Natural convection from a pair of differentially-heated horizontal cylinders aligned side by side in a nanofluid-filled square enclosure

A two-phase model based on the double-diffusive approach is used to perform a numerical study on natural convection from a pair of differentially-heated horizontal cylinders set side by side in a nanofluid-filled adiabatic square enclosure. The study is conducted under the assumption that Brownian diffusion and thermophoresis are the only slip mechanisms by which the solid phase can develop a significant relative velocity with respect to the liquid phase. The system of the governing equations of continuity, momentum and energy for the nanofluid, and continuity for the nanoparticles, is solved by the way of a computational code which incorporates three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity, and the thermophoretic diffusion coefficient, all based on a wide number of literature experimental data. The pressure-velocity coupling is handled through the SIMPLE-C algorithm. Simulations are executed for three different nanofluids, using the diameter and the average volume fraction of the suspended nanoparticles, as well as the cavity width, the inter-cylinder spacing, the average temperature of the nanofluid, and the temperature difference imposed between the cylinders, as controlling parameters, whose effects are thoroughly analyzed and discussed. It is found that the impact of the nanoparticle dispersion into the base liquid increases remarkably with increasing the average temperature, whereas it increases just moderately as the nanoparticle size decreases, as well as the imposed temperature difference and the cavity width increase. Conversely, the distance between the cylinders seems to have marginal effects. Moreover, an optimal particle loading for maximum heat transfer is detected for most configurations investigated.