Authors
-
Priya SARKAR
National Institute of Technology,
India
0000-0003-1902-2747
-
Krishna Prasad MADASU
National Institute of Technology,
India
0000-0002-1819-3651
Abstract
An analytical study for the creeping flow of a couple stress fluid past a cylinder embedded in a porous medium is presented using the slip condition. The uniform flow is considered far away from a cylinder. The boundary conditions used are zero couple stress and tangential slip conditions. The modified Bessel functions represent the stream function (the velocity). The drag exerted on a solid cylinder immersed in a porous medium is derived. The impacts of the couple stress, permeability, and slip parameters on the normalized drag force are presented graphically. The drag forces of well-known exceptional cases are reduced. The drag force is a decreasing function of the permeability and couple stress parameters and an increasing function of the slip parameter.
Keywords:
couple stress fluid, cylinder, Brinkman’s equation, saturated porous medium, slip coefficient, drag forceReferences
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34. Madasu K.P., Sarkar P., Couple stress fluid past a sphere embedded in a porous medium, Archive of Mechanical Engineering, 69(1): 5–19, 2022, https://doi.org/10.24425/ame.2021.139314
35. Madasu K.P., Sarkar P., Slow flow past a slip sphere in cell model: magnetic effect, [In:] Recent Trends in Fluid Dynamics Research, Lecture Notes in Mechanical Engineering, Bharti R.P., Gangawane K.M. (Eds.), pp. 25–36, Springer, Singapore, 2022, https://doi.org/10.1007/978-981-16-6928-6_3
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39. Happel J., Brenner H., Low Reynolds number hydrodynamics with special applications to particulate media, Springer Science & Business Media, 2012.
2. Ehlers W., Bluhm J. [Eds.], Porous Media: Theory, Experiments and Numerical Applications, Springer Science & Business Media, 2002.
3. Bejan A., Dincer I., Lorente S., Miguel A.F., Reis H.A., Porous and Complex Flow Structures in Modern Technologies, Springer Science & Business Media, 2004.
4. Nield D.A., Bejan A., Convection in porous media, Springer, 2006.
5. Bear J., Dynamics of Fluids in Porous Media, Courier Corporation, 1988.
6. Brinkman H.C., A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Flow, Turbulence and Combustion, 1(1): 27–34, 1949, https://doi.org/10.1007/BF02120313
7. Durlofsky L., Brady J.F., Analysis of the Brinkman equation as a model for flow in porous media, The Physics of Fluids, 30(11): 3329–3341, 1987, https://doi.org/10.1063/1.866465
8. Phillips R.J, Deen W.M., Brady J.F., Hindered transport in fibrous membranes and gels: effect of solute size and fiber configuration, Journal of Colloid and Interface Science, 139(2): 363–373, 1990, https://doi.org/10.1016/0021-9797%2890%2990110-A
9. Auriault J.L., On the domain of validity of Brinkman’s equation, Transport in Porous Media, 79(2): 215–223, 2009, https://doi.org/10.1007/s11242-008-9308-7
10. Spielman L., Goren S.L., Model for predicting pressure drop and filtration efficiency in fibrous media, Environmental Science & Technology, 2(4): 279–287, 1968, https://doi.org/10.1021/es60016a003
11. Pop I., Cheng P., Flow past a circular cylinder embedded in a porous medium based on the Brinkman model, International Journal of Engineering Science, 30(2): 257–262, 1992, https://doi.org/10.1016/0020-7225%2892%2990058-O
12. Wang C.Y., Darcy-Brinkman flow with solid inclusions, Chemical Engineering Communications, 197(3): 261–274, 2009, https://doi.org/10.1080/00986440903088603 h
13. Leontev N.E., Flow past a cylinder and a sphere in a porous medium within the framework of the Brinkman equation with the Navier boundary condition, Fluid Dynamics, 49(2): 232–237, 2014, https://doi.org/10.1134/S0015462814020112
14. Madasu K.P., Srinivasacharya D., Micropolar fluid flow through a cylinder and a sphere embedded in a porous medium, International Journal of Fluid Mechanics Research, 44(3): 229–240, 2017, https://doi.org/10.1615/InterJFluidMechRes.2017015283
15. Martin P.A., Two-dimensional Brinkman flows and their relation to analogous Stokes flows, IMA Journal of Applied Mathematics, 84(5): 912–929, 2019, https://doi.org/10.1093/imamat/hxz020
16. Stokes V.K., Couple stresses in fluids, [In:] Theories of Fluids with Microstructure, pp. 34–80, Springer, 1984, https://doi.org/10.1007/978-3-642-82351-0_4
17. Murthy J.V.R., Nagaraju G., Flow of a couple stress fluid generated by a circular cylinder subjected to longitudinal and torsional oscillations, Contemporary Engineering Sciences, 2(10): 451–461, 2009.
18. Khan N.A., Mahmood A., Ara A., Approximate solution of couple stress fluid with expanding or contracting porous channel, Engineering Computations, 30(3): 399–408, 2013, https://doi.org/10.1108/02644401311314358
19. Devakar M., Sreenivasu D., Shankar B., Analytical solutions of some fully developed flows of couple stress fluid between concentric cylinders with slip boundary conditions, International Journal of Engineering Mathematics, 2014: Article ID 785396, 2014, https://doi.org/10.1155/2014/785396
20. Srinivasacharya D., Srinivasacharyulu N., Odelu O., Flow of couple stress fluid between two parallel porous plates, IAENG International Journal of Applied Mathematics, 41(2): 5, 2011.
