Comment on "model for heat conduction in nanofluids".

In a recent Letter, Kumar et al. [1] introduced a model for heat conduction in nanofluids (liquid suspensions of nanosized particles) that was capable of describing experimental results on thermal conductivity of nanofluids. The model was built in two steps. In the first step, a static problem (immobile particles) was considered in which the total heat flux was a sum of heat conduction by the liquid and particles. In the second step, the effective thermal conductivity of nanoparticles was calculated in terms of their Brownian motion and the kinetic theory of heat flow. The authors claimed that the resulting formula for the thermal conductivity, using parameters consistent with reasonable physical assumptions, quantitatively described the experimental data. In this Comment we point out that the treatment of the Brownian motion by the authors of the Letter requires an unphysical assumption about the nanoparticle mean free path and thus overestimates the contribution of Brownian motion to heat flow by several orders of magnitude, thus invalidating the physical justification for the proposed model. According to the kinetic theory of heat flow, in agreement with Eq. (9) and the last paragraph on page 3 of the Letter [1], the contribution of Brownian motion of nano-particles to the thermal conductivity, p , is given by [2] p ˆ 1 3 nlc p ; (1) where n is the number particle density, l is the particle mean free path, is the average velocity, and c p is the heat capacity per particle. In the estimate of p the authors of the Letter [1] use the velocity that is the ratio of the particle size to time of the diffusive motion over which the particle moves by its size. However, to reach high values of p the authors estimate the mean free path l to be of the order of 1 cm. This assumption is not only unphysical but also inconsistent with the authors reasoning, since the elementary treatment of the diffusive motion leads to the diffusion constant D being proportional to l. For internal consistency , with the authors' definition of the velocity, the mean free path should be equal to the particle size. Considering that the particle size is 10 nm, the effective p would be 6 orders of magnitude smaller than estimated by the authors , thus effectively irrelevant for the heat transport characteristics. A similar conclusion is reached with a more rigorous treatment …