Study of Longitudinal Roughness on Hydromagnetic Squeeze Film Between Conducting Rotating Circular Plates

  • Jatinkumar V. Adeshara
  • M. B. Prajapati
  • G. M. Deheri
  • R. M. PatelEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1057)


This investigation addresses the problem of squeeze film with electrical conduction between longitudinally rough surfaces and electrical lubricant in the existence of a transverse magnetic field for rotating circular plates. The surfaces are taken to be longitudinally rough in nature. In view of Christensen and Tonder’s stochastic averaging method, the arbitrary irregularity of the bearing surfaces is modeled by a stochastic arbitrary inconstant with non-zero variance, skewness, and mean. The Reynolds’ type equation for the distribution of pressure is stochastically averaged with regards to the arbitrary roughness constraint. A solution for SF pressure is obtained by using suitable Reynolds’ type BC, which is further used to calculate the LBC. Based on the results obtained, the bearing is generally suffering due to longitudinal roughness. On the whole, the hydromagnetic effect characterized by the Hartmann number produces an increase in LCC as compared to the classical NL case. However, in the case of (−ve) roughness (skewed) in particular, the condition can be retrieved to some extent when (−ve) variance occurs by selecting the appropriate plate conductivity and standard deviation.


Load-bearing capacity Circular plates Longitudinal roughness Rotation Hydromagnetization 



Radial coordinate


Plate’s radius


Velocity of squeeze film


Transverse magnetic field applied between the plates


Initial film thickness


Lubricant film thickness


Electrical conductivity of the lubricant




\(B_{ 0} h\left( {\frac{s}{\mu }} \right)^{ 1 / 2}\) = Hartmann number

\(h_{ 0}^{{\prime }}\)

Lower plate’s width surface

\(h_{ 1}^{{\prime }}\)

Upper plate’s width surface


Lower surface’s electrical conductivity


Upper surface’s electrical conductivity


\(\frac{{s_{ 0} h_{ 0}^{{\prime }} }}{sh}\) = Lower surface’s electrical permeability


 = \(\frac{{s_{ 1} h_{ 1}^{{\prime }} }}{sh}\) = Upper surface’s electrical permeability


Density of lubricant


Upper plate’s angular velocity


Lower plate’s angular velocity


Ωu − Ωl


Ωlu—Rotation ratio


 = \(- \frac{{h^{ 3} \rho \,\Omega _{u}^{ 2} }}{{\mu \dot{h}}}\) = rotational inertia in non-dimensional form


Pressure of Lubricant


Load-carrying capacity


Non-dimensional standard deviation (σ/h)


Dimensionless variance (α/h)


Dimensionless skewness (ε/h3)


Dimensionless pressure


Dimensionless load-carrying capacity


Load-carrying capacity


Load-bearing capacity




Hydrodynamic lubrication


Hydromagnetic squeeze film


Magnetic fluid


Boundary conditions.



Comments and constructive suggestions for improving the overall quality of this article have been acknowledged.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Jatinkumar V. Adeshara
    • 1
  • M. B. Prajapati
    • 1
  • G. M. Deheri
    • 2
  • R. M. Patel
    • 3
    Email author
  1. 1.Mathematics DepartmentH. N. G. UPatanIndia
  2. 2.Mathematics DepartmentS. P. UVallabh VidyanagarIndia
  3. 3.AhmedabadIndia

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