Effect of Slip Velocity on a Ferrofluid-Based Longitudinally Rough Porous Plane Slider Bearing

  • Mohmmadraiyan M. MunshiEmail author
  • A. R. Patel
  • G. M. Deheri
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1048)


This paper studies the changes on a Ferrofluid (FF)-based longitudinally rough porous plane slider bearing (PSB) caused by the slip velocity (SV). The impact of magnetic fluid (MF) lubrication has been analyzed by using the Neuringer and Rosensweig model. The changes exerted by longitudinal roughness have been studied using the stochastic averaging model of Christensen and Tonder. The effects of SV are calculated by using the slip model of Beavers–Joseph. The pressure distribution (PD) expression has been calculated by solving the related nondimensional Reynolds’ type equation. These calculations have been used to calculate the load carrying capacity (LCC). According to the results, LCC increases due to MF lubricant. The surface roughness, on the other hand, has a negative impact on the performance. The same goes for the SV. However, it has been found that these adversities caused by surface roughness, SV, and porosity can be partially neutralized by the positive impact of magnetization, though it can be said that SV in general decreases the bearing performance.


Slip velocity Magnetic fluid Load carrying capacity 


\( h \)

Film thickness (mm)

\( \overline{h} \)

Mean film thickness (mm)

\( h_{s} \)

Deviation from mean level

\( \varvec{H} \)

Nondimensional film thickness

\( H_{0} \)

Thickness of porous facing (mm)

\( \overline{H} \)

Magnetic field (Gauss)

\( H^{2} \)

Magnitude of magnetic field (N/A.m)

\( p \)

Pressure found in the area covered by the film (N/mm2)

\( \overline{p} \)

Anticipated degree of pressure

\( P \)

Nondimensional pressure generated due to the film

\( Q \)

Integrating constant

\( \overline{S} \)

Slip parameter

\( u,v,w \)

Fluid film velocity components in \( x,y,z \) directions, respectively

\( W \)

Load capacity (N)

\( \overline{W} \)

Nondimensional load capacity

\( \alpha \)

Variance (mm)

\( \overline{\alpha } \)

Nondimensional variance

\( \varepsilon \)

Skewness (mm3)

\( \overline{\varepsilon } \)

Skewness in dimensionless form

\( \mu_{0} \)

Permeability of the free space (N/A2)

\( \overline{\mu } \)

Magnetic susceptibility of particles

\( \mu^{ * } \)

Dimensionless magnetization parameter

\( \sigma \)

Standard deviation (mm)

\( \overline{\sigma } \)

Dimensionless standard deviation

\( \phi \)

Permeability of porous facing (m2)

\( \psi \)




The authors acknowledge with regards the constructive comments, fruitful suggestions and remarks of the reviewer/Editor, leading to an overhauling of the materials presented in the paper.


