Lattice boltzmann method for mixed convection with non-uniform and fractal Al2O3/water nanofluid in differently vertical moving lid cavities

Mesoscale Lattice Boltzmann simulation is used to solve the mixed convection of Al₂O₃/H₂O nanofluid medium in two-sided lid-driven cavities. Flow governing equations like Navier-Stokes and energy equations in the form of particle distribution functions have been solved by the Lattice Boltzmann Method (LBM). The effect of fractal dimension (minimum to maximum diameter) and non-uniform diameter of Al₂O₃ nanoparticles for different concentrations in water inside the cavities has been considered. Based on the vertical walls motion, three different cases of lid-driven problems have been considered. First, only the left wall is moving in the upward direction (Case-I), second, when the vertical walls are moving in the same direction (Case-II), and third, when the vertical walls are moving in the opposite direction (Case-III). Results are depicted in the form of streamline, isotherms, Nusselt number, and vertical velocity variation. A significant decrease in Nusselt number is found for the range of mean nanoparticle diameter from 1 nm to 20 nm. Increasing the fractal dimension of Al₂O₃ increases the heat transfer in all three different cases. Fractal distribution R = 0.001 has the capability of a lower heat transfer rate than at R = 0.007. Quantitatively a maximum of 51 % increment in $\overline{Nu}$ for Case III is observed in comparison to Case I at Ri = 0.1 for the same parameters. This increment is 46 % for Case II in comparison to Case I, which is observed. Case-III with a higher value of fractal distribution and smaller mean diameter of nanoparticles is suggested for better heat transfer.