of surgery. In addition, an increase in the Reynolds model viscosity parameter \(\alpha \) reduces the size of a trapped bolus and ultimately vanishes when the viscosity parameter is large. Finally, with increasing Helmholtz–Smoluchowski velocity axial flow is decelerated and the trapped bolus decreases in size.

Keywords

Peristaltic transport Magnetohydrodynamic flow Electro osmosis Variable viscosity Velocity slip 

Notes

Acknowledgements

Authors are very grateful to the anonymous referees for their valuable remarks and comments which significantly contributed to the quality of the paper.

References

  1. Abd Elmaboud Y, Mekheimer KS, Abdellatif A (2013) Thermal Properties of couple-stress fluid in an asymmetric channel with peristalsis. J Heat Transf 135(4):044502CrossRefGoogle Scholar
  2. Abo-Elkhair RE, Mekheimer KS, Moawad AMA (2017) Cilia walls influence on peristaltically induced motion of magneto-fluid through a porous medium at moderate Reynolds number: Numerical study. J Egypt Math Soc 25(2):238–251MathSciNetCrossRefzbMATHGoogle Scholar
  3. Akbar NS (2017) Double-diffusive natural convective peristaltic Prandtl flow in a porous channel saturated with a nanofluid. Heat Transf Res 48(4):283–290MathSciNetCrossRefGoogle Scholar
  4. Akbar NS, Khan ZH (2017) Variable fluid properties analysis with water based CNT nanofluid over a sensor sheet: numerical solution. J Mol Liq 232:471–477CrossRefGoogle Scholar
  5. Akbar NS, Tripathi D, Khan ZH, Bég OA (2016) A numerical study of magnetohydrodynamic transport of nanofluids from a vertical stretching sheet with exponential temperature-dependent viscosity and buoyancy effects. Chem Phys Lett 661:20–30CrossRefGoogle Scholar
  6. Akbar NS, Abid SA, Tripathi D, Mir NA (2017) Nanostructures study of CNT nanofluids with temperature dependent variable viscosity in a muscular tube. Eur Phys J Plus 132:110CrossRefGoogle Scholar
  7. Akbar NS, Tripathi D, Bég OA (2017) MHD convective heat transfer of nanofluids through a flexible tube with buoyancy: a study of nano-particle shape effects. Adv Powder Technol 28:453–462CrossRefGoogle Scholar
  8. Akram S, Mekheimer KS, Abd Elmaboud Y (2016) Particulate suspension slip flow induced by peristaltic waves in a rectangular duct: effect of lateral walls. Alexandr Eng J.  https://doi.org/10.1016/j.aej.2016.09.011 (article in press)
  9. Awais M, Malik MY, Bilal S, Salahuddin T, Arif H (2017) Magnetohydrodynamic (MHD) flow of Sisko fluid near the axisymmetric stagnation point towards a stretching cylinder. Result Phys 7:49–56CrossRefGoogle Scholar
  10. Burgreen D, Nakache FR (1964) Electrokinetic flow in ultrafine capillary slits. J Phys Chem 68:1084–1091CrossRefGoogle Scholar
  11. Chakraborty S (2006) Augmentation of peristaltic microflows through electro-osmotic mechanism. J Phys D Appl Phys 39:5356–5363CrossRefGoogle Scholar
  12. Ebaid A (2008) A new numerical solution for the MHD peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube via Adomian decomposition method. Phys Lett A 372(32):5321–5328MathSciNetCrossRefzbMATHGoogle Scholar
  13. El Hakeem A, El Naby A, El Misery AM, El Shamy II (2003) Hydromagnetic flow of fluid with variable viscosity in a uniform tube with peristalsis. J Phys A Math Gen 36:8535–8547MathSciNetCrossRefzbMATHGoogle Scholar
  14. El Misery AM, El Hakeem A, El Naby A, El Nagar AH (2003) Effects of a fluid with variable viscosity and an endoscope on peristaltic motion. J Phys Soc Jpn 72:89–93CrossRefzbMATHGoogle Scholar
  15. Ellahi R, Bhatti MM, Ioan P (2016) Effects of hall and ion slip on MHD peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct. Int J Numer Methods Heat Fluid Flow 26(6):1802–1820MathSciNetCrossRefzbMATHGoogle Scholar
  16. Ellahi R, Mubashir BM, Fetecau C, Vafai K (2016) Peristaltic flow of couple stress fluid in a non-uniform rectangular duct having compliant walls. Commun Theor Phys 65:66–72MathSciNetCrossRefzbMATHGoogle Scholar
  17. Elsoud SN, Kaldas SF, Mekheimer KS (1998) Interaction of peristaltic flow with pulsatile couple-stress fluid. J Biomath 13:417–425Google Scholar
  18. Hayat T, Ali N (2008) Effect of variable viscosity on the peristaltic transport of a Newtonian fluid in an asymmetric channel. Appl Math Model 32(5):761–774MathSciNetCrossRefzbMATHGoogle Scholar
  19. Hayat T, Farooq S, Alsaedi A, Ahmad B (2016) Influence of variable viscosity and radial magnetic field on peristalsis of copper–water nanomaterial in a non-uniform porous medium. Int J Heat Mass Transf 103:1133–1143CrossRefGoogle Scholar
