Optimal formulation of nanofluids for maximum free convection heat transfer from horizontal isothermal cylinders

Free convection heat transfer in nanofluids from horizontal isothermal cylinders is investigated theoretically. The main idea upon which the present work is based is that nanofluids behave more like a single-phase fluid rather than like a conventional solid-liquid mixture. 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 proposed 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, the nanoparticle size decreases, and the Rayleigh number of the base fluid decreases.