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[en] The CFD simulation has been undertaken concerning natural convection heat transfer of a nanofluid in vertical square enclosure, whose dimension, width height length (mm), is 40 40 90, respectively. The nanofluid used in the present study is -water with various volumetric fractions of the alumina nanoparticles ranging from 0-3%. The Rayleigh number is . Fluent v6.3 is used to simulate nanofluid considering it as a single phase. The effect of Brownian motion on the heat transfer is examined. A comparison between the two studies of with and without the Brownian motion, shows that when the Brownian motion is considered, the solid volume fraction of nanoparticles has dissimilar effects on the heat transfer. The numerical results show a decrease in heat transfer with increase in particle volume fraction considering Brownian motion effects. Moreover, computed result demonstrates an increase of Nusselt number with Rayleigh number as depicted by experimental results.