A theoretical investigation of magnetohydrodynamics, couple stress and viscosity variation on squeeze film lubrication between a cylinder and rough porous flat surface

Authors

  • Suresha Ramareddy Department of Mathematics, Jain (Deemed-to-be University), Kanakapura Taluk, Ramanagara District 562112, Karnataka, India
  • Arunkumar Rudrappa Department of Mathematics, Sai Vidya Institute of Technology, Bangalore 560064, Karnataka, India
  • Bannihalli Naganagowda Hanumagowda Department of Mathematics, GM University, Davangere 577006, Karnataka, India
  • Subramanya Raghavendra Department of Mechanical Engineering, Sai Vidya Institute of Technology, Bangalore 560064, Karnataka, India

DOI:

https://doi.org/10.24425/ather.2025.156845

Keywords

magnetohydrodynamics, porous rough surface, viscosity variation

Abstract

Squeeze film lubrication involving couple stress fluids, viscosity variation and magnetohydrodynamics is critically important for high-performance applications in automotive systems, aerospace mechanisms and biomedical devices. This study aims to examine the combined influence of these effects on lubrication performance between a cylinder and a rough porous flat surface. To achieve this, we developed a generalised modified Reynolds equation by integrating Christensen’s stochastic model for surface roughness, Darcy’s law for porous media flow, and Stokes flow theory. This equation was solved with appropriate boundary conditions to derive analytical expressions for pressure, enabling the calculation of load-carrying capacity and squeeze film time for both longitudinal and transverse roughness patterns. Key findings demonstrate that couple stress, magnetohydrodynamics effects, and viscosity variation significantly enhance pressure distribution, increasing load-carrying capacity by up to 85.29% and squeeze film time by up to 85.34% under optimal conditions. Notably, longitudinal roughness pattern degrades tribological performance, whereas transverse roughness pattern enhances it. Furthermore, three-dimensional analysis demonstrates that optimal tuning of roughness and porosity parameters maximises the system performance. These findings, validated against established results like Lin et al. [31], provide valuable design guidelines for optimising tribological systems in fields requiring precise and durable lubrication, particularly in precision manufacturing and microelectromechanical systems.

References

[1] Bujurke, N. M., Naduvinamani, N. B., & Basti, D. P. (2007). Effect of surface roughness on the squeeze film lubrication between curved annular plates. Industrial Lubrication and Tribology, 59(4), 178–185. doi:10.1108/00368790710753572

[2] Christensen, H. (1969). Stochastic models for hydrodynamic lubrication of rough surfaces. Proceedings of the Institution of Mechanical Engineers, 184(1), 1013–1026. doi:10.1243/PIME_PROC_1969_184_074_02

[3] Daliri, M., & Jalali-Vahid, D. (2015). Combined effects of piezo-viscous coupled stress lubricant and rotational inertia upon squeeze film performance of rough circular discs. Industrial Lubrication and Tribology, 67(6), 564–571. doi:10.1108/ILT-01-2015-0009

[4] Mouda, M., Nabhani, M., & El Khlifi, M. (2021). Surface roughness effects on non-Newtonian MHD non-parallel squeeze film bearing. Industrial Lubrication and Tribology, 73(1), 45–51. doi:10.1108/ILT-02-2020-0071

[5] Dass, T. D., Gunakala, S. R., & Comissiong, D. M. (2022). Combined effect of variable-viscosity and surface roughness on the squeeze film characteristics of infinitely wide rectangular plate with couple stress fluid, velocity-slip and ferrofluid lubricant. Materials Today: Proceedings, 56, 1717–1725. doi:10.1016/j.matpr.2021.10.355

[6] Ullah, I., Rahim, M. T., Khan, H., & Qayyum, M. (2016). Analytical analysis of squeezing flow in porous medium with MHD effect. University of Bucharest Scientific Bulletin Series A: Applied Mathematics and Physics, 78(2), 281–292.

[7] Johny, A., Sujatha, E., & Sree, M. G. (2024). Effect of MHD on porous circular stepped plate lubricated with micropolar fluid. IAENG International Journal of Applied Mathematics, 54(9), 1847–1854.

