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Slip effects on creeping flow of slightly non-Newtonian fluid in a uniformly porous slit

  • Hameed UllahEmail author
  • Abdul Majeed Siddiqui
  • Huafei Sun
  • Tahira Haroon
Technical Paper
  • 26 Downloads

Abstract

This study demonstrates the analysis of slip effects for the steady, creeping flow of incompressible slightly non-Newtonian fluid through the permeable slit with uniform reabsorption. A system of two-dimensional partial differential equations which completely describe the flow phenomenon along with non-homogeneous boundary conditions are considered and non-dimensionalized. The resulting equations are then linearized using recursive approach. Expressions for all flow properties like stream function, velocity components, volumetric flow rate, pressure distribution, shear and normal stresses in general and on the walls of the slit, fractional absorption and leakage flux are derived which are strongly dependent on slip coefficient. The points of maximum velocity components are also identified. The behavior of the flow variables is also discussed graphically for involved parameters at various positions of the channel. The results indicate that slip coefficient considerably influences the flow variables. The obtained results are in good agreement with the previous solutions as the slip coefficient tends to zero.

Keywords

Creeping flow Slip condition Slightly non-Newtonian fluid Porous slit Recursive approach 

Notes

References

  1. 1.
    Beavers CS, Joseph DD (1967) Boundary conditions at a naturally permeable wall. J Fluid Mech 30:197–207CrossRefGoogle Scholar
  2. 2.
    Beavers GS, Sparrow EM, Magnuson RA (1970) Experiments on coupled parallel flows in a channel and a bounding porous medium. J Basic Eng 92:843–848CrossRefGoogle Scholar
  3. 3.
    Kohler JP (1973) An investigation of laminar flow through a porous-wailed channel, Ph.D. Thesis, University of Massachusetts, AmherstGoogle Scholar
  4. 4.
    Sing R, Laurence RL (1979) Influence of slip velocity at a membrane surface on ultrafiltration performance-I, channel flow system. Int J Heat Mass Transf 22:721–729CrossRefGoogle Scholar
  5. 5.
    Eldesoky IM (2014) Unsteady MHD pulsatile blood flow through porous medium in stenotic channel with slip at permeable walls subjected to time dependent velocity (injection/suction). Walailak J Sci Technol 11(11):901–922Google Scholar
  6. 6.
    Eldesoky IM (2012) Slip effects on the unsteady MHD pulsatile blood flow through porous medium in an artery under the effect of body acceleration. Int J Math Math Sci 2012:1–26MathSciNetCrossRefGoogle Scholar
  7. 7.
    Eldesoky IM (2013) Effect of relaxation time on MHD pulsatile flow of blood through porous medium in an artery under the effect of periodic body acceleration. J Bio Syst 21(02):1350011MathSciNetCrossRefGoogle Scholar
  8. 8.
    Elshehawy EF, Eldabe NT, Eldesoky IM (2006) Slip effects on the peristaltic flow of a non-Newtonian Maxwellian fluid. Acta Mech 186(1–4):141–159CrossRefGoogle Scholar
  9. 9.
    Ahmad S, Ahmad N (2011) On flow through renal tubule in case of periodic radial velocity component. Int J Emerg Multi Fluid Sci 4:201–208Google Scholar
  10. 10.
    Haroon T, Siddiqui AM, Shahzad A (2016) Creeping flow of viscous fluid through a proximal tubule with uniform reabsorption: a mathematical study. Appl Math Sci 10(16):795–807Google Scholar
  11. 11.
    Haroon T, Siddiqui AM, Shahzad A, Smeltzer JH (2017) Steady creeping slip flow of viscous fluid through a permeable slit with exponential reabsorption. Appl Math Sci 11(50):2477–2504Google Scholar
  12. 12.
    Siddiqui AM, Siddiqa S, Naqvi AS (2018) Effect of constant wall permeability and porous media on the creeping flow through round vessel. J Appl Comput Math 7(2):1–6Google Scholar
