Particle concentration and tube size dependence of viscosities of Al2O3-water nanofluids flowing through micro- and minitubes

Abstract

An experimental and theoretical investigation has been performed on the effective viscosity of Al2O3-water nanofluids flowing through micrometer- and millimeter-sized circular tubes in the fully developed laminar flow regime. We have discovered that the effective viscosity of Al2O3-water nanofluids increases nonlinearly with the volume concentration of nanoparticles even in the very low range of 0.02–0.3vol% and strongly depends on the ratio of the nanoparticle diameter to the tube diameter. We have developed a modified Einstein model that accounts for the slip mechanism in nanofluids. The new model captures these new rheological features of nanofluids.

Response to “Comment on ‘Particle concentration and tube size dependence of viscosities of Al2O3-water nanofluids flowing through micro-and minitubes’” [Appl. Phys. Lett. 94, 066101 (2009)]

“…Thus, the ag- gregation theory is not applicable to the nanofluids used in the work of Jang et al. 1 Furthermore, the mean diameter of 26.7 nm obtained from TEM measurement is slightly smaller than that of 30 nm provided by the nanoparticle supplier. Therefore, the nanoparticles used by Jang et al 1 are approximately seven to ten times smaller than the mean diameter of the aggregates 225 nmϽ D a Ͻ 315 nm as unrealistically estimated by Ayela and Chevalier.…”

“…1 Furthermore, the mean diameter of 26.7 nm obtained from TEM measurement is slightly smaller than that of 30 nm provided by the nanoparticle supplier. Therefore, the nanoparticles used by Jang et al 1 are approximately seven to ten times smaller than the mean diameter of the aggregates 225 nmϽ D a Ͻ 315 nm as unrealistically estimated by Ayela and Chevalier. 2 The volume fraction of aggregates a can be calculated from the following equation: 6…”

“…1 In this response paper, we address the two main issues raised in the comment of Ayela and Chevalier. 2 First, Ayela and Chevalier argued that we have severely underestimated the uncertainty in effective viscosity of nanofluids mainly due to a strong underestimation of the uncertainty in tube diameter.…”

“…2,5 This finding is significant in understanding how Ayela and Chevalier 2 unrealistically estimated the mean diameter of the aggregates 225 nmϽ D a Ͻ 315 nm, which led them to their wrong interpretations of the results of previous experiments. 1 Using Eq. ͑2͒ with maximum values of 1.2%, 0.2%, 0.02% and 0.03% for the measurement uncertainty u / , where represents the pressure drop, tube diameter, volumetric flow rate, and tube length, respectively, the fractional uncertainty in the effective viscosity of nanofluids is estimated to be less than 1.5%.…”

“…2 As a result, they get a mean diameter of the aggregates 225 nmϽ D a Ͻ 315 nm. However, the water-based Al 2 O 3 nanofluids used in the work of Jang et al 1 were produced in house using a two-step method.…”