A Non-Homogeneous Equilibrium Model for Convective Transport in Flowing Nanofluids

Abstract

A base fluid (e.g., water, ethanol, oil) in which nano-sized (1–100 nm) particles of a different material are dispersed, is known as a nanofluid. Nanofluids are attractive because the presence of the nanoparticles enhances energy transport considerably. As a result, nanofluids have higher thermal conductivity and single-phase heat transfer coefficients than their base fluids. In particular, the heat transfer coefficient increases appear to go beyond the mere thermal-conductivity effect, and cannot be predicted by traditional pure-fluid correlations such as Dittus-Boelter’s. In the nanofluid literature this behavior is generally attributed to thermal dispersion and intensified turbulence, brought about by nanoparticle motion. To test the validity of this assumption, we have considered seven slip mechanisms that can produce a relative velocity between the nanoparticles and the base fluid. These are inertia, Brownian diffusion, thermophoresis, diffusiophoresis, Magnus effect, fluid drainage and gravity. We concluded that, of these seven, only Brownian diffusion and thermophoresis are important slip mechanisms in nanofluids. Based on this finding, we developed a two-component four-equation non-homogeneous equilibrium model for mass, momentum and heat transport in nanofluids. A non-dimensional analysis of the equations suggests that energy transfer by nanoparticle dispersion is negligible, and thus cannot explain the abnormal heat transfer coefficient increases. Furthermore, a comparison of the nanoparticle and turbulent eddy scales clearly indicates that the nanoparticles move homogeneously with the fluid in the presence of turbulent eddies, so an effect on turbulence intensity is also doubtful.