Skip to main content
SpringerLink
Log in

Flow and heat transfer in porous squeeze film of ferro-nanofluid with couple stresses

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

Flow and heat transfer of an incompressible ferro-nanofluid squeeze film with couple stresses and an external magnetic field in a porous geometry is theoretically studied. Based on the Neuringer–Rosensweig model for ferro-hydrodynamics and Stokes’ microcontinuum theory accounting for the couple stresses, the governing Navier–Stokes’ equations for the fluid region are determined. The governing equations for the porous region are obtained based on the modified Darcy law. Further, Beavers–Joseph tangential velocity slip condition is considered at the fluid–porous interface and the problem is solved using a regular perturbation method. Two important applications taken into consideration are the bio-lubrication in articular cartilages with small permeabilities and ferro-hydrodynamic lubrication in porous bearings with comparatively large permeabilities. The combined effects of various parameters such as couple stress parameter, magnetization parameter, Darcy number, microstructure-pore size ratio, Beavers–Joseph constant, Prandtl number, Eckert number and heat generation or absorption parameter on the flow behavior, contact time, mean temperature and heat transfer rate are investigated assuming a constant force squeezing state. The results are compared with the results of existing literature and are found to agree well.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

References

  1. Ramanaiah, G., Dubey, J.N.: Micropolar fluid lubricated squeeze films and thrust bearings. Wear 32(3), 343–351 (1975)

    Article  Google Scholar 

  2. Usha, R., Vimala, P.: Magnetohydrodynamic disk braking. J. Appl. Math. Mech. 78(4), 283–288 (1998)

    MathSciNet  MATH  Google Scholar 

  3. Bhat, M.V., Deheri, G.M.: Magnetic-fluid based squeeze film in curved porous circular discs. J. Magn. Magn. Mater. 127(1–2), 159–162 (1993)

    Article  MATH  Google Scholar 

  4. Shah, R.C., Patel, N.I., Kataria, R.C.: Some porous squeeze film-bearings using ferrofluid lubricant: a review with contributions. Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol. 230(9), 1157–1171 (2016)

    Article  Google Scholar 

  5. Shimpi, M.E., Deheri, G.M.: Surface roughness and elastic deformation effects on the behaviour of the magnetic fluid based squeeze film between rotating porous circular plates with concentric circular pockets. Tribol. Ind. 32(2), 21–30 (2010)

    Google Scholar 

  6. Vimala, P., Sumathi, G.: Couple stress fluids in porous circular squeeze films. Appl. Math. Sci. 9(65), 3227–3237 (2015)

    Google Scholar 

  7. Beavers, G.S., Joseph, D.D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30(1), 197–207 (1967)

    Article  Google Scholar 

  8. Kapur, V.K., Agarwal, M.: Poroelastic effects on the performance of synovial joints. Wear 71(3), 283–291 (1981)

    Article  Google Scholar 

  9. Sinha, P., Singh, C.: Lubrication of a cylinder on a plane with a non-Newtonian fluid considering cavitation. J. Lubr. Technol. 104(2), 168–172 (1982)

    Article  Google Scholar 

  10. Collins, R.: A model of lubricant gelling in synovial joints. J. Appl. Math. Phys. 33(1), 93–123 (1982)

    MATH  Google Scholar 

  11. Hou, J.S., Holmes, M.H., Lai, W.M., Mow, V.C.: Boundary conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications. J. Biomech. Eng. 111(1), 78–87 (1989)

    Article  Google Scholar 

  12. Knox, D.J., Wilson, S.K., Duffy, B.R., McKee, S.: Porous squeeze-film flow. IMA J. Appl. Math. 80(2), 376–409 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  13. Karmakar, T., Raja Sekhar, G.P.: Squeeze-film flow between a flat impermeable bearing and an anisotropic porous bed. Phys. Fluids 30(4), 043604-1–043604-17 (2018)