21. Nagaraju G., Matta A., Aparna P., Heat transfer on the MHD flow of couple stress fluid between two concentric rotating cylinders with porous lining, International Journal of Advances in Applied Mathematics and Mechanics, 3(1): 77–86, 2015.
22. Adesanya S.O., Kareem S.O., Falade J.A., Arekete S.A., Entropy generation analysis for a reactive couple stress fluid flow through a channel saturated with porous material, Energy, 93(Part 1): 1239–1245, 2015, https://doi.org/10.1016/j.energy.2015.09.115
23. Hassan A.R., The entropy generation analysis of a reactive hydromagnetic couple stress fluid flow through a saturated porous channel, Applied Mathematics and Computation, 369: 124843, 2020, https://doi.org/10.1016/j.amc.2019.124843
24. Yadav D., Mahabaleshwar U.S., Wakif A., Chand R., Significance of the inconstant viscosity and internal heat generation on the occurrence of Darcy-Brinkman convective motion in a couple- stress fluid saturated porous medium: An analytical solution, International Communications in Heat and Mass Transfer, 122: 105165, 2021, https://doi.org/10.1016/j.icheatmasstransfer.2021.105165
25. Palaiah S.S., Basha H., Reddy G.J., Magnetized couple stress fluid flow past a vertical cylinder under thermal radiation and viscous dissipation effects, Nonlinear Engineering, 10(1): 343–362, 2021, https://doi.org/10.1515/nleng-2021-0027
26. Madasu K.P., Sarkar P., A study of couple stress fluid past an isotropic porous medium, Special Topics & Reviews in Porous Media: An International Journal, 13(4): 23–31, 2022, https://doi.org/10.1615/SpecialTopicsRevPorousMedia.2022043960
27. Madasu K.P., Sarkar P., An analytical study of couple stress fluid through a sphere with an influence of the magnetic field, Journal of Applied Mathematics and Computational Mechanics, 21(3): 99–110, 2022, https://doi.org/10.17512/jamcm.2022.3.08
28. Tretheway D.C., Meinhart C.D., Apparent fluid slip at hydrophobic microchannel walls, Physics of Fluids, 14(3): L9–L12, 2002, doi: 1070-6631/2002/14(3)/9/4.
29. Neto C., Evans D.R., Bonaccurso E., Butt H.J., Craig V.S.J., Boundary slip in Newtonian liquids: a review of experimental studies, Reports on Progress in Physics, 68(12): 2859–2897, 2005, https://doi.org/10.1088/0034-4885/68/12/R05
30. Navier C.L.M.H., Me ́moire sur les lois du Mouvement dea Fluides, Mémoires de l’Acade ́mie Royale de Sciences de l’Institut de France, 1823.
31. Sherief H.H., Faltas M.S., Ashmawy E.A., Nashwan M.G., Slow motion of a slip spherical particle along the axis of a circular cylindrical pore in a micropolar fluid, Journal of Molecular Liquids, 200(Part B): 273–282, 2014, https://doi.org/10.1016/j.molliq.2014.10.030
32. Ashmawy E.A., Drag on a slip spherical particle moving in a couple stress fluid, Alexandria Engineering Journal, 55(2): 1159–1164, 2016, https://doi.org/10.1016/j.aej.2016.03.032
33. Madasu K.P., Kaur M., Bucha T., Slow motion past a spheroid implanted in a Brinkman medium: slip condition, International Journal of Applied and Computational Mathematics, 7(4): 162, 2021, https://doi.org/10.1007/s40819-021-01104-4
34. Madasu K.P., Sarkar P., Couple stress fluid past a sphere embedded in a porous medium, Archive of Mechanical Engineering, 69(1): 5–19, 2022, https://doi.org/10.24425/ame.2021.139314
35. Madasu K.P., Sarkar P., Slow flow past a slip sphere in cell model: magnetic effect, [In:] Recent Trends in Fluid Dynamics Research, Lecture Notes in Mechanical Engineering, Bharti R.P., Gangawane K.M. (Eds.), pp. 25–36, Springer, Singapore, 2022, https://doi.org/10.1007/978-981-16-6928-6_3
36. Texier B.D., Ibarra A., Melo F., Helical locomotion in a granular medium, Physical Review Letters, 119(6): 068003, 2017, https://doi.org/10.1103/PhysRevLett.119.068003
37. Chen Y., Lordi N., Taylor M., Pak O.S., Helical locomotion in a porous medium, Physical Review E, 102(4): 043111, 2020, https://doi.org/10.1103/PhysRevE.102.043111
38. Nganguia H., Zhu L., Palaniappan D., Pak O.S., Squirming in a viscous fluid enclosed by a Brinkman medium, Physical Review E, 101(6): 063105, 2020, https://doi.org/10.1103/PhysRevE.101.063105
39. Happel J., Brenner H., Low Reynolds number hydrodynamics with special applications to particulate media, Springer Science & Business Media, 2012.
