Theoretical study of nanofluids behavior at critical Rayleigh numbers

The present work investigates the natural convection of nanofluids in Rayleigh–Benard problem. New models, particularly some enhancement factors, are presented in this research to calculate the heat transfer characteristics of nanofluids around critical Rayleigh numbers, including the criteria in which the creation of Rayleigh–Benard and transition to turbulent flow occurs. The present models are compared with available models in the literature to reveal discrepancies of theoretical models in prediction of nanofluids heat transfer characteristics. This research is conducted for ${\text{SiO}}_2$, $\text{Cu},\text{CuO}$ and ${\text{Al}}_2{\text{O}}_3$ as nanoparticle and water as the base fluid and discussed the SiO₂–water nanofluid in more detail. Results indicate that the Nusselt number and convective heat transfer ratio are reduced for SiO₂–water nanofluid for almost all volume fractions and as a result using ${\text{SiO}}_2$ as nanoparticle into water (the base fluid) is not desired for a natural convection in Rayleigh–Benard problem. Moreover, the onset of natural convection is delayed due to the reduction in enhancement factor.