[8] Yadav, P. K., & Srivastava, P. (2024). Impact of porous material and slip condition on the MHD flow of immiscible couple stress-Newtonian fluids through an inclined channel: Head loss and pressure difference. Chinese Journal of Physics, 89, 1198–1221. doi:10.1016/j.cjph.2024.03.046

[9] Patel, N. C., Patel, J. R., & Deheri, G. M. (2023). An effect of a porous structure, slip velocity and Rosensweig’s viscosity on the ferrofluid based squeeze film in porous curved annular plates. Journal of Nanofluids, 12(2), 498–505. doi:10.1166/jon.2023.1906

[10] Khan, M. S., Shah, R. A., & Khan, A. (2019). Effect of variable magnetic field on the flow between two squeezing plates. The European Physical Journal Plus, 134(5), 219. doi:10.1140/epjp/i2019-12595-0

[11] Patel, S. J., & Deheri, G. (2023). Slip effect on Shliomis model based magnetic fluid lubrication of a squeeze film in circular cylinder near a plane. Acta Technica Corviniensis – Bulletin of Engineering, 16(4).

[12] Lin, J. R., Chu, L. M., Hung, C. R., & Wang, P. Y. (2013). Derivation of two-dimensional couple-stress hydromagnetic squeeze film Reynolds equation and application to wide parallel rectangular plates. Meccanica, 48(1), 253–258. doi:10.1007/s11012-012-9613-7

[13] Nabhani, M., & El Khlifi, M. (2016). Non-Newtonian inertial magnetohydrodynamic porous squeeze film lubrication between circular discs. Tribology International, 94, 373–382. doi:10.1016/j.triboint.2015.09.047

[14] Ramasamy, P. (2020). Effects of magnetic force and non-Newtonian characteristics on squeeze film bearings. Asia-Pacific Journal of Chemical Engineering, 15(5), e2510. doi:10.1002/apj.2510

[15] Jyothi, V., Hanumagowda, B. N., & Verma, A. (2023). Analysis of pressure load-carrying capacity and squeezing time on magnetohydrodynamic couple stress fluid flow between sphere and flat plate with slip velocity. International Journal of Modern Physics B, 38(26), 2450349. doi:10.1142/S0217979224503491

[16] Prakash, J., & Tiwari, K. (1985). Effect of surface roughness on the squeeze film between rotating porous annular discs with arbitrary porous wall thickness. International Journal of Mechanical Sciences, 27(3), 135–144. doi:10.1016/0020-7403(85)90054-2

[17] Shah, R. C. (2022). Ferrofluid lubrication of porous-rough circular squeeze film bearings. The European Physical Journal Plus, 137(2), 1–16. doi:10.1140/epjp/s13360-022-02344-z

[18] Thakkar, P. L., & Patel, H. C. (2020). Effect of surface roughness on characteristics of magnetic fluid based squeeze film between porous circular plates. Journal of the Serbian Society for Computational Mechanics, 14(1), 90–98. doi:10.24874/jsscm.2020.14.01.08

[19] Vadher, P. A., Deheri, G., & Patel, R. M. (2008). The effect of surface roughness on the performance of hydromagnetic squeeze films between two conducting rough porous elliptical plates. Turkish Journal of Engineering and Environmental Sciences, 32(4), 219–227.

[20] Deheri, G. M., & Patel, J. R. (2011). Magnetic fluid based squeeze film in a rough porous parallel plate slider bearing. Annals of the Faculty of Engineering Hunedoara, 9(3), 443–448.

