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Flow past composite cylindrical shell of porous layer with a liquid core: magnetic effect

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Abstract

The creeping flow of a magnetic fluid perpendicular to a porous cylindrical shell is investigated, employing the unit cell model. The viscous fluid is assumed to be flowing in three zones divided as fluid, annular porous, and cavity regions, respectively. We apply a uniform magnetic field in a transverse direction of flow and then emphasize the influence of the Hartmann layers which are developed in their vicinity. Modified Stokes and modified Brinkman’s equations are employed in the liquid and porous regions, respectively. Happel and Kuwabara cell models are used as the interface conditions at the cell surface, and at the fluid–porous interface, continuity of velocity components, continuity of normal stresses, and stress jump condition for tangential stresses are applied. An expression for Kozeny constant for the cylindrical shell is presented. Representation of Kozeny constant under the influences of the pertinent parameters such as Hartmann numbers, stress jump coefficient, fractional void volume, viscosity ratios, permeability, and separation is displayed through graphs and a table. The results are compared with the cases which do not involve magnetic effect. They reveal the strong impact of Hartmann’s numbers on the resisting force experienced on the cylindrical shell. The results agree well with previous available works.

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References

  1. Dragos L (1975) Magnetofluid dynamics. Abacus Press, New York

    Google Scholar 

  2. Mehryan SAM, Ghalambaz M, Ismael MA, Chamkha AJ (2017) Analysis of fluid-solid inter-action in MHD natural convection in a square cavity equally partitioned by a vertical flexible membrane. J Magn Magn Mater 424:161–173

    Google Scholar 

  3. Alsabery AI, Sheremet MA, Chamkha AJ, Hashim I (2018) MHD Convective heat transfer in a discretely heated square cavity with conductive inner block using two phase nanofluid model. Sci Rep 8:7410

    Google Scholar 

  4. Darcy HPG (1910) Les fontaines publiques de la ville de dijon. Proc R Soc Lond Ser 83:357–369

    Google Scholar 

  5. Brinkman HC (1947) A calculation of viscous force exerted by flowing fluid on dense swarm of particles. Appl Sci Res A1:27–34

    MATH  Google Scholar 

  6. Beavers GS, Joseph DD (1967) Boundary conditions at a naturally permeable wall. J Fluid Mech 30:197–207

    Google Scholar 

  7. Saffman PG (1971) On the boundary condition at the surface of a porous medium. Stud Appl Math 50:93

    MATH  Google Scholar 

  8. Ochoa-Tapia JA, Whitaker S (1995) Momentum transfer at the boundary between a porous medium and a homogeneous fluid I. Theoretical development. Int J Heat Mass Transf 38:2635–2646

    MATH  Google Scholar 

  9. Ochoa-Tapia JA, Whitaker S (1995) Momentum transfer at the boundary between a porous medium and a homogeneous fluid II. Comparison with experiment. Int J Heat Mass Transf 38:2647–2655

    MATH  Google Scholar 

  10. Happel J, Brenner H (1965) Low Reynolds number hydrodynamics. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  11. Happel J (1958) Viscous flow in multiparticle systems: slow motion of fluids relative to beds of spherical particles. AIChE J 4:197–201

    Google Scholar 

  12. Kuwabara S (1959) The forces experienced by randomly distributed parallel circular cylinders or spheres in a viscous flow at small Reynolds numbers. J Phys Soc Jpn 14:527–532

    MathSciNet  Google Scholar 

  13. Mehta GD, Morse TF (1975) Flow through charged membranes. J Chem Phys 63(5):1878–1889

    Google Scholar 

  14. Kvashnin AG (1979) Cell model of suspension of spherical particles. Fluid Dyn 14:598–602

    MATH  Google Scholar 

  15. Cunningham E (1910) On the velocity of steady fall of spherical particles through fluid medium. Proc R Soc Lond Ser A Contain Pap Math Phys Charact 83:357–365

    MATH  Google Scholar 

  16. Spielman L, Goren SL (1968) Model for predicting pressure drop and filtration efficiency in fibrous media. Environ Sci Technol 2:279–287

    Google Scholar 

  17. Singh MP, Gupta JL (1971) The flow of a viscous fluid past an inhomogeneous porous cylinder. ZAMM 51:17

    MATH  Google Scholar 

  18. Brown GR (1975) Doctoral dissertation. The institute of paper chemistry

  19. Verma PD, Bhatt BS (1976) Flow past a porous circular cylinder at small Reynolds number. J Pure Sci 9:908

    MATH  Google Scholar 

  20. Pop I, Cheng P (1992) Flow past a circular cylinder embedded in a porous medium based on the Brinkman model. Int J Eng Sci 30:257–262

