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Combined effect of viscosity variation and non-Newtonian Rabinowitsch fluid in wide parallel rectangular-porous plate with squeeze-film characteristics

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Abstract

The present article carries out the study of viscosity variation of non-Newtonian fluid with the homogeneous porous wall on wide parallel rectangular-plate based on the Rabinowitsch fluid model. The non-linear modified Reynolds equation is derived for the lubrication of rectangular squeeze film bearing with viscosity variation and porous parameter. Using the Morgan–Cameron approximation, the nonlinear Reynolds-type equation for squeeze-film which governs the film pressure is solved within the fundamentals of small perturbation technique. The characteristic of the wide parallel rectangular-porous plate is numerically computed for different physical quantities such as film pressure, load carrying capacity and response time. Moreover, as limiting cases some of the results from the available literature are recovered also. Further, the findings reveal that the viscosity variation of non-Newtonian fluid and the presence of porous wall lead to reduction in the load capacity and the response time respectively. Here, the porous matrix consists of a system of capillaries of very small radii with the homogeneous porous wall. The impact of porosity is incorporated as a result it acts as self-lubrication on bearing surface. Also, the effect of viscosity variation is one of the most important characteristics of fluid which helps in the design of bearings for lubrication in engineering and industrial applications.

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Abbreviations

\(D,\,a\) :

Width and length of the plate

\(h_{0} ,\,h_{1}\) :

Inlet and outlet film thickness

\(h\) :

Film thickness

\(h^{ * }\) :

Dimensionless film thickness defined in Eq. (23)

\({{dh} \mathord{\left/ {\vphantom {{dh} {dt}}} \right. \kern-0pt} {dt}}\) :

Squeeze velocity

\(x,\,z\) :

Horizontal and vertical rectangular coordinates

\(x^{ * }\) :

Non-dimensional coordinate defined in Eq. (23)

\(w_{H}\) :

Velocity of a through-flow on the upper bound of the porous layer

\(u,\,w\) :

Velocity components in \(x\) and \(z\) directions

\(u_{p} ,\,w_{p}\) :

Axial and radial velocity component the porous region

\(H_{0}\) :

Porous pad thickness

\(H_{0}^{ * }\) :

Dimensionless porous pad thickness defined in Eq. (23)

\(R\) :

The radius of the capillary tube

\(R^{ * }\) :

Dimensionless radius of the capillary tube defined in Eq. (23)

\(k\) :

Nonlinear factor accounting for non-Newtonian effects

\(Q\) :

Viscosity variation factor

\(\bar{p}\) :

Pressure in the porous region

\(p\) :

Film pressure

\(P^{ * }\) :

Dimensionless film pressure defined in Eq. (23)

\(W\) :

Load carrying capacity

\(W^{ * }\) :

Dimensionless load-carrying capacity defined in Eq. (33)

\(t\) :

Squeeze response time

\(t^{ * }\) :

Dimensionless squeeze response time defined in Eq. (34)

\(\mu_{0} ,\,\mu_{1}\) :

Inlet and outlet viscosity coefficient

\(\mu\) :

Viscosity of the Newtonian fluid

\(\tau_{xz}\) :

Shear stress

\(\psi\) :

Permeability of the fluid the porous region

\(\phi\) :

Coefficient of porosity

\(\beta\) :

Dimensionless non-linear factor defined in Eq. (23)

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Acknowledgements

The authors wish to express sincere thanks to the Department of Mathematics & Computing IIT (ISM), Dhanbad-826004 for providing the necessary facilities. A. K. Rahul expresses his gratitude to Nagmani Prasad (IIT Dhn) for his healthy discussion to bring the manuscript in the present form. P. S. Rao acknowledges the financial support of 25 (0252)/16/EMR-II Project financed by CSIR (Council of Scientific & Industrial Research), India.

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  1. Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, 826004, India

    P. S. Rao & A. K. Rahul

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  1. P. S. Rao
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Rao, P.S., Rahul, A.K. Combined effect of viscosity variation and non-Newtonian Rabinowitsch fluid in wide parallel rectangular-porous plate with squeeze-film characteristics. Meccanica 54, 2399–2409 (2019). https://doi.org/10.1007/s11012-019-01092-2

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