LBM simulation of MHD nanofluid heat transfer in a square cavity with a cooled porous obstacle: effects of various temperature boundary conditions

Nanofluid natural convection inside a cavity with a porous square obstacle in the presence of magnetic field is simulated by lattice Boltzmann method. The porous obstacle is adopted by Sierpinski carpets fractal pattern, and three kinds of temperature boundary conditions are set up on the hot walls. The combination of five topics including LBM, Sierpinski carpets, nanofluid, magnetic field and various temperature boundary conditions is the main novelty of the present paper. The effects of temperature boundary condition, configuration of Sierpinski carpets porous obstacle, Rayleigh number, nanoparticle volume fraction and Hartmann number on the flow pattern, temperature distribution and heat transfer characteristics are studied. The results show that the local and average Nusselt numbers are increasing functions of ϕ and Ra, but a decreasing function of Ha, regardless of the boundary conditions. The heat transfer enhancement by adding nanoparticles is more effective at low ϕ. The rate of heat transfer with different temperature boundary conditions is Case 3 ˃ Case 2 ˃ Case 1. At high Hartmann number, the obstacle configuration affects the rate of heat transfer very slightly. However, at low Hartmann number, the effect of obstacle configuration on the average Nusselt number should be considered. The effect of obstacle configuration on the rate heat transfer is also influenced by the temperature boundary conditions.