  13. 13.
    Ullah H, Sun H, Siddiqui AM, Haroon T (2019) Creeping flow analysis of slightly non-Newtonian fluid in a uniformly porous slit. J Appl Anal Comput 9(1):140–158MathSciNetGoogle Scholar
  14. 14.
    Khan AA, Zaib F, Zaman A (2017) Effects of entropy generation on Powell Eyring fluid in a porous channel. J Braz Soc Mech Sci Eng 39(12):5027–5036CrossRefGoogle Scholar
  15. 15.
    Khan AA, Tariq H (2018) Influence of wall properties on the peristaltic flow of a dusty Walter’s B fluid. J Braz Soc Mech Sci Eng 40:368CrossRefGoogle Scholar
  16. 16.
    Hayat T, Khan AA, Bibi F, Farooq S (2019) Activation energy and non-Darcy resistance in magneto peristalsis of Jeffrey material. J Phys Chem Solids 129:155–161CrossRefGoogle Scholar
  17. 17.
    Khan AA, Farooq A, Vafai K (2018) Impact of induced magnetic field on synovial fluid with peristaltic flow in an asymmetric channel. J Magn Magn Mater 446:54–67CrossRefGoogle Scholar
  18. 18.
    Rivlin RS, Ericksen JL (1955) Stress-deformation relations for isotropic materials. J Ration Mech Anal 4:323–354MathSciNetzbMATHGoogle Scholar
  19. 19.
    Dunn JE, Fosdick RL (1974) Thermodynamics, stability and boundedness of fluids of complexity 2 and fluids of second grade. Arch Ration Mech Anal 56:191–252MathSciNetCrossRefGoogle Scholar
  20. 20.
    Fosdick RL, Rajagopal KR (1979) Anomalous features in the model of second order fluids. Arch Ration Mech Anal 70:145–152MathSciNetCrossRefGoogle Scholar
  21. 21.
    Kacou A, Rajagopal KR, Szeri AZ (1987) Flow of a fluid of the differential type in a journal bearing. ASME J Tribol 109:100–107CrossRefGoogle Scholar
  22. 22.
    Rajagopal K R, Fosdick R L (1980) Thermodynamics and stability of fluids of third grade. Proc R Soc Lond Ser A 339:351–377MathSciNetzbMATHGoogle Scholar
  23. 23.
    Rajagopal KR (1984) On the creeping flow of the second order fluid. J Non Newton Fluid Mech 15:239–246CrossRefGoogle Scholar
  24. 24.
    Charcosset C, Choplin L (1995) Concentration by membrane ultrafiltration of a shear thinning fluid. Sep Sci Technol 30(19):3649–3662CrossRefGoogle Scholar
  25. 25.
    Charcosset C, Choplin L (1996) Ultrafiltration of non-Newtonian fluids. J Membr Sci 115(2):147–160CrossRefGoogle Scholar
  26. 26.
    Said BB, Boucherit H, Lahmar M (2012) On the influence of particle concentration in a lubricant and its rheological properties on the bearing behavior. Mech Ind 13:111–121CrossRefGoogle Scholar
  27. 27.
    Kacou A, Rajagopal KR, Szeri AZ (1988) A thermodynamics analysis of journal bearings lubricated by non Newtonian fluid. ASME J Tribol 110:414–420CrossRefGoogle Scholar
  28. 28.
    Ng CW, Saibel E (1962) Non-linear viscosity effects in slide bearing lubrication. ASME J Lubr Technol 7:192–196Google Scholar
  29. 29.
    Langlois WE (1963) A recursive approach to the theory of slow steady-state viscoelastic flow. Trans Soc Rheol 7:75–99CrossRefGoogle Scholar
  30. 30.
    Langlois WE (1964) The recursive theory of slow viscoelastic flow applied to three basic problems of hydrodynamics. Trans. Soc. Rheol. 8:33–60CrossRefGoogle Scholar
  31. 31.
    Siddiqui AM, Kaloni PN (1986) Certain inverse solutions of a non-Newtonian fluid. Int J Non Linear Mech 21(6):459–473MathSciNetCrossRefGoogle Scholar
  32. 32.
    Siddiqui AM (1990) Some more inverse solutions of a non-Newtonian fluid. Mech Res Commun 17(3):157–163MathSciNetCrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingChina
  2. 2.Department of MathematicsCOMSATS University IslamabadSahiwalPakistan
  3. 3.Department of MathematicsPennsylvania State UniversityYorkUSA

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