Heat transfer features of buoyancy-driven nanofluids inside rectangular enclosures differentially heated at the sidewalls

The heat transfer features of buoyancy-driven nanofluids inside rectangular enclosures differentially heated at the vertical walls, are investigated theoretically. The main idea upon which the present work is based is that nanofluids behave more like a single-phase fluid rather than a conventional solid-liquid mixture, which implies that all the convective heat transfer correlations available for single-phase flows can be extended to nanoparticle suspensions, provided that the thermophysical properties appearing in them are the nanofluid effective properties calculated at the reference temperature. In this connection, two empirical equations, based on a wide variety of experimental data reported in the literature, are developed for the evaluation of the nanofluid effective thermal conductivity and dynamic viscosity, whereas the other effective properties are evaluated by the conventional mixing theory. The heat transfer enhancement across the differentially heated enclosure that derives from the dispersion of nano-sized solid particles into a host liquid is calculated for different operating conditions, nanoparticle diameters, combinations of suspended nanoparticles and base liquid, and cavity aspect ratios. The fundamental result obtained is the existence of an optimal particle loading for maximum heat transfer. Specifically, for any assigned combination of solid and liquid phases, the optimal volume fraction is found to increase slightly with decreasing the nanoparticle size, and to increase much more remarkably with increasing both the nanofluid average temperature and the slenderness of the enclosure.