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Nowadays, the use of Newtonian fluid as a lubricant is diminishing day by day, and the use of non-Newtonian fluids has gained importance. This paper presents an analysis of the static characteristics of Rayleigh step slider bearing lubricated with non-Newtonian Rabinowitsch fluid, which has not been studied so far. The purpose of this paper is to derive the modified Reynolds equation for Rabinowitsch fluids for two regions and to obtain the optimum bearing parameters for the Rayleigh step slider bearings.

The governing equations relevant to the problem under consideration are derived. The modified Reynolds equation is derived, and it is found to be highly non-linear and hence small perturbation method is adopted to find solution.

From this study it is found that there is an increase in the load-carrying capacity, pressure and frictional coefficients for dilatant fluids as compared to the corresponding Newtonian case. Further, for dilatant lubricants the maximum load-carrying capacity is attained for the slightly larger values of entry region length of Rayleigh step bearing as compared to Newtonian and pseudoplastic lubricants.

Rabinowitsch fluid is used for the study of lubrication characteristics of Rayleigh step bearings. The author believes that the paper presents these results for the first time.

This paper aims to present a numerical model to examine the finite magneto-hydrodynamic (MHD) journal bearings performances including both non-Newtonian couple stress and bearing deformation impacts.

Based upon the MHD and Stokes theories, a novel expression of modified Reynolds equation including bearing deformation is obtained. The bearing elastic deformation impact is predicted by means of the Winkler model. Using the numerical differentiation approach, the film pressure is iteratively solved. Different bearing characteristics are then numerically calculated. The validity of the proposed model was verified by comparing with some particular cases from literature.

From the numerical presented results, it is demonstrated that the conducting couple stress lubricant with an applied radial magnetic field results in an induced electric current density and thus significantly improves the performances of elastic journal bearings. Particularly, the load-carrying capacity is increased, whereas a reduction in friction factor is observed.

This numerical model is original, which combines both non-Newtonian couple stress and bearing deformation impacts on finite MHD journal bearings performances. It provides useful information in designing MHD journal bearings, given the lack of experimental studies.