Oberbeck–Boussinesq free convection of water based nanoliquids in a vertical channel using Dirichlet, Neumann and Robin boundary conditions on temperature

Abstract

A numerical investigation is carried out into the flow and heat transfer within a fully-developed mixed convection flow of water–alumina (Al2O3–water), water–titania (TiO2–water) and water–copperoxide (CuO–water) in a vertical channel by considering Dirichlet, Neumann and Robin boundary conditions. Actual values of thermophysical quantities are used in arriving at conclusions on the three nanoliquids. The Biot number influences on velocity and temperature distributions are opposite in regions close to the left wall and the right wall. Robin condition is seen to favour symmetry in the flow velocity whereas Dirichlet and Neumann conditions skew the flow distribution and push the point of maximum velocity to the right of the channel. A reversal of role is seen between them in their influence on the flow in the left-half and the right-half of the channel. This leads to related consequences in heat transport. Viscous dissipation is shown to aid flow and heat transport. The present findings reiterate the observation on heat transfer in other configurations that only low concentrations of nanoparticles facilitate enhanced heat transport for all three temperature conditions. Significant change was observed in Neumann condition, whereas the changes are too extreme in Dirichlet condition. It is found that Robin condition is the most stable condition. Further, it is also found that all three nanoliquids have enhanced heat transport compared to that by base liquid, with CuO–water nanoliquid shows higher enhancement in its Nusselt number, compared to Al2O3 and TiO2.

Keywords

• Mixed convection
• Vertical channel
• Nanoliquids
• Heat generation
• Dirichlet
• Neumann
• Robin boundary conditions