Spin-Up Ferrofluid Dynamics over an Off-Centered Rotating Rough Surface

The spin-up flow dynamics of ferrofluids provides reliable predictions for understanding the rheological behavior, heat-transfer characteristics, and stress management of ferrofluids. These properties are practically useful in applications such as magnetic cooling systems, biomedical drug targeting, seals and dampers, rotating machinery with ferrofluid lubrication, and heat-transfer devices. This study develops a theoretical framework to study the spin-up flow of a ferrofluid over an off-centered rotating rough surface under the influence of a magnetic field. Along with the conservation of mass, momentum, and energy equations, the spin-up flow equation is incorporated into the theoretical model. These equations incorporate the micropolar rheological effects of ferrofluids, including the bulk spin viscosity, shear spin viscosity, and vortex viscosity. Due to the misalignment of the center of the disk, the induced flow components are also considered in the model. The governing equations are first nondimensionalized, and then, a finite element method is used to solve them numerically. Proper validation of the numerical solution is presented in a separate section. The results for the velocity functions, induced flow, microrotation velocity function, and temperature profiles are demonstrated for various physical parameters. In addition, a comparison table for stress and heat-transfer characteristics is provided to determine the influence of different physical parameters on these quantities.