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RETRACTED: Squeeze film lubrication between two different spheres: MHD- couple stress fluid model

Javeria AnjumResearch Scholar, SOAS, REVA University, Bangalore, IndiaAsem SalmaDepartment of Mathematics, SOAS, REVA University, Bangalore, IndiaB. N. HanumagowdaDepartment of Mathematics, SOAS, REVA University, Bangalore, IndiaJagadish V. TawadeDepartment of Mathematics, Vishwakarma University, Pune, IndiaOumaima SaidaniDepartment of Information Systems, College of Computer and Information Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaYahia SaidCenter for Scientific Research and Entrepreneurship, Northern Border University, 73213 Arar, Saudi ArabiaBarno AbdullaevaDepartment of Mathematics and Information Technologies, Vice-Rector for Scientific Affairs, Tashkent State Pedagogical University, Tashkent, UzbekistanNadia BatoolDepartment of Physics-Chemistry, College of Natural Sciences, University of Potsdam, GermanyM. Ijaz KhanDepartment of Mechanical Engineering, College of Engineering, Prince Mohammad Bin Fahd University, AL-Khobar, Saudi Arabia
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This study explores the squeeze film lubrication between two dissimilar spheres using a couple stress non-Newtonian fluid subjec to characteristics of an external magnetic field. A modified Reynolds-type expression is derived by applying Stokes theory alongside magneto-hydrodynamic (MHD) motion equations and the continuity eq. A closed-form expression for the squeeze film pressure is captured and used to analyse the lubrication performance. The impacts of key non-dimensional variables—including the Hartmann number, couple stress parameter, radius ratio, and film height—are thoroughly examined. The obtained outcomes show that the existence of a magnetic field significantly improves squeeze film features. Specifically, increasing the Hartmann number enhances pressure generation and load-carrying capacity due to stronger electromagnetic damping effects. The incorporation of couple stress fluid behaviour, accounting for the microstructure of the lubricant, leads to greater film stability and resistance to deformation. The radius ratio of the spherical surfaces plays a crucial role in improving lubrication efficiency, with larger values providing better performance. On the other hand, an increase in film height shows a reverse effect, lowering the squeeze film pressure and overall performance. These insights demonstrate the sensitivity of the system to both fluid properties and geometrical configurations. This work is particularly relevant to high-performance applications where precise lubrication and stability are essential. Potential applications include magnetic bearings, automotive dampers, precision manufacturing, and biomedical devices such as artificial joints and implants. The study highlights how MHD and couple stress effects can be leveraged to design more robust and efficient lubrication systems.

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