[21] Anthony, J., & Elamparithi, S. (2023). Effect of MHD and surface roughness on porous step-slider bearing lubricated with couple-stress fluid. International Journal of Heat and Technology, 41(1), 135–142. doi:10.18280/ijht.410114

[22] Ali, N., Khan, S. U., Sajid, M., & Abbas, Z. (2016). MHD flow and heat transfer of couple stress fluid over an oscillatory stretching sheet with heat source/sink in porous medium. Alexandria Engineering Journal, 55(2), 915–924. doi:10.1016/j.aej.2016.02.018

[23] Naduvinamani, N. B., & Siddangouda, A. (2007). Combined effects of surface roughness and couple stresses on squeeze film lubrication between porous circular stepped plates. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 221(4), 525–534. doi:10.1243/13506501JET204

[24] Vashi, Y., Patel, R. M., & Deheri, G. M. (2018). Ferrofluid based squeeze film lubrication between rough stepped plates with couple stress effect. Journal of Applied Fluid Mechanics, 11(3), 597–612. doi:10.29252/jafm.11.03.27854

[25] Prakash, J., & Gururajan, K. (1999). Effect of velocity slip in an infinitely long rough porous journal bearing. Tribology Transactions, 42(3), 661–667. doi:10.1080/10402009908982267

[26] Rahul, A. K., & Rao, P. S. (2021). Rabinowitsch fluid flow with viscosity variation: Application of porous rough circular stepped plates. Tribology International, 154, 106635. doi:10.1016/j.triboint.2020.106635

[27] Sangeetha, S., & Kesavan, S. (2018). Pressure distribution with surface roughness effect between porous infinitely long rectangular plates with MHD couple stress squeeze film lubrication. IOP Conference Series: Journal of Physics: Conference Series, 1000, 012006. doi:10.1088/1742-6596/1000/1/012006

[28] Masood, F. A., & Elamparithi, S. (2023). Effects of surface roughness and MHD on squeeze film characteristics for various finite porous plate geometries with couple-stress fluid. International Journal of Heat and Technology, 41(3), 730–736. doi:10.18280/ijht.410328

[29] Sangeetha, S., Govindarajan, A., & Sujatha, E. (2020). Effect of roughness on porous triangular plates with MHD and viscosity variation. AIP Conference Proceedings, 2277, 030019. doi:10.1063/5.0025774

[30] Sekar, S., Nathan, S. L., & Saravanathan, L. P. (2022). Velocity slip with viscosity variation for rough porous circular stepped plates using couple stress fluid. Mathematical Modelling of Engineering Problems, 9(6), 1631–1638. doi:10.18280/mmep.090624

[31] Lin, J. R., Liao, W. H., & Hung, C. R. (2004). The effects of couple stresses in the squeeze film characteristics between a cylinder and a plane surface. Journal of Marine Science and Technology, 12(2).

[32] Kumar, S., & Sachidananda, S. V. (1979). Effects of viscosity variation and surface roughness in short journal bearings. Wear, 52(2), 341–346. doi:10.1016/0043-1648(79)90071-1

[33] Rajashekar, M., & Kashinath, B. (2012). Effect of surface roughness on MHD couple stress squeeze-film characteristics between a sphere and a porous plane surface. Advances in Tribology, 2012, 935690. doi:10.1155/2012/935690

[34] Baksh, S. A., & Naganagowda, H. B. (2022). Study of surface roughness with MHD and couple stress fluid on porous curved annular plates. Acta Polytechnica, 62(6), 574–588. doi:10.14311/AP.2022.62.0574

[35] Barus, C. (1891). Note on the Dependence of Viscosity on Pressure and Temperature. Proceedings of the American Academy of Arts and Sciences, 27, 13–18. doi:10.2307/20020462

[36] Barus, C. (1893). Isothermals, Isopiestics and Isometrics Relative to Viscosity. American Journal of Science, Series 3, 45(266), 87–96. doi:10.2475/ajs.s3-45.266.87

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Published

2025-12-30

How to Cite

Ramareddy, Suresha, et al. “A Theoretical Investigation of Magnetohydrodynamics, Couple Stress and Viscosity Variation on Squeeze Film Lubrication Between a Cylinder and Rough Porous Flat Surface”. Archives of Thermodynamics, vol. 46, no. 4, Dec. 2025, pp. 141-56, doi:10.24425/ather.2025.156845.

Issue

Vol. 46 No. 4 (2025)

Section

Articles