TABLE I.

Material properties used in the simulation.^23,33

Symbol	Description	Value
$M_s$	Residual magnetization of the magnet	1.05 × 1$0^6$ A/m
$c_0$	Original ferrofluid concentration (1× EMG 408)	1.2%
d	Diameter of magnetic nanoparticles in ferrofluids	10 nm
$M_d$	Saturation moment of magnetic nanoparticles in ferrofluids	4.38 × 1$0^5$ A/m
$\eta$	Dynamic viscosity of ferrofluids	1.05 × 1$0^{-3}$ kg/ms
$\rho$	Mass density of ferrofluids	1070 kg/${\mathrm{m}}^3$