Nanofluids is a term to describe fluids engineered by dispersing nanometer-scale structures such as particles, tubes and fibers in base fluids. Nanofluids are viewed as effective means of enhancing heat and mass transfer and thus they can be implemented in many engineering applications. The present paper examines the two dimensional-steady state-natural convection during the buoyancy-induced flow of the incompressible Al2O3-water nanofluid along a vertical plate under two different scenarios: the uniform and non-uniform heated plate. Both dynamic and static models are proposed in the literature for the conductivity and viscosity of the nanofluids. Nevertheless, in this work, dynamic models for the nanofluids thermal conductivity and viscosity have been assumed so as the Brownian motion of the nanoparticles to be considered. The governing equations of continuity, momentum and energy are reduced to a system of two non-linear differential equations by means of introducing the Pohlhausen stream function, and are solved numerically with the Runge-Kutta method with the Prandtl number being the only parameter of the dimensionless differential equations. The results show that the convection heat transfer coefficient is enhanced due to the nanofluids and it increases further by augmenting the volume concentration of the nanoparticles. The results of the aforementioned analysis are validated with the Finite Difference Method (FDM) selecting the proper grid density for the field. In addition, the impact of the nanoparticle diameter and the type of the base fluid on maximizing heat transfer through free convection for the isothermal plate is investigated. Finally, the two ways of expressing the temperature of the plate are compared in terms of influencing the convection coefficient.

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