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Hydromagnetic Squeeze Film in a Longitudinally Rough Conducting Conical 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)

Abstract

This article wishes to study the presentation of the longitudinally rough and hydromagnetically conducting conical plates. Here, both the plates are chosen to be conducting electrically while an electrically conducting lubricant fills the clearance space between the plates. A transverse magnetic field is applied. Christensen and Tonder’s used stochastic averaging process regarding roughness, the associated stochastically averaged Reynolds’ type equation is resolved. This gives pressure and consequently, the load taking capacity. It is indicated by the graphical results that an augmented performance is registered by the bearing system in comparison with traditional fluid-based lubrication. The results demonstrate that longitudinal roughness is more helpful as compared to transverse roughness. Here, the role of standard deviation remains crucial even if suitable numerical values of the angle of the cone are considered. Thus, this investigation gives ample measures for bettering the bearing performance with appropriate choice of hydromagnetization and conductivity parameters.

Keywords

Conical plates Squeeze film with hydromagnetization Longitudinal roughness Electrical conductivity Load bearing capacity 

Nomenclature

x, y

Cartesian coordinates

H

Lubricant film thickness

\(\dot{h}\)

Squeeze film velocity

μ

Viscosity

B0

Applied (transverse) magnetic field between both plates

s

Lubricant conductivity

M

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

ω

Cone’s Vertical angle

p

Lubricant pressure

w

Load bearing capacity

σ*

Standard deviation in non-dimensional form (σ/h)

α*

Non-dimensional variance (α/h)

ε*

Skewness in non-dimensional form (ε/h3)

P

Dimensionless pressure

W

Dimensionless load bearing capacity.

Notes

Acknowledgements

Fruitful comments and constructive suggestions for improving the quality of the article are acknowledged with thanks.

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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
    • 2
    • 3
    Email author
  1. 1.Department of MathematicsHemchandracharya North Gujarat UniversityPatanIndia
  2. 2.Department of MathematicsSardar Patel UniversityVallabh VidyanagarIndia
  3. 3.Gujarat Arts and Science CollegeAhmedabadIndia

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