Natural convection of power-law nanofluid in a square enclosure with a circular cylinder: An immersed boundary-lattice Boltzmann study

In this paper, natural convection of power-law Al2O3-water nanofluids with temperature-dependent properties in a square enclosure with a circular cylinder is studied. The governing equations of the flow and temperature fields are solved by the lattice Boltzmann method (LBM), and the curved velocity and thermal boundary conditions are treated by immersed boundary method (IBM). The effects of Rayleigh number, power-law index, nanoparticle volume fractions, radius of circular cylinder, nanoparticle diameter and temperature difference on flow and heat transfer characteristics are discussed in detail. The results indicate that the heat transfer rate is increased with the increases of Rayleigh number, radius of circular cylinder and temperature difference, while it generally decreases with an increase in power-law index and nanoparticle diameter. Additionally, it is observed that there is an optimal volume fraction at which the maximum heat transfer enhancement is obtained, and the value of it is found to increase slightly with decreasing the nanoparticle diameter, and to increase remarkably with increasing the temperature difference.