  1. 1.
    Murti, P.R.K.: Analysis of porous slider bearings. Wear 28(1), 131–134 (1974)CrossRefGoogle Scholar
  2. 2.
    Patel, K.C., Gupta, J.L.: Hydrodynamic lubrication of a porous slider bearing with slip velocity. Wear 85(3), 309–317 (1983)CrossRefGoogle Scholar
  3. 3.
    Tichy, J.A., Chen, S.H.: Plane slider bearing load due to fluid inertia-experiment and theory. J. Tribol. 107(1), 32–38 (1985)CrossRefGoogle Scholar
  4. 4.
    Patel, S.J., Deheri, G.M., Patel, J.R.: Ferrofluid lubrication of a rough porous hyperbolic slider bearing with slip velocity. Tribol. Ind. 36(3), 259–268 (2014)Google Scholar
  5. 5.
    Patel, P.A., Deheri, G.M., Patel, A.R.: The performance of an idealized rough porous hydrodynamic plane slider bearing. Int. J. Appl. Math. Sci. 8(3), 187–196 (2015)Google Scholar
  6. 6.
    Tzeng, S.T., Saibel, E.: Surface roughness effect on slider bearing lubrication. ASLE Trans. 10(3), 334–338 (1967)CrossRefGoogle Scholar
  7. 7.
    Andharia, P.I., Gupta, J.L., Deheri, G.M.: Effect of longitudinal surface roughness on hydrodynamic lubrication of slider bearings. In: Proceedings of Tenth International Conference on Surface Modification Technologies, pp. 872–880. The Institute of Materials, Singapore (1997)Google Scholar
  8. 8.
    Andharia, P.I., Gupta, J.L., Deheri, G.M.: On the shape of the lubricant film for the optimum performance of a longitudinal rough slider bearing. Ind. Lubr. Tribol. 52(6), 273–276 (2000)CrossRefGoogle Scholar
  9. 9.
    Chiang, H.L., Hsu, C.H., Chou, T.L., Hsu, C.H., Lin, J.R.: Surface roughness effects on the dynamic characteristics of finite slider bearings. J. Chung Cheng Inst. Technol. 34(1), 1–11 (2005)Google Scholar
  10. 10.
    Christensen, H., Tonder, K.C.: Tribology of rough surfaces: stochastic models of hydrodynamic lubrication. SINTEF Report No. 10/69–18 (1969a)Google Scholar
  11. 11.
    Christensen, H., Tonder, K.C.: Tribology of rough surfaces: parametric study and comparison of lubrication model. SINTEF Report No. 22/69–18 (1969b)Google Scholar
  12. 12.
    Christensen, H., Tonder, K.C.: The hydrodynamic lubrication of rough bearing surfaces of finite width. In: ASME-ASLE Lubrication Conference, Cincinnati, Ohio, USA (1970)Google Scholar
  13. 13.
    Deheri, G.M., Andharia, P.I., Patel, R.M.: Longitudinally rough slider bearings with squeeze film formed by a magnetic fluid. Ind. Lubr. Tribol. 56(3), 177–187 (2004)CrossRefGoogle Scholar
  14. 14.
    Patel, J.R., Deheri, G.M.: Magnetic fluid based squeeze film in a rough porous parallel plate slider bearing. Ann. Facul. Eng. Hunedoara-Int. J. Eng. 9(3), 443–463 (2011)Google Scholar
  15. 15.
    Patel, N.D., Deheri, G.M., Patel, H.C.: Magnetic fluid lubrication of a rough, porous composite slider bearing. Int. J. Surf. Eng. Interdiscip. Mater. Sci. 1(2), 46–65 (2013)CrossRefGoogle Scholar
  16. 16.
    Panchal, G.C., Patel, H.C., Deheri, G.M.: Influence of magnetic fluid through a series of flow factors on the performance of a longitudinally rough finite slider bearing. Global J. Pure Appl. Math. 12(1), 783–796 (2016)Google Scholar
  17. 17.
    Patel, J.R., Deheri, G.M.: The effect of slip velocity on the ferrofluid based squeeze film in longitudinally rough conical plates. J. Serb. Soc. Comput. Mech. 10(2), 18–29 (2016)CrossRefGoogle Scholar
  18. 18.
    Shukla, J.B., Kumar, D.: A theory for ferromagnetic lubrication. J. Mag. Mag. Mater. 65(2–3), 375–378 (1987)CrossRefGoogle Scholar
  19. 19.
    Bagci, C., Singh, A.P.: Hydrodynamic lubrication of finite slider bearing: effect of one dimensional film shape and their computer aided optimum designs. J. Lubr. Technol. 105(1), 48–66 (1983)CrossRefGoogle Scholar