  14. Neuringer, J.L., Rosensweig, R.E.: Ferrohydrodynamics. Phys. Fluids 7(12), 1927–1937 (1964)

    Article  MathSciNet  Google Scholar 

  15. Verma, P.D.S.: Magnetic fluid-based squeeze film. Int. J. Eng. Sci. 24(3), 395–401 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  16. Bujurke, N.M., Kudenatti, R.B., Awati, V.B.: Effect of surface roughness on squeeze film poroelastic bearings with special reference to synovial joints. Math. Biosci. 209(1), 76–89 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Ahmad, N., Singh, J.P.: A model for couple-stress fluid film mechanism with reference to human joints. Proc. Inst. Mech. Eng. Part J.: J. Eng. Tribol. 221(6), 755–759 (2007)

    Article  Google Scholar 

  18. Vashi, Y.D., Patel, R.M., Deheri, G.M.: Ferrofluid based squeeze film lubrication between rough stepped plates with couple stress effect. J. Appl. Fluid Mech. 11(3), 597–612 (2018)

    Article  Google Scholar 

  19. Celik, I., Ozturk, H.K.: Heat transfer and velocity in the squeezing flow between two parallel disks by Gegenbauer Wavelet Collocation Method. Arch. Appl. Mech. 91(1), 443–461 (2021)

    Article  Google Scholar 

  20. Fardi, M., Pishkar, I., Alidousti, J., Khan, Y.: Numerical investigation of the MHD suction-injection model of viscous fluid using a kernel-based method. Arch. Appl. Mech. 91(10), 4205–4221 (2021)

    Article  Google Scholar 

  21. Zhang, G., Tong, B., Zhang, X., Wang, T., Yin, Y.: Thermo-hydrodynamic modeling and analysis for circular bilayer self-lubricating bearing. J. Braz. Soc. Mech. Sci. Eng. 42(1), 1–11 (2020)

    Article  Google Scholar 

  22. Bali, R., Sharma, S.K.: A model for intra-articular heat exchange in a knee joint. Tribol. Lett. 41(2), 379–386 (2011)

    Article  Google Scholar 

  23. Lu, D., Ramzan, M., Mohammad, M., Howari, F., Chung, J.D.: A thin film flow of nanofluid comprising carbon nanotubes influenced by Cattaneo–Christov heat flux and entropy generation. Coatings 9(5), 296 (2019)

    Article  Google Scholar 

  24. Huang, X., Zhang, X., Wang, Y.: Numerical simulation of ferrofluid-lubricated rough elliptical contact with start-up motion. Appl. Math. Model. 91, 232–260 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  25. Singh, J.P., Ahmad, N.: Analysis of a porous-inclined slider bearing lubricated with magnetic fluid considering thermal effects with slip velocity. J. Braz. Soc. Mech. Sci. Eng. 33, 351–356 (2011)

    Article  Google Scholar 

  26. Ram, P., Kumar, A.: Analysis of heat transfer and lifting force in a ferro-nanofluid based porous inclined slider bearing with slip conditions. Nonlinear Eng. 8, 206–215 (2019)

    Article  Google Scholar 

  27. Ram, P., Kumar, A.: Investigation of thermal effects in a ferrofluid-based porous inclined slider bearing with slip conditions. In: Numerical Heat Transfer and Fluid Flow, pp. 39–46 (2019)

  28. Ram, P., Kumar, A.: Hematite suspension based absorbent pad inclined slider influenced by slip and squeeze velocity with altering film ratio. Def. Sci. J. 71, 185–191 (2020)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Anna University, Chennai, Tamil Nadu, 600025, India

    P. Vimala & K. Manimegalai

Authors
  1. P. Vimala
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Manimegalai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Vimala.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vimala, P., Manimegalai, K. Flow and heat transfer in porous squeeze film of ferro-nanofluid with couple stresses. Arch Appl Mech 92, 3877–3895 (2022). https://doi.org/10.1007/s00419-022-02268-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-022-02268-1

Keywords

Search

Navigation