Slow flow of couple stress fluid past a cylinder embedded in a porous medium: slip effect

• Autorzy: Sarkar Priya , Madasu Krishna Prasad

Identyfikatory

DOI

10.24423/EngTrans.2707.20231010

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

couple stress fluid; cylinder; Brinkman’s equation; saturated porous medium; slip coefficients; drag force

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2023
• Tom: Vol. 71, iss. 4
• Strony: 537--551
• Opis fizyczny: Bibliogr. 39 poz., rys., wykr.

Twórcy

autor

Sarkar Priya

• Department of Mathematics, National Institute of Technology Raipur, 492010, Chhattisgarh, India

autor

Madasu Krishna Prasad

• Department of Mathematics, National Institute of Technology Raipur, 492010, Chhattisgarh, India

Bibliografia

• 1. Pop I., Ingham D.B., Convective heat transfer: mathematical and computational modelling of viscous fluids and porous media, Elsevier Science, 2001.
• 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, doi: 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, doi: 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, doi: 10.1016/0021-9797(90)90110-A.
• 9. Auriault J.L., On the domain of validity of Brinkman’s equation, Transport in Porous Media, 79(2): 215–223, 2009, doi: 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, doi: 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, doi: 10.1016/0020-7225(92)90058-O.
• 12. Wang C.Y., Darcy-Brinkman flow with solid inclusions, Chemical Engineering Communications, 197(3): 261–274, 2009, doi: 10.1080/00986440903088603.
• 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, doi: 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, doi: 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, doi: 10.1093/imamat/ hxz020.
• 16. Stokes V.K., Couple stresses in fluids, [in:] Theories of Fluids with Microstructure, pp. 34– 80, Springer, 1984, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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: 10.1063/1.1432696.
• 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, doi: 10.1088/0034-4885/68/12/R05.
• 30. Navier C.L.M.H., Me´moire sur les lois du Mouvement dea Fluides, M´emoires 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 10.1103/Phys RevE.101.063105.
• 39. Happel J., Brenner H., Low Reynolds number hydrodynamics with special applications to particulate media, Springer Science & Business Media, 2012.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).