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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)

Abstract

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.

Keywords

Load-bearing capacity Circular plates Longitudinal roughness Rotation Hydromagnetization 

Nomenclature

r

Radial coordinate

a

Plate’s radius

\(\dot{h}\)

Velocity of squeeze film

B0

Transverse magnetic field applied between the plates

h0

Initial film thickness

h

Lubricant film thickness

s

Electrical conductivity of the lubricant

μ

Viscosity

M

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

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

Lower plate’s width surface

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

Upper plate’s width surface

s0

Lower surface’s electrical conductivity

s1

Upper surface’s electrical conductivity

ϕ0(h)

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

ϕ1(h)

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

ρ

Density of lubricant

Ωu

Upper plate’s angular velocity

Ωl

Lower plate’s angular velocity

Ωr

Ωu − Ωl

Ωf

Ωlu—Rotation ratio

S

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

p

Pressure of Lubricant

w

Load-carrying capacity

σ*

Non-dimensional standard deviation (σ/h)

α*

Dimensionless variance (α/h)

ε*

Dimensionless skewness (ε/h3)

P

Dimensionless pressure

W

Dimensionless load-carrying capacity

LCC

Load-carrying capacity

LBC

Load-bearing capacity

MHD

Magnetohydrodynamic

HL

Hydrodynamic lubrication

HSF

Hydromagnetic squeeze film

MF

Magnetic fluid

BC

Boundary conditions.

Notes

Acknowledgements

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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