  20. Huda AB, Akbar NS, Bég OA, Khan MY (2017) Dynamics of variable-viscosity nanofluid flow with heat transfer in a flexible vertical tube under propagating waves. Result Phys 7:413–425CrossRefGoogle Scholar
  21. Hussain A, Malik MY, Bilal S, Awais M, Salahuddin T (2017) Computational analysis of magnetohydrodynamic Sisko fluid flow over a stretching cylinder in the presence of viscous dissipation and temperature dependent thermal conductivity. Results Phys 7:139–146CrossRefGoogle Scholar
  22. Lachiheb M (2014) Effect of coupled radial and axial variability of viscosity on the peristaltic transport of Newtonian fluid. Appl Math Comput 244:761–771MathSciNetzbMATHGoogle Scholar
  23. Loughran M, Tsai SW, Yokoyama K, Karube I (2003) Simultaneous iso-electric focusing of proteins in a micro-fabricated capillary coated with hydrophobic and hydrophilic plasma polymerized films. Curr Appl Phys 3:495–499CrossRefGoogle Scholar
  24. Malik MY, Arif H, Salahuddin T, Awais M (2016) Numerical solution of MHD Sisko fluid over a stretching cylinder and heat transfer analysis. Int J Numer Methods Heat Fluid Flow 26(6):1787–1801MathSciNetCrossRefzbMATHGoogle Scholar
  25. Malik MY, Khan M, Salahuddin T, Khan I (2016) Variable viscosity and MHD flow in Casson fluid with Cattaneo-Christov heat flux model: using Keller box method. Eng Sci Technol Int J 19(4):1985–1992CrossRefGoogle Scholar
  26. Mekheimer KS (2003) Non- linear peristaltic transport of MHD flow in an inclined planar channel. Arab J Sci Eng 28(2A):183–201Google Scholar
  27. Mekheimer KS (2004) Peristaltic flow of blood under effect of a magnetic field in a non uniform channels. Appl Math Comput 153:763–777MathSciNetzbMATHGoogle Scholar
  28. Mekheimer KS (2005) Peristaltic transport through a uniform and non-uniform annulus. Arab J Sci Eng 30(1A):1–15Google Scholar
  29. Mekheimer KS (2008) Effect of the induced magnetic field on peristaltic flow of a couple stress fluid. Phys Lett A 372:4271–4278CrossRefzbMATHGoogle Scholar
  30. Mekheimer KS, Abd Elmaboud Y (2008) The influence of heat transfer and magnetic field on peristaltic transport of a Newtonian fluid in a vertical annulus. Phys Lett A 372:1657–1665CrossRefzbMATHGoogle Scholar
  31. Mekheimer KS, Husseny SZA, Abd Elmaboud Y (2010) Effects of heat transfer and space porosity on peristaltic flow in a vertical asymmetric channel. Numer Methods Part Differ Equ 26:747–770MathSciNetzbMATHGoogle Scholar
  32. Mekheimer KS, Hemada KA, Raslan KR, Abo-Elkhair RE, Moawad AMA (2014) Numerical study of a non-linear peristaltic transport: application of adomian decomposition method (ADM). Gen Math Note 20:22–49Google Scholar
  33. Probstein RF (1994) Physicochemical hydrodynamics—an introduction, 2nd edn. Wiley, New YorkCrossRefGoogle Scholar
  34. Salahuddin T, Malik MY, Hussain A, Bilal S, Awais M (2015) Effects of transverse magnetic field with variable thermal conductivity on tangent hyperbolic fluid with exponentially varying viscosity. AIP Adv 5:127103CrossRefGoogle Scholar
  35. Salahuddin T, Malik MY, Hussain A, Bilal S, Awais M (2016) Combined effects of variable thermal conductivity and MHD flow on pseudoplastic fluid over a stretching cylinder by using Keller box M. Inf Sci Lett 5(1):11–19CrossRefGoogle Scholar
  36. Sinha A, Shit GC (2015) Electromagnetohydrodynamic flow of blood and heat transfer in a capillary with thermal radiation. J Magn Magn Mater 378:143–151CrossRefGoogle Scholar
  37. Srivastava LM, Srivastava VP (1984) Peristaltic transport of blood: casson model-II. J Biomech 17:821–829CrossRefGoogle Scholar
  38. Tripathi D, Akbar NS, Khan ZH, B\(\acute{e}\)g OA, (2017) Peristaltic transport of bi-viscosity fluids through a curved tube: a mathematical model for intestinal flow. Proc IMech E Part H J Eng Med 230(9):817–828CrossRefGoogle Scholar
  39. Tso CP, Sundaravadivelu K (2001) Capillary flow between parallel plates in the presence of an electromagnetic field. J Phys D Appl Phys 34:3522CrossRefGoogle Scholar
  40. Zu YQ, Yan YY (2006) Numerical simulation of electro-osmotic flow near Earthworm surface. J Bionic Eng 3:179–186CrossRefGoogle Scholar

Copyright information

© Shiraz University 2017

Authors and Affiliations

  • R. E. Abo-Elkhair
    • 1
  • Kh. S. Mekheimer
    • 1
  • A. M. A. Moawad
    • 1
    Email author
  1. 1.Mathematical Department, Faculty of ScienceAl-Azhar UniversityNasr City, CairoEgypt

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