Thermal conductivity enhancement of magnetic fluids under magnetic field based on percolation theory

Abstract

Controversy exists over how the magnetic field (MF) enhances the thermal conductivity (TC) of magnetic fluids. We explain the MF enhancement of the ferrofluid TC using four key parameters based on percolation theory. The percolation of magnetic particles is governed by the particle size distribution, particle volume fraction, magnetic dipole-dipole coupling constant, and Langevin parameter. The magnitudes of the coupling constant and Langevin parameter have been used to indicate the possibility of long chain aggregate formation in MF. Given a fixed magnetization, the coupling constant and Langevin parameter are linearly proportional to the particle volume. Larger particles can more easily form long chain aggregates. In addition, chain aggregates form quickly at a higher volume fraction because the particle-particle collision frequency is quadratically proportional to the number concentration, which is proportional to the volume fraction. However, the particle size and volume fraction should be limited to prevent sedimentation or a significant increase in viscosity.