Effects of uncertainties of viscosity models for Al2O3–water nanofluid on mixed convection numerical simulations

The effects of uncertainties in the effective dynamic viscosity of Al2O3–water nanofluid in the laminar mixed convection fluid flow and heat transfer in a square cavity are investigated. The left and the right vertical walls of the enclosure as well as its horizontal top wall are maintained at a constant temperature Tc. The horizontal bottom wall of the cavity, which moves in its own plane from left to right with a constant speed ub, is kept at a constant temperature Th, with Th > Tc. The governing equations written in terms of the primitive variables are solved numerically using the finite volume method. Two different models proposed in the literature are considered for the effective dynamic viscosity of the nanofluid. Using the developed code, a parametric study is performed incorporating the two viscosity formulas, and the effects of the Richardson number and the volume fraction of the nanoparticles on the fluid flow and heat transfer inside the enclosure are investigated in each case. The results show that significant differences exist between the magnitudes of heat transfer enhancement in the cavity for the two viscosity models employed. Moreover, in general, the average Nusselt number of the hot wall increases with increasing the volume fraction of the nanoparticles for both of the viscosity models.