Theory for anisotropic thermal conductivity of magnetic nanofluids

Abstract

Effective thermal conductivity tensor for magnetic nanofluids containing magnetizable nanoparticles suspended in a base liquid is theoretically investigated with a two-step homogenization method. First, we adopt differential effective medium theory to determine the equivalent thermal conductivity of magnetizable nanoparticle chains. Second, we generalize self-consistent anisotropic effective medium theory to study the effective thermal conductivity tensors of magnetic nanofluids. Numerical results show that the aspect ratio of chain-like aggregated clusters plays an important role in enhancement of anisotropic thermal conductivity. In addition, our theoretical results on the elements of thermal conductivity parallel to the fields K e z and perpendicular to the fields K e x are in good agreement with experimental data. Furthermore, we predict the nonmonotonic dependence of effective thermal conductivity on magnetic field strength, in accordance with experimental reports.