Laminar Natural Convection of Water-Based Alumina Nanofluids in a Square Enclosure

Steady-state, laminar, natural convection of water-based alumina nanofluids in a square enclosure with partial heating from the bottom and symmetrical cooling from the sides has been investigated based on numerical simulations. The effects of Rayleigh number, normalized heat source length and nanoparticle volume fraction on the heat transfer behavior have been investigated. An increase in Rayleigh number, for given values of normalized heat source length and nanoparticle volume fraction, leads to an increase in Nusselt number. For a given set of values of Rayleigh number based on base-fluid properties and normalized heat source length, the Nusselt number does not vary significantly with increasing nanoparticle volume fraction because the strengthening viscous effects with increasing volume fraction for water-based alumina nanofluids counteracts the enhanced thermal diffusion in nanofluids. However, when effective Rayleigh number is based on nanofluid properties, Nusselt number decreases with increasing nanoparticle volume fraction. For a given set of values of Rayleigh number and nanoparticle volume fraction, the Nusselt number increases with increasing normalized heat source length due to the strengthening of advective transport. A correlation for mean Nusselt number is proposed which adequately captures qualitative and quantitative behavior obtained from the simulations across the considered parameter range.