Asymptotic solution for pressure-driven flows of magnetic fluids in pipes

This work focuses on laminar pipe-flows of a magnetic fluid composed of super-paramagnetic particles. The deviations from the equilibrium magnetization arise due to vorticity effects on the flow. In the regime of small deviations of magnetization, the problem is reduced to a weakly nonlinear ordinary differential equation for the velocity. The resulting equation is solved by a regular perturbation method, and explicit expressions for the velocity profile and the friction factor of the flow are presented as a function of magnetic and hydrodynamic physical parameters.