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Hydromagnetic Squeeze Film in a Longitudinally Rough Conducting Conical Plates

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Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1057))

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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.

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Abbreviations

x, y:

Cartesian coordinates

H :

Lubricant film thickness

\(\dot{h}\) :

Squeeze film velocity

μ :

Viscosity

B 0 :

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.

References

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Acknowledgements

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

Author information

Authors and Affiliations

  1. Department of Mathematics, Hemchandracharya North Gujarat University, Patan, Gujarat, 384 265, India

    Jatinkumar V. Adeshara & M. B. Prajapati

  2. Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Gujarat, 388 120, India

    G. M. Deheri & R. M. Patel

  3. Gujarat Arts and Science College, Ellis bridge, Ahmedabad, Gujarat, 380 006, India

    R. M. Patel

Authors
  1. Jatinkumar V. Adeshara
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  2. M. B. Prajapati
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  3. G. M. Deheri
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  4. R. M. Patel
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Corresponding author

Correspondence to R. M. Patel .

Editor information

Editors and Affiliations

  1. Department of Mathematics, National Institute of Technology Silchar, Silchar, Assam, India

    Kedar Nath Das

  2. Department of Mathematics, South Asian University, New Delhi, Delhi, India

    Jagdish Chand Bansal

  3. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Kusum Deep

  4. Department of Mathematics, Faculty of Science, Liverpool Hope University, Liverpool, UK

    Atulya K. Nagar

  5. School of Electrical Engineering, VIT University, Vellore, Tamil Nadu, India

    Ponnambalam Pathipooranam

  6. School of Electrical Engineering, VIT University, Vellore, Tamil Nadu, India

    Rani Chinnappa Naidu

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Adeshara, J.V., Prajapati, M.B., Deheri, G.M., Patel, R.M. (2020). Hydromagnetic Squeeze Film in a Longitudinally Rough Conducting Conical Plates. In: Das, K., Bansal, J., Deep, K., Nagar, A., Pathipooranam, P., Naidu, R. (eds) Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 1057. Springer, Singapore. https://doi.org/10.1007/978-981-15-0184-5_10

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