In this article a ‘two-component four-equation non-homogeneous equilibrium’ model has been adopted to accurately simulate the process of natural convection of Al2O3–water nanofluid inside a vertical square cavity. The aforementioned model considers conservation equation of nanoparticles which is highly coupled to other equations (mass, momentum, and energy equations for nanofluid) and includes the effects of Brownian motion and thermophoresis as the two most important mechanisms of slip velocity in laminar flow. The distribution of nanoparticles volume fraction is obtained by solving these four equations simultaneously. Renewing the effective properties of nanofluid from the nanoparticles, volume fraction distribution is another advantage of this model. Numerical results are in good agreement with published experimental data and emphasize that the use of the nanofluid for natural convection heat transfer enhancement in enclosure is impracticable for the studied range of solid volume fraction . Also, heat transfer rate decreases with an increase in nanoparticle volume fraction.
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