On the anisotropic thermal conductivity of magnetorheological suspensions

The thermal conductivity of an iron-based magnetorheological suspension is experimentally investigated for varying particle volume fractions and magnetic-field strengths. Under a magnetic field, the thermal-conductivity component in the field direction increases significantly (by 100% in one case), while the two components perpendicular to the field direction remain virtually unchanged. We propose and test two models for the thermal conductivity in the limiting case when the suspension’s internal structure is saturated by the imposed magnetic field. A two-level homogenization model that first uses the Bruggeman method to calculate the effective conductivity of particle chains, and then an effective-medium theory model to determine the overall conductivity of the suspension, is found to fit accurately the components of the thermal-conductivity tensor. Utilizing this modeling procedure, we determine the effective conductivity of the field-induced, iron-particle chains to be 0.966 W/mK at saturation. This conductivity is equivalent to a particle volume fraction within the chains of φint=0.495, which is smaller than the φint=0.698 predicted for an ideal body-centered-tetragonal arrangement of particles. This suggests that the microstructure in this case differs from perfectly aligned crystals, having either lattice defects or otherwise waviness in the particle chains.