Natural convection from a pair of differentially-heated horizontal cylinders aligned side by side in a nanofluid-filled inclined 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 cylinders aligned side by side in a nanofluid-filled inclined square enclosure, assuming 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. Numerical simulations are executed for alumina-water nanofluids, using the average volume fraction of the suspended nanoparticles, the tilting angle of the enclosure, and the average temperature as independent variables. It is found that the impact of the nanoparticle dispersion into the base liquid increases remarkably with increasing the average temperature, whereas, by contrast, the other controlling parameters have moderate effects. Moreover, an optimal tilting angle of the cavity and an optimal particle loading for maximum heat transfer are detected for the several configurations investigated.