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Archive of Applied Mechanics

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27-10-2021 | Original

Magnetic effect on the creeping flow around a slightly deformed semipermeable sphere

Authors: Ravendra Prasad Namdeo, Bali Ram Gupta

Published in: Archive of Applied Mechanics | Issue 1/2022

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Abstract

This paper presents steady axisymmetric creeping motion of a conducting, incompressible viscous fluid past a weakly permeable slightly deformed sphere in the presence of transverse magnetic field. The Stokes approximation of momentum equation and Darcy’s law together with Lorentz force are used for the flow outside and within the semi-permeable particle. The governing equations are changed into dimensionless form, and resulting equations are solved using separation of variables method. We have determined the resistance force exerted on the oblate spheroid in the presence of magnetic field as a particular case of an approximate sphere. The impact of Hartmann numbers, permeability and deformation parameter on the coefficient of drag and the streamline pattern is exhibited graphically. Some special cases are deduced from the current study and compared with some previous results. The outcome clarifies that the Hartmann numbers enhance the drag on the oblate spheroid in comparison with prolate spheroid.

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Darcy, H.: Les Fontaines Publiques. De La Ville De Dijon. Lond. Ser. Proc. R. Soc. 83, 357–369 (1910)

Joseph, D.D., Tao, L.N.: The effect of permeability on the slow motion of a porous sphere in a viscous. ZAMM 44, 361–364 (1964). https://doi.org/10.1002/zamm.19640440804CrossRefMATH

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

Palaniappan, D.: Creeping flow about a slightly deformed sphere. ZAMP 45, 832–838 (1994). https://doi.org/10.1007/BF00942756MathSciNetCrossRefMATH

Ramkissoon, H.: Slip flow past an approximate spheroid. Acta Mech. 123, 227–233 (1997). https://doi.org/10.1007/BF01178412MathSciNetCrossRefMATH

Ramkissoon, H.: Stokes flow past a slightly deformed fluid sphere. J. Appl. Math. Phys. 37, 859–866 (1986). https://doi.org/10.1007/BF00953677CrossRefMATH

Srinivasacharya, D.: Creeping flow past a porous approximate sphere. Zeitschrift fur Angew. Math. und Mech. 83, 499–504 (2003). https://doi.org/10.1002/zamm.200310023CrossRefMATH

Srinivasacharya, D., Madasu, K.P.: Creeping flow past a porous approximate sphere—stress jump boundary condition. Zeitschrift fur Angew. Math. und Mech. 91, 824–831 (2011). https://doi.org/10.1002/zamm.201000138MathSciNetCrossRefMATH

Deo, S., Gupta, B.R.: Stokes flow past a swarm of porous approximately spheroidal particles with Kuwabara boundary condition. Acta Mech. 203, 241–254 (2009). https://doi.org/10.1007/s00707-008-0048-0CrossRefMATH

10.

Shapovalov, V.M.: Viscous fluid flow around a semipermeable particle. J. Appl. Mech. Tech. Phys. 50, 584–588 (2009). https://doi.org/10.1007/s10808-009-0079-xCrossRefMATH

11.

Deo, S., Gupta, B.R.: Drag on a porous sphere embedded in another porous medium. J. Porous Media. 13, 1009–1016 (2010). https://doi.org/10.1615/JPorMedia.v13.i11.70CrossRef

12.

Yadav, P.K., Tiwari, A., Deo, S., Filippov, A., Vasin, S.: Hydrodynamic permeability of membranes built up by spherical particles covered by porous shells: effect of stress jump condition. Acta Mech. 215, 193–209 (2010). https://doi.org/10.1007/s00707-010-0331-8CrossRefMATH

13.

Yadav, P.K., Deo, S., Yadav, M.K., Filippov, A.: On hydrodynamic permeability of a membrane built up by porous deformed spheroidal particles. Colloid J. 75, 611–622 (2013). https://doi.org/10.1134/S1061933X13050165CrossRef

14.

Yadav, P.K., Deo, S.: Stokes flow past a porous spheroid embedded in another porous medium. Meccanica 47, 1499–1516 (2012). https://doi.org/10.1007/s11012-011-9533-yMathSciNetCrossRefMATH

15.

Jaiswal, B.R., Gupta, B.R.: Stokes flow over composite sphere: liquid core with permeable shell. J. Appl. Fluid Mech. 8, 339–350 (2015). https://doi.org/10.18869/acadpub.jafm.67.222.23135CrossRef

16.

Yadav, P.K., Tiwari, A., Singh, P.: Hydrodynamic permeability of a membrane built up by spheroidal particles covered by porous layer. Acta Mech. 229(4), 1869–1892 (2018). https://doi.org/10.1007/s00707-017-2054-6MathSciNetCrossRefMATH

17.

Tiwari, A., Yadav, P.K., Singh, P.: Stokes flow through assemblage of non-homogeneous porous cylindrical particles using cell model technique. Natl. Acad. Sci. Lett. 41(1), 53–57 (2018). https://doi.org/10.1007/s40009-017-0605-yMathSciNetCrossRef

18.

Mishra, V., Gupta, B.R.: Drag experienced by a composite sphere in an axisymmetric creeping flow of micropolar fluid. J. Appl. Fluid Mech. 11, 995–1004 (2018). https://doi.org/10.29252/jafm.11.04.27870CrossRef

19.

