Natural convection in cavities is an interesting subject for many researchers. Especially, in recent years, the number of articles written in this regard has grown enormously. This work provides a review of recent natural convection studies. At first, experimental studies were reviewed and, then, numerical studies were examined. Then, the articles were classified based on effective parameters. In each section, numerical studies were examined the parameters added to the cavity such as magnetic forces, fin, porous media and cavity angles. Moreover, studies on non-rectangular cavities were investigated. Free convection in enclosures depends more on the fluid velocity relative to the forced convection, leading to the opposite effect of some parameters that should essentially enhance rate of heat transfer. Nanoparticle addition, magnetic fields, fins, and porous media may increase forced convection. However, they can reduce free convection due to the reduction in fluid velocity. Thus, these parameters need more precision and sometimes need the optimization of effective parameters.

In this paper, free heat transfer ( H T ) and the entropy generation ( E g e n ) of Alumina/ H 2 O nanofluid (NF) in an square cavity (CV) are simulated owing to its application in solar collectors. For this purpose, a square CV with an angle γ is placed under a fixed magnetic field. The upper wall has a temperature of T _c and sidewalls are insulated. On the lower wall of the CV, which is also insulated, two half-pipe with a temperature of T _h are mounted. In the middle of the CV, there is a partition with a conductivity coefficient. The Control volume method is employed to follow the SIMPLE algorithm for the simulation. The variable parameter included 10 3 < Ra < 10 6 , 1 < k s < 1000 , 0 < Ha < 40 , 0 < φ < 0.06 , 0 < γ < 90. The simulation results demonstrated that growing the Rayleigh (Ra) number increased the rate of H T and E g e n , while the increase in the Hartmann (Ha) number decreased both these parameters. Furthermore, the addition of nanoparticles (NPs) resulted in more H T . Increasing the thermal conductivity of the partition in strong free convective H T mode enhanced the H T , while, in poor free convective H T , it reduced the H T . The lowest H T and E g e n occurred in the horizontal CV.

In this study, the free convection with volumetric radiation in a water–alumina nanofluid flowing between two inclined concentric cylinders was simulated. The enclosure, or the cavity between the two circular quadrants in which the inner and outer pipes were respectively at high and low temperatures, was exposed to a magnetic field, and the remaining walls were insulated. Simulations were performed using control volume and the SIMPLE algorithm. The effects of the Rayleigh and Hartmann numbers, cavity or enclosure angle, magnetic field angle, nanopowder volume fraction, radiation intensity, and aspect ratio were investigated on the Nusselt number, irreversibilities and the Bejan number. According to the results, the Rayleigh number, hot pipe diameter, and adding more nanopowder have increasing and the Hartmann number has decreasing effect on the thermal performance and irreversibilities. Adding more nanopowder and increasing the enclosure angle also improved heat transfer. Increasing the magnetic field angle first increased and then decreased irreversibilities. In fact, increasing the magnetic field angle increased up to 15°, the heat transfer rate increased, and further increase of the magnetic field angle from 15° to 90° decreased the heat transfer rate.