In this study, for the first time natural convection heat transfer of Al2O3-water nanofluid with constant and variable
properties is investigated within square shape porous media using the lattice Boltzmann method. The horizontal walls of the
cavity are insulated, and left and right vertical walls are hot and cold, respectively. The Study have been carried out for Rayleigh
numbers of 103, 104, 105, 106, Darcy numbers of 10-2, 10-4, porosity coefficients of 0.4, 0.6, 0.9 and solid volume fraction of 0, 0.01,
0.02 and 0.03. In order to consider the effect of porous media, Darcy-Forchheimer model is used. The results show that the presence of the porous media decreases the velocity of nanofluid and consequently decreases the strength of the flow. With decreasing Darcy number and porosity coefficient, natural convection heat transfer weakens and the mechanism of natural convection of nano-fluids tends to that of thermal conduction. With increasing Rayleigh number, the strength of flow in cavity and average Nusselt number increases. In all cases studied, increase in volume fraction improves heat transfer. In constant properties model, by increasing solid volume fraction, average Nusselt number increases more than that of variable properties model. The results show that Lattice Boltzmann method has the ability to simulate flow in porous media.

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