Yadav, P.K.: Motion through a non-homogeneous porous medium: hydrodynamic permeability of a membrane composed of cylindrical particles. Eur. Phys. J. Plus 133, 1–26 (2018). https://doi.org/10.1140/epjp/i2018-11804-8CrossRef

20.

Tiwari, A., Shah, P.D., Chauhan, S.S.: Analytical study of micropolar fluid flow through porous layered micro vessels with heat transfer approach. Eur. Phys. J. Plus 135(2), 1–32 (2020). https://doi.org/10.1140/epjp/s13360-020-00128-xCrossRef

21.

Yadav, P.K., Tiwari, A., Singh, P.: Motion through spherical droplet with non-homogenous porous layer in spherical container. Appl. Math. Mech. 41, 1069–1082 (2020). https://doi.org/10.1007/s10483-020-2628-8MathSciNetCrossRefMATH

22.

Stewartson, K.: Motion of a sphere through a conducting fluid in the presence of a strong magnetic field. Math. Proc. Camb. Philos. Soc. 52, 301–316 (1956). https://doi.org/10.1017/S0305004100031285MathSciNetCrossRefMATH

23.

Rudraiah, N., Ramaiah, B.K., Rajasekhar, B.M.: Hartmann flow over a permeable bed. Int. J. Eng. Sci. 13, 1–24 (1975). https://doi.org/10.1016/0020-7225(75)90070-1CrossRefMATH

24.

Devi, S.P.A., Raghavachar, M.R.: Magnetohydrodynamic stratified flow past a sphere. Int. J. Eng. Sci. 20, 1169–1177 (1982). https://doi.org/10.1016/0020-7225(82)90097-0CrossRefMATH

25.

Cramer, K.R., Pai, S.I.: Magnetofluid dynamics for engineers and applied physicists. MacGraw-Hill, New York (1973)

26.

Davidson, P.A.: An introduction to magnetohydrodynamics. Cambridge University Press, London (2001)CrossRef

27.

Geindreau, C., Auriault, J.L.: Magnetohydrodynamic flows in porous media. J. Fluid Mech. 466, 343–363 (2002). https://doi.org/10.1017/S0022112002001404MathSciNetCrossRefMATH

28.

Jayalakshmamma, D.V., Dinesh, P.A., Sankar, M.: Analytical study of creeping flow past a composite sphere: solid core with porous shell in presence of magnetic field. Mapana J. Sci. 10, 11–24 (2011). https://doi.org/10.12723/mjs.19.2CrossRef

29.

Srivastava, B.G., Yadav, P.K., Deo, S., Singh, P.K., Filippov, A.: Hydrodynamic permeability of a membrane composed of porous spherical particles in the presence of uniform magnetic field. Colloid J. 76, 725–738 (2014). https://doi.org/10.1134/S1061933X14060167CrossRef

30.

Verma, V.K., Singh, S.K.: Magnetohydrodynamic flow in a circular channel filled with a porous medium. J. Porous Media. 18, 923–928 (2015). https://doi.org/10.1615/JPorMedia.v18.i9.80CrossRef

31.

Yadav, P.K., Deo, S., Singh, S.P., Filippov, A.: Effect of magnetic field on the hydrodynamic permeability of a membrane built up by porous spherical particles. Colloid J. 79, 160–171 (2017). https://doi.org/10.1134/S1061933X1606020XCrossRef

32.

Ansari, I.A., Deo, S.: Magnetohydrodynamic viscous fluid flow past a porous sphere embedded in another porous medium. Spec. Top. Rev. Porous Media 9, 191–200 (2018). https://doi.org/10.1615/SpecialTopicsRevPorousMedia.v9.i2.70CrossRef

33.

Saad, E.I.: Effect of magnetic fields on the motion of porous particles for happel and Kuwabara models. J. Porous Media. 21, 637–664 (2018). https://doi.org/10.1615/JPorMedia.v21.i7.50CrossRef

34.

Madasu, K.P., Bucha, T.: Effect of magnetic field on the steady viscous fluid flow around a semipermeable spherical particle. Int. J. Appl. Comput. Math. 5, 1–10 (2019). https://doi.org/10.1007/s40819-019-0668-1MathSciNetCrossRefMATH

35.

Yadav, P.K.: Influence of magnetic field on the stokes flow through porous spheroid: Hydrodynamic permeability of a membrane using cell model technique. Int. J. Fluid Mech. Res. 47, 273–290 (2020). https://doi.org/10.1615/InterJFluidMechRes.2020030464CrossRef

36.

Yadav, P.K., Jaiswal, S., Puchakatla, J.Y., Yadav, M.K.: Flow through membrane built up by impermeable spheroid coated with porous layer under the influence of uniform magnetic field: effect of stress jump condition. Eur. Phys. J. Plus 136, 1–34 (2021). https://doi.org/10.1140/epjp/s13360-020-00990-9CrossRef

37.

Madasu, K.P., Bucha, T.: Effect of magnetic field on the slow motion of a porous spheroid: Brinkman’s model. Arch. Appl. Mech. 91, 1739–1755 (2021). https://doi.org/10.1007/s00419-020-01852-7CrossRef

Title: Magnetic effect on the creeping flow around a slightly deformed semipermeable sphere
Authors: Ravendra Prasad Namdeo
Bali Ram Gupta
Publication date: 27-10-2021
Publisher: Springer Berlin Heidelberg
Published in: Archive of Applied Mechanics / Issue 1/2022
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI: https://doi.org/10.1007/s00419-021-02053-6

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