Buoyancy-induced convection from a pair of heated and cooled horizontal circular cylinders inside an adiabatic tilted cavity filled with alumina/water nanofluids

This paper aims to investigate numerically buoyancy-induced convection from a pair of differentially heated horizontal circular cylinders set side by side in a nanofluid-filled adiabatic square enclosure, inclined with respect to gravity so that the heated cylinder is located below the cooled one, using a two-phase model based on the double-diffusive approach assuming that the 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 a computational code based on the SIMPLE-C algorithm. Numerical simulations are performed for Al₂O₃ + H₂O nanofluids using the average volume fraction of the suspended solid phase, the tilting angle of the enclosure, the nanoparticle size, the average nanofluid temperature and the inter-cylinder spacing, as independent variables.

The main results obtained may be summarized as follows: at high temperatures, the nanofluid heat transfer performance relative to that of the pure base liquid increases with increasing the average volume fraction of the suspended solid phase, whereas at low temperatures it has a peak at an optimal particle loading; the relative heat transfer performance of the nanofluid has a peak at an optimal tilting angle of the enclosure; the relative heat transfer performance of the nanofluid increases notably as the average temperature is increased, and just moderately as inter-cylinder spacing is increased and the nanoparticle size is decreased.

The two-phase computational code used in the present study incorporates three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity and the coefficient of thermophoretic diffusion, all based on a high number of literature experimental data.