Natural convection heat transfer of nanofluids in annular spaces between horizontal concentric cylinders

Natural convection heat transfer of nanofluids in annular spaces between long horizontal concentric cylinders maintained at different uniform temperatures is investigated theoretically. The main idea upon which the present work is based is that nanofluids behave more like single-phase fluids rather than like conventional solid–liquid mixtures. This assumption implies that all the convective heat transfer correlations available in the literature 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 used for the evaluation of the nanofluid effective thermal conductivity and dynamic viscosity. Conversely, the other effective properties are computed by the traditional mixing theory. The heat transfer enhancement that derives from the dispersion of nano-sized solid particles into the base liquid is calculated for different operating conditions, nanoparticle diameters, and combinations of solid and liquid phases. The fundamental result obtained is the existence of an optimal particle loading for maximum heat transfer. In particular, for any assigned combination of suspended nanoparticles and base liquid, it is found that the optimal volume fraction increases as the nanofluid average temperature increases and the nanoparticle size decreases.