The Nusselt number can

be expressed as: (32) The heat transfer coefficient is computed from: (33) The thermal conductivity of the nanofluid is defined by: (34) Substituting Equations 33 and 34 into Equation 32, the local Nusselt number along the left wall can be written as: (35) The average Nusselt number is determined from: (36) In order to perform a grid independence test and validate the Lattice Boltzmann model proposed in this work, we used another selleck screening library square enclosure, because there are exact solutions for this square enclosure. The left wall is kept at a high constant temperature (T H), and the right wall is kept at a low constant temperature (T C). The boundary conditions of the other walls (top wall and bottom wall) are all adiabatic, and the other conditions are the same as those in Figure 1. As shown in Table 2, the grid independence test is performed in a square enclosure using successively sized grids, 128 × 128, 192 × 192, 256 × 256, and 320 × 320 at Ra = 1 × 105, Pr = 0.7. It can be seen from Table 2 that there

is a bigger difference between the result obtained with grid sizes 128 × 128 and 192 × 192 and the result available from the literature [30] than when compared with the result obtained with grids 256 × 256 and 320 × 320. In learn more addition, the result with grid 256 × 256 and the result with grid 320 × 320 are very close. In order to accelerate the numerical simulation, a grid size of 256 × 256 was chosen as a suitable

one which can guarantee a grid-independent solution. Table 2 Comparison of the mean Nusselt numbers with different grids ( Ra = 1 × 10 5 , Pr = 0.7) Physical properties 128 × 128 192 × 192 256 × 256 320 × 320 Literature[30] Nu avg 4.5466 4.5251 4.5220 4.5218 4.5216 In order to validate the Lattice Boltzmann model proposed in this work, the temperature distribution at midsections of the enclosure at Ra = 1 × 105, Pr = 0.7 is compared with the numerical results from Khanafer et al. [31] and experimental results from Krane et al. (-)-p-Bromotetramisole Oxalate [32] in Figure 2. It can be seen that the results of this paper have a good agreement with those numerical [31] and experimental [32] results. They are closer to the experimental [32] than the numerical [31] results. In addition, the Nusselt number results at different Rayleigh numbers of this paper are compared with other Y-27632 supplier published literature listed in Table 3, and it can be seen that the results are in good agreement. Figure 2 Temperature distribution at horizontal midsections-sections of the enclosure ( Ra = 10 5 , Pr = 0.7). Table 3 Comparison of average Nusselt numbers with other published data ( Pr = 0.7)   Ra = 103 Ra = 104 Ra = 105 Ra = 106 Present work 1.118 2.247 4.522 8.808 D’Orazio et al. [33] 1.117 2.235 4.504 8.767 De Vahl Davis [34] 1.118 2.243 4.519 8.800 Khanafer et al. [31] 1.118 2.245 4.522 8.