Numerical evaluation of the ferrofluid behaviour under the influence of three-dimensional non-uniform magnetic field

Abstract

Ferrofluids have always been the centre of interest for a broad range of applications where the flow manipulation is achieved using different types of magnetic fields. In the present work, a Finite Volume Method based numerical study is performed to investigate the ferrofluid behaviour in the laminar flow regime using the complete set of Ferrohydrodynamics equations. Four distinct single layer finite solenoids of different Ls/Ds (length to diameter ratio) are considered to replicate a 3D (three-dimensional) non-uniform magnetic field, and a twofold validation is also reported to authenticate the generated field distributions. Moreover, a magnetic field dependent viscosity model is used to take into account the variation of ferrofluid viscosity in the presence of a non-uniform magnetic field. To accommodate the varying particle size distribution of ferrofluid, an effective relaxation time constant is used that can accurately predict the magnetization using Debye relaxation mechanism. The obtained flow characteristics are then further discussed and compared along with the case of stationary ferrofluid for all solenoid configurations. New insights about the flow structures are provided using the λ2 criteria of vortex identification technique and the critical point theory analysis. It is observed that each solenoid arrangement have a distinct magnetic field distribution which leads to the occurrence of unique vortex structures and fluid deformations. Also, different flow trajectories are noticed within the fluid domain owing to the peculiar distribution of Kelvin force density. Results from the present work have direct implications in all ferrofluid based momentum transport devices and can be effectively used to further improve our understanding about their performances.