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Abstract

This study investigates the steady rotation of a sphere in a viscous fluid with constant angular velocity, a phenomenon crucial for understanding thermal instability in rotating systems affected by viscosity. Theoretical analysis reveals that temperature increase at the sphere's surface, at the fluid-solid interface, is unstable and leads to spontaneous temperature escalation. We demonstrate that this temperature increase is a nonlinear process. Furthermore, we establish that the sphere's surface temperature should rise due to frictional effects as it moves through the dense medium. Employing the Navier-Stokes equations and the unsteady heat equation, we elucidate the significantly nonlinear nature of the unsteady heat process. Finally, we derive a general formula for fluid flows and present the results graphically.

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Constant rotation stickiness temperature angular velocity nonlinearity contact boundary

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