Heat transfer transitions of natural convection flows in a differentially heated square enclosure filled with nanofluids

Numerical investigations are carried out for steady natural convection of Al2O3-H2O nanofluids having temperature-dependent properties inside a differentially heated square enclosure by using Buongiorno's two-phase mixture model, where Brownian diffusion and thermophoresis are regarded as the primary slip mechanisms between solid and liquid phases. Influence of the Rayleigh number on the heat transfer behavior with increasing nanoparticle volume fraction to 6%, are systematically investigated for various physical conditions, including averaged temperature, temperature difference and nanoparticle diameter. There are three scenarios in general, except the type 1 (heat transfer rate enhances continuously) and the type 3 (optimum volume fraction exists) mentioned in previous references, the transition between these types, namely, type 2 (heat transfer rate becomes constant) is detected. By increasing the Rayleigh number, the heat transfer behavior of rising volume fraction experiences transition from type 1, type 2 and then to type 3 in sequence, and the transition is valid for low Ra only. The corresponding critical Rayleigh number is found to increase in pace with the rise of averaged temperature and temperature difference, but is found to decrease with the growth of the nanoparticle diameter. Finally, one correlation equation for reproducing the critical Rayleigh number with averaged temperature ranging from 300 K to 320 K is presented.