Ferrofluid flow over a rotating disk with sinusoidal vertical reciprocation

The current study investigates ferrofluid flow over a rotating disk undergoing sinusoidal vertical reciprocation. Oscillatory slip is introduced to represent the wobbling nature of the disk, while a magnetic field-dependent (MFD) viscosity is incorporated to mitigate this effect. By applying similarity transformations, the coupled transport equations for flow and heat transfer are reduced to a system of nonlinear ordinary differential equations and computed through a built-in MATLAB solver. Representative plots of velocity fields, streamlines, isotherms, velocity, and thermal profiles are provided to demonstrate the physical mechanisms. The results show that the MFD parameter acts as a stabilizer with damping fluctuations in velocity and temperature distributions. Enhanced disk reciprocation consistently amplifies velocity magnitude, where streamline patterns exhibiting sharper bending and greater outward momentum transport under stronger reciprocation. The oscillatory amplitude of radial velocity is suppressed under stronger ferromagnetic interactions. Disk rotation strengthens tangential transport through centrifugal shear, and reciprocation and oscillatory slip enhance thermal transport. Moreover, increasing oscillatory slip produces a distinctive horseshoe-shaped high-shear region for the skin friction coefficient. These findings highlight the practical control strategies for ferrofluidic devices such as magnetic dampers, adaptive lubrication systems, vibration-responsive cooling, and microfluidic mixers.