Bell wavelet operational matrix integration method for dynamically loaded couple stress journal bearings lubricated with nanofluids using the Brinkman viscosity model

This paper investigates the lubrication performance of dynamically loaded journal bearings lubricated with couple stress nanofluids. The modified Reynolds equation is formulated using the couple stress fluid theory together with the Brinkman nanofluid viscosity model, which accounts for the influence of nanoparticle interactions on the effective lubricant viscosity. The resulting nonlinear governing equation is solved using the Bell Wavelet Operational Matrix of Integration (BWOMI) method. The effects of the couple stress parameter, eccentricity ratio, and dynamic load parameter on pressure distribution, load-carrying capacity, attitude angle, and friction coefficient are systematically examined. The results show that increasing the couple stress parameter enhances hydrodynamic pressure generation and improves the load-carrying capacity of the bearing due to the strengthening of the lubricant film. An increase in eccentricity ratio leads to higher pressure development and greater load support owing to the reduction in minimum film thickness, while dynamic loading significantly influences pressure distribution, attitude angle, and friction characteristics. The analysis further indicates that both the attitude angle and friction coefficient are sensitive to variations in eccentricity ratio, couple stress effects, and dynamic loading conditions, reflecting their important role in determining bearing operating performance. Compared with the conventional lubricant, the nanofluid model exhibits an increase of up to 16.73% in hydrodynamic pressure and load-carrying capacity under the operating conditions considered. Furthermore, the enhanced effective viscosity of the nanofluid improves lubricant film integrity and overall bearing performance. The computational results demonstrate that the BWOMI technique provides accurate, stable, and efficient solutions for nonlinear lubrication problems involving complex rheological behavior. Therefore, the proposed methodology offers a reliable numerical framework for the analysis of tribological systems lubricated with couple stress nanofluids.