Numerical analysis of laminar mixed convection heat transfer of the Al$_2$O$_3$–H$_2$O nanofluid in a square channel

In this study, the Al$_2$O$_3$–H$_2$O nanofluid flow through a duct with a square cross section under a constant heat flux is simulated using a single-phase model. According to the chosen values of the Reynolds and modified Richardson numbers, this flow is laminar, and it is considered in mixed convection. The dynamic and thermal parameters of this flow are determined numerically by using the CFD-Fluent software based on the finite volume method by introducing the Boussinesq approximation. The analysis is carried out for Reynolds numbers ranging from 100 to 1000 and modified Richardson numbers equal to 0.1 and 0.5. The results obtained show that gravitational forces generate two thermo-convective cells in each cross section along the channel, and asymmetric temperature and velocity profiles are formed. The effects of the volume fraction of nanoparticles, Reynolds number, and modified Richardson number on the flow structure, Nusselt number, and pressure drop are analyzed. With the use of nanofluids, the Nusselt number increases, which ensures heat transfer enhancement. Finally, a correlation is proposed for the Nusselt number as a function of the nanoparticle volume fraction, which can be used for heat transfer predictions.