The natural convection in a square enclosure with two hot inner cylinders, Part I: The effect of one elliptical cylinder with various aspect ratios in a vertical array

This study numerically investigates the two-dimensional natural convection in a square enclosure with a vertical array of one circular cylinder and one elliptical cylinder at Rayleigh numbers of 104 ≤ Ra ≤ 106. A simulation was carried out based on the immersed boundary method to obtain an accurate solution. The effects of the aspect ratio of the elliptical cylinder in the range of 0.25 ≤ AR ≤ 4.00 were investigated. When the Rayleigh number increases to Ra = 106, the numerical solutions reach an unsteady state for all cases of the lower elliptical cylinder and the case of the upper elliptical cylinder except at AR = 2.00 and AR = 4.00. The transition of the flow regime from the unsteady state to the steady state depends on the variation in the ratio of the elliptical cylinder. In addition, in the case of the upper elliptical cylinder at AR = 0.50 the time- and surface-averaged Nusselt numbers for the walls of the enclosure increase by 2.1% in the case of two circular cylinders at Ra = 106.