    MATH  Google Scholar 

  21. Li Y, Park CW (2000) Effective medium approximation and deposition of colloidal particles in fibrous and granular media. Adv Colloid Interface Sci 87:1–74

    Google Scholar 

  22. Datta S, Shukla M (2003) Drag on flow past a cylinder with slip. Bull Calcutta Math Soc 95(1):63–72

    MathSciNet  MATH  Google Scholar 

  23. Kim AS, Yuan R (2005) A new model for calculating specific resistance of aggregated colloidal cake layers in membrane filtration processes. J Membr Sci 249(1–2):89–101

    Google Scholar 

  24. Vasin S, Fillipov A (2009) Cell models for flows in concentrated media composed of rigid impenetrable cylinders covered with a porous layer. Colloid J 71(2):141–155

    Google Scholar 

  25. Deo S, Filippov A, Tiwari A, Vasin S, Starov V (2011) Hydrodynamic permeability of aggregates of porous particles with an impermeable core. Adv Colloid Interface Sci 164:21–37

    Google Scholar 

  26. Leontov NE (2014) Flow past a cylinder and a sphere in a porous medium within the framework of the Brinkman equation with the Navier boundary condition. Fluid Dyn 49(2):232–237

    MathSciNet  Google Scholar 

  27. Sherief HH, Faltas MS, Ashwamy EA, Adel-Hamied AM (2014) Parallel and perpendicular flow of a micropolar fluid between slip cylinder and coaxial fictitious cylindrical shell in cell models. Eur Phys J Plus 129:217

    Google Scholar 

  28. Krishna Prasad M, Srinivasacharya D (2017) Micropolar fluid flow through a cylinder and a sphere embedded in a porous medium. Int J Fluid Mech Res 44(3):229–240

    Google Scholar 

  29. Yadav PK (2018) Motion through a non-homogeneous porous medium: hydrodynamic permeability of a membrane composed of cylindrical particles. Eur Phys Plus 133(1):133

    Google Scholar 

  30. Krishnan R, Shukla P (2019) Drag on a fluid sphere embedded in a porous medium with solid core. Int J Fluid Mech Res 46(3):219–228

    Google Scholar 

  31. Yu Khanukaeva D, Filippov AN, Yadav PK, Tiwari A (2019) Creeping flow of micropolar fluid parallel to the axis of cylindrical cells with porous layer. Eur J Mech B Fluids 76:73–80

    MathSciNet  MATH  Google Scholar 

  32. Krishna Prasad M, Bucha T (2019) Steady viscous flow around a permeable spheroidal particle. Int J Appl Comput Math 5(4):109

    MathSciNet  MATH  Google Scholar 

  33. Stewartson K (1956) Motion of a sphere through a conducting fluid in the presence of strong magnetic field. J Fluid Mech 52:301–316

    MathSciNet  MATH  Google Scholar 

  34. Globe S (1959) Laminar steady-state magnetohydrodynamic flow in an annular channel. Phys Fluids 2:404–407

    MathSciNet  MATH  Google Scholar 

  35. Gold RR (1962) Magnetohydrodynamic pipe flow part-I. J Fluid Mech 13:505–512

    MathSciNet  MATH  Google Scholar 

  36. Cramer KR, Pai SI (1973) Magnetofluid dynamics for engineers and applied physicists. McGraw-Hill, New York

    Google Scholar 

  37. Davidson PA (2001) An introduction to magnetohydrodynamics. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  38. Geindreau GE, Aurialt JL (2002) Magnetohydrodynamic flows in porous media. J Fluid Mech 466:343–363

    MathSciNet  MATH  Google Scholar 

  39. Verma VK, Datta S (2010) Magnetohydrodynamic flow in a channel with varying viscosity under transverse magnetic field. Adv Theory Appl Mech 3:53–66

    MATH  Google Scholar 

  40. Tiwari A, Deo S, Fillipov A (2012) Effect of magnetic field on the hydrodynamic permeability of a membrane. Colloid J 74(4):512–522

    Google Scholar 

  41. Srivastava BG, Deo S (2013) Effect of magnetic field on the viscous fluid flow in a channel filled with porous medium of variable permeability. Appl Math Comput 219:8959–8964

    MathSciNet  MATH  Google Scholar 

  42. Jayalakshmamma DV, Dinesh PA, Sankar M (2014) Flow of conducting fluid on solid core surrounded by a cylindrical region in presence of transverse magnetic field. Mapana J Sci 13(3):13–29

    Google Scholar 

  43. Verma VK, Singh SK (2015) Magnetohydrodynamic flow in a circular channel filled with a porous medium. J Porous Media 18:923–928

