Mixed convection in a lid-driven cavity with an inside hot obstacle filled by an $\mathrm{Al}_2\mathrm{O}_3$–water nanofluid

The present paper focuses on the problem of a mixed convection fluid flow and heat transfer of an $\mathrm{Al}_2\mathrm{O}_3$–water nanofluid with the thermal conductivity and effective viscosity dependent on temperature and nanoparticle concentration inside a lid-driven cavity having a hot rectangular obstacle. The governing equations are discretized by using the finite volume method, and the SIMPLE algorithm is employed to couple the velocity and pressure fields. By using the developed code, the effects of the Richardson number and the diameter and volume fraction of $\mathrm{Al}_2\mathrm{O}_3$ nanoparticles on the flow, thermal fields, and heat transfer inside the cavity are studied. The obtained results show that the average Nusselt number for the entire range of the solid volume fraction decreases with an increase in the Richardson number and the nanoparticle diameter. The results also clearly indicate that addition of $\mathrm{Al}_2\mathrm{O}_3$ nanoparticles produces a remarkable enhancement on heat transfer with respect to that of the pure fluid.