Load Bearing Capacity for a Ferrofluid Squeeze Film in Double Layered Porous Rough Conical Plates

  • Yogini D. VashiEmail author
  • Rakesh M. Patel
  • Gunamani B. Deheri
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1048)


This article goals to determine the enactment of double layered porous rough conical plates with ferrofluid based squeeze film lubrication. The Neuringer–Roseinweig model has been employed for magnetic fluid flow. For the characterization of roughness two different forms of polynomial distribution function have been used and comparison is made between both roughness structure. The stochastic model of Christensen and Tonder regarding transverse roughness has been invoked to develop the associated Reynolds’ equation from which the pressure circulation is found. This provides growth to the calculation of load-bearing capacity. From the graphical appearance it is established that from the design point of view roughness pattern G1 is more suitable compared to G2. The results presented here confirm that the introduction of double layered plates results in improved load carrying capacity. This is further enhanced by the ferrofluid lubrication. Further, the roughness affects the bearing system significantly, however, the situation enhanced in the case of negatively skewed roughness. A noticeable fact is that the porosity of the outer layer influences more as compared to the inner layer even in the presence of mild magnetic strength.


Squeeze film Conical plates Roughness Ferrofluid Load carrying capacity 


\( a \)

Dimension of bearing (mm)

\( \varvec{h} \)

Uniform fluid film thickness(mm)

\( h \)

Mean film thickness

\( h_{s} \)

Deviation from the mean film thickness

\( \mathop {h_{0} }\limits^{ \bullet } \)

Normal velocity of bearing surface

\( H_{1} \)

The thickness of the inner layer of the porous plate (mm)

\( H_{2} \)

The thickness of the outer layer of the porous plate (mm)

\( \overline{H} \)

Magnetic field vector

\( p \)

Pressure distribution(N/m2)

\( \overline{p} \)

Non dimensional Pressure distribution

\( W \)

Load carrying capacity (N)

\( \overline{W} \)

Non dimensional Load bearing capacity

\( \eta \)

Dynamic viscosity of fluid (NS/m2)

\( \mu_{0} \)

Permeability of free space (N/A2)

\( \overline{\mu } \)

Magnetic susceptibility of magnetic field

\( \sigma \)

Standard deviation (mm)

\( \alpha \)

Variance (mm)

\( \varepsilon \)

Skewness (mm)

\( \phi_{1} \)

The permeability of the inner layer (m2)

\( \phi_{2} \)

The permeability of the outer layer (m2)

\( \psi_{1} \)

Porosity of inner layer

\( \psi_{2} \)

Porosity of outer layer

\( \alpha^{*} \)

Non dimensional variance

\( \varepsilon^{*} \)

Non dimensional skewness

\( \sigma^{*} \)

Non dimensional standard deviation

\( \rho \)

Density of fluid

\( \overline{q} \)

Velocity of fluid

\( \eta \)

Fluid viscosity

\( \overline{M} \)

Magnetization vector



The authors would like to thank both the reviewers and the editor for their fruitful comments and constructive suggestions for improving the overall presentation and quality of the article.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Yogini D. Vashi
    • 1
    Email author
  • Rakesh M. Patel
    • 2
  • Gunamani B. Deheri
    • 3
  1. 1.Department of Applied Sciences and HumanityAlpha College of Engineering and TechnologyKhatraj, KalolIndia
  2. 2.Department of MathematicsGujarat Arts and Science CollegeAhmedabadIndia
  3. 3.Department of MathematicsSardar Patel UniversityVallabh VidyanagarIndia

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