Effect of Brownian motion on thermal conductivity of nanofluids

Nanofluids, i.e. colloidal suspensions comprised of nanometer sized metallic or non-metallic solid particles show a remarkable increase in thermal conductivity compared to that of the pure base liquid. Conventional continuum based theoretical models for finding the effective thermal conductivity of solid-liquid suspensions underestimate this increase, and as a result several other potential mechanisms including Brownian motion, liquid layering, nanoparticle clustering and ballistic heat transport have been proposed.; This work analyzes the role of Brownian motion and interparticle potential on the thermal conductivity enhancement of nanofluids. A general expression for the effective thermal conductivity of a colloidal suspension is derived by using ensemble averaging under the assumption of small departures from equilibrium and the presence of pair-wise additive interaction potential between the nanoparticles. The resulting expression for the thermal conductivity enhancement is applied to the nanofluids with a polar base fluid, such as water or ethylene glycol, by assuming an effective double layer repulsive potential between pairs of nanoparticles. It is shown that the model predicts a particle size and temperature dependent thermal conductivity enhancement. The results of the calculation are compared with the experimental data for various nanofluids containing metallic and non-metallic nanoparticles.; The theoretical analysis is further extended to model heat transfer in carbon nanotube suspensions by treating nanotubes as straight rigid rods. The macroscopic contribution to the effective thermal conductivity is computed by replacing infinitely thin rigid rods by a series of spheres. The hydrodynamic contribution is obtained by accounting for the Brownian relaxation of both position and rotational coordinates of the center of mass of the nanotube.