Two-phase mixture modeling of natural convection of nanofluids with temperature-dependent properties

• A two-phase model is used to study natural convection of nanofluids in enclosures.
• The slip effects due to Brownian diffusion and thermophoresis are considered.
• The effects of temperature-dependent physical properties are accounted for.
• The existence of an optimal particle loading is demonstrated and discussed.
• Correlations useful for thermal engineering design purposes are developed.

A two-phase mixture model is used to study natural convection in side-heated square enclosures 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. Simulations are performed using the diameter of the suspended nanoparticles and their average concentration, as well as the size of the cavity and the temperatures of its sidewalls, as independent variables. It is found that the heat transfer performance has a peak at an optimal particle loading which increases as all the mentioned controlling parameters are magnified. On the basis of the results obtained, a set of correlations is developed.