    Google Scholar 

  44. Verma VK, Gupta AM (2017) Analytical solution of the flow in a composite cylindrical channel partially filled with a porous media in the presence of magnetic field. Spec Top Rev Porous Media Int J 8(10):39–48

    Google Scholar 

  45. Alizadeh-Haghighi E, Jafarmadar S, Khalil Arya Sh, Rezazadeh G (2017) Study of micropolar fluid flow inside a magnetohydrodynamic micropump. J Braz Soc Mech Sci Eng 39(12):4955–4963

    Google Scholar 

  46. Ansari IF, Deo S (2018) Magnetohydrodynamic viscous fluid flow past a porous sphere embedded in another porous medium. Spec Top Rev Porous Media Int J 9(2):191–200

    Google Scholar 

  47. Saad EI (2018) Effect of magnetic fields on the motion of porous particles for Happel and Kuwabara models. J Porous Media 21(7):637–664

    Google Scholar 

  48. Prasad MK, Bucha T (2019) Impact of magnetic field on flow past cylindrical shell using cell model. J Braz Soc Mech Sci Eng 41(8):320

    Google Scholar 

  49. Prasad MK, Bucha T (2019) Effect of magnetic field on the steady viscous fluid flow around a semipermeable spherical particle. Int J Appl Comput Math 5(3):98

    MathSciNet  MATH  Google Scholar 

  50. Prasad MK, Bucha T (2019) Creeping flow of fluid sphere contained in a spherical envelope: magnetic effect. SN Appl Sci 1(12):1594

    Google Scholar 

  51. Prasad MK, Bucha T (2020) Magnetohydrodynamic creeping flow around a weakly permeable spherical particle in cell models. Pramana J Phys 94:24

    Google Scholar 

  52. Prasad MK, Bucha T (2020) MHD viscous flow past a weakly permeable cylinder using Happel and Kuwabara cell models. Iran J Sci Technol Trans Sci 44:1063–1073

    MathSciNet  Google Scholar 

  53. Maxworthy T (1968) Experimental studies in magneto-fluid dynamics: pressure distribution measurements around a sphere. J Fluid Mech 31(4):801

    Google Scholar 

  54. Maxworthy T (1969) Experimental studies in magneto-fluid dynamics: flow over a sphere with a cylindrical afterbody. J Fluid Mech 35(2):411

    Google Scholar 

  55. Baylis JA, Hunt JCR (1971) MHD flow in an annular channel; theory and experiment. J Fluid Mech 48(3):423

    Google Scholar 

  56. Stelzer Z, Cebron D, Miralles S, Vantieghem S, Noir J, Scarfe P, Jackson A (2015) Experimental and numerical study of electrically driven magnetohydrodynamic flow in a modified cylindrical annulus. I. Base flow. Phys Fluids 27:077101

    Google Scholar 

  57. Valenzuela-Delgado M, Ortiz-Pérez AS, Flores-Fuentes W, Bravo-Zanoguera ME, Acuña-Ram-rez A, Ocampo-Diaz JD, Hernández-Balbuena D, Rivas-López M, Sergiyenko O (2018) Theoretical and experimental study of low conducting fluid MHD flow in an open annular channel. Int J Heat Mass Transf 127:322

    Google Scholar 

  58. Chorlton F (2005) Text book of fluid dynamics. CBS Publishers and Distributors, Chennai

    Google Scholar 

  59. Yadav PK, Jaiswal S, Asim T, Mishra R (2018) Influence of a magnetic field on the flow of a micropolar fluid sandwiched between two Newtonian fluid layers through a porous medium. Eur Phys J Plus 133:247

    Google Scholar 

  60. Nield DA, Bejan A (2006) Convection in porous media. Springer, New York

    MATH  Google Scholar 

  61. Avellaneda M, Torquato S (1991) Rigorous link between fluid permeability, electrical conductivity, and relaxation times for transport in porous media. Phys Fluids A Fluid Dyn 3:2529

    MathSciNet  MATH  Google Scholar 

  62. Carman PC (1956) Flow of Gases through Porous media. Academic Press, New York

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Raipur, 492010, India

    Krishna Prasad Madasu & Tina Bucha

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  1. Krishna Prasad Madasu
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  2. Tina Bucha
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Correspondence to Krishna Prasad Madasu.

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Madasu, K.P., Bucha, T. Flow past composite cylindrical shell of porous layer with a liquid core: magnetic effect. J Braz. Soc. Mech. Sci. Eng. 42, 452 (2020). https://doi.org/10.1007/s40430-020-02539-4

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  • DOI: https://doi.org/10.1007/s40430-020-02539-4

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