  20. 20.
    Pinkus, O., Sternlicht, B.: Theory of Hydrodynamic Lubrication. McGraw Hill Book Company, New York (1961)zbMATHGoogle Scholar
  21. 21.
    Andharia, P.I., Gupta, J.L., Deheri, G.M.: Effect of surface roughness on hydrodynamic lubrication of slider bearings. Tribol. Trans. 44(2), 291–297 (2001)CrossRefGoogle Scholar
  22. 22.
    Hamrock, B.J.: Fundamentals of Fluid Film Lubrication. McGraw Hill, New York (1994)Google Scholar
  23. 23.
    Morgan, V.T., Cameron, A.: Mechanism of lubrication in porous metal Bearings. In: Proceedings of Conference on Lubrication and Wear. Institution of Mechanical Engineers, London (1957)Google Scholar
  24. 24.
    Patel, N.S., Vakharia, D.P., Deheri, G.M.: A study on the performance of a magnetic fluid based hydrodynamic short porous journal bearing. J. Serb. Soc. Comput. Mech. 6(2), 28–44 (2012)Google Scholar
  25. 25.
    Bhat, M.V., Deheri, G.M.: Porous composite slider bearing lubricated with magnetic fluid. Jpn. J. Appl. Phys. 30(10), 2513–2514 (1991)CrossRefGoogle Scholar
  26. 26.
    Neuringer, J.L., Rosensweig, R.E.: Magnetic fluids. Phys. Fluids 7(12), 1927–1937 (1964)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Shah, R.C., Bhat, M.V.: Ferrofluid lubrication in porous inclined slider bearing with velocity slip. Int. J. Mech. Sci. 44(12), 2495–2502 (2002)CrossRefGoogle Scholar
  28. 28.
    Snyder, W.T.: The magnetohydrodynamic slider bearing. J. Basic Eng. 84(1), 197–202 (1962)CrossRefGoogle Scholar
  29. 29.
    Shimpi, M.E., Deheri, G.M.: Effect of bearing deformation on the performance of a magnetic fluid-based infinitely rough short porous journal bearing. In: Proceedings of International Conference on Advances in Tribology and Engineering Systems-SPRINGER, Gujarat, India, pp. 19–34, Gujarat Technological University (2013)Google Scholar
  30. 30.
    Lin, J.R.: Dynamic characteristics of magnetic fluid based sliding bearings. Mechanika 19(5), 554–558 (2013)CrossRefGoogle Scholar
  31. 31.
    Sparrow, E.M., Beavers, G.S., Hwang, I.T.: Effect of velocity slip on porous walled squeeze films. J. Lubr. Technol. 94(3), 260–265 (1972)CrossRefGoogle Scholar
  32. 32.
    Deheri, G.M., Patel, R.U.: Effect of slip velocity on the performance of a short bearing lubricated with a magnetic fluid. Acta Polytechn. 53(6), 890–894 (2013)CrossRefGoogle Scholar
  33. 33.
    Shukla, S.D., Deheri, G.M.: Effect of slip velocity on magnetic fluid lubrication of rough porous Rayleigh step bearing. J. Mech. Eng. Sci. 4, 532–547 (2013)CrossRefGoogle Scholar
  34. 34.
    Munshi, M.M., Patel, A.R., Deheri, G.M.: Effect of slip velocity on a magnetic fluid based squeeze film in rotating transversely rough curved porous circular plates. Ind. Eng. Lett. 7(8), 28–42 (2017)Google Scholar
  35. 35.
    Patel, N.D., Deheri, G.M.: Effect of surface roughness on the performance of a magnetic fluid based parallel plate porous slider bearing with slip velocity. J. Serb. Soc. Comput. Mech. 5(1), 104–118 (2011)Google Scholar
  36. 36.
    Andharia, P.I., Deheri, G.M.: Performance of a magnetic fluid based longitudinally rough plane slider bearing. Indian Str. Res. J. 4(4), 1–8 (2014)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Alpha College of Engineering and TechnologyGujarat Technological UniversityKalolIndia
  2. 2.Vishwakarma Government Engineering CollegeGujarat Technological UniversityAhmedabadIndia
  3. 3.Sardar Patel UniversityVallabh VidyanagarIndia

Personalised recommendations