A two-phase numerical study of buoyancy-driven convection of alumina–water nanofluids in differentially-heated horizontal annuli

A two-phase mixture model is used to study buoyancy-driven convection in differentially-heated horizontal annuli filled with alumina–water nanofluids having temperature-dependent properties, in the hypothesis that Brownian diffusion and thermophoresis are the primary slip mechanisms between solid and liquid phases. A computational code based on the SIMPLE-C algorithm is used to solve the system of the mass, momentum and energy transfer governing equations. Numerical simulations are performed using the diameter of the suspended nanoparticles and their average concentration, as well as the radii of both concentric cylinders and their temperatures, as independent variables. It is found that the thermal performance of the nanofluid increases with increasing the nanoparticle concentration up to an optimal particle loading at which the heat transfer performance has a peak. The impact of the nanoparticle dispersion on the thermal performance increases as the nanoparticle size and the radius of the inner cylinder decrease, and the radius ratio, the temperature of the cooled cylinder and the temperature difference increase. The optimal particle loading increases as the radius of the inner cylinder decreases, and the nanoparticle size, the temperature of the cooled cylinder and the temperature difference increase, being practically independent of the radius ratio. Based on the results obtained, a set of correlations is developed.