Lattice Boltzmann simulation of natural convection and fluid flow around a heated cylinder in an enclosed square Abstract In this paper, simulations of two-dimensional natural convection and fluid flow around a heated cylinder in an enclosed square are performed. The temperature of the square wall and of the cylinder is maintained constant and uniform with the cylinder temperature is greater than that of the square. An incompressible lattice Boltzmann method is brought as numerical tool due to its flexibility in the treatment of boundary conditions. The basic idea in lattice Boltzmann method is to solve the velocity field and the temperature fields using two different distribution functions. It is observed that the heat transfer mechanism is significantly depends on the value of Rayleigh numbers.