Natural convection in a square enclosure with two inner circular cylinders positioned at different vertical locations

The present study investigates the natural convection induced by a temperature difference between a cold outer square enclosure and two hot inner circular cylinders. A two-dimensional solution for natural convection in an enclosure with inner cylinders is obtained using an accurate and efficient immersed boundary method. The immersed boundary method based on the finite volume method is used to handle inner cylinders located at different vertical centerline positions of the enclosure for different Rayleigh numbers in the range 103⩽Ra⩽106. The results in the case of two cylinders are compared with those in the case of the single cylinder in order to see the effect of the interaction between the adjacent two inner hot cylinders in addition to the interaction between two hot inner cylinders and the cold walls of the enclosure. The distribution of isotherms and streamlines eventually reaches a steady state or changes its state from steady to unsteady, depending on the values of the Rayleigh number and the cylinder position in the enclosure. The distribution of the local and surface-averaged Nusselt numbers is obtained for different Rayleigh numbers and the cylinder positions.