Magnetization diffusion in duct flow: The magnetic entrance length and the interplay between hydrodynamic and magnetic timescales

Abstract

In this work, computational fluid dynamics simulations of a ferrofluid plane Poiseuille flow in the presence of a constant applied magnetic field are performed. The orientation of the field is perpendicular to the direction of the flow. An original numerical methodology for calculating magnetic and hydrodynamic fields is proposed, including an important discussion about an identified magnetization entrance region. Three different magnetization models are considered to calculate the magnetization field. These models are implemented and validated according to analytic and asymptotic theories, including the one developed in this manuscript. Discrepancies between the models are discussed and interpreted physically. An intricate balance between different physical mechanisms is shown to be responsible for a diffusive-like behavior of the magnetization field. This balance is governed by a competition between the flow’s vorticity and the mechanisms of magnetic relaxation. The physical parameters responsible for this non-equilibrium magnetization dynamics are identified and interpreted using the problem’s timescales. It seems that the combination of three different timescales governs the dynamics of non-equilibrium magnetization: the Brownian diffuse timescale, a hydrodynamic (convective) timescale, and a controllable magnetic timescale associated with the intensity of the applied magnetic field. The results indicate toward the possibility of controlling the development of the flow’s magnetization field through the applied magnetic field, particle size distribution, fluid concentration, and flow rate. In addition, several results are presented regarding the fully developed flow, including magnetization profiles and angles between the applied field H and the magnetization field M.