In the present research, the maximization of natural convective heat transfer in a quadrilateral enclosure filled with pure fluids or nanofluids was reviewed. The governing equations have been transformed into a dimensionless form based on the base fluid thermophysical properties.The governing equations are solved using the finite element method. Based on the experimental results available in literature, two new dimensionless parameters, namely thermal conductivity parameter (Nc) and thermal viscosity parameter (Nv) are utilized. The mentioned parameters depend on the type of nanoparticles, and the base fluid, size and shape of the nanoparticles and the working temperature of the nanofluid. Dispersing nanoparticles in the fluid could result in enhancement of the thermal conductivity of the working fluid; hence, utilizing a nanofluid may enhance the heat transfer in an enclosure. On the other hand, the geometrical optimization of the enclosure could also boost the heat transfer. In order to perform a geometrical optimization in the enclosure, two parameters of aspect ratio (the ratio of height to length of enclosure) and the tilted angle (y) are adopted as the optimization variables for the enclosure. The analysis and optimizations were performed for various Rayleigh numbers and volume fractions of nanoparticles. The results show that the increase of Rayleigh number would result in the increase of the enclosure aspect ratio (a thinner enclosure) as well as the decrease of the tilted angle (y) of the optimized enclosure.