Study on natural convection in a cold square enclosure with a pair of hot horizontal cylinders positioned at different vertical locations

A numerical study was conducted to investigate natural convection induced by a temperature difference between a cold outer square enclosure and two hot inner circular cylinders. The immersed boundary method (IBM) based on the finite volume method was used to simulate a two-dimensional natural convection for Rayleigh numbers in the range 103⩽Ra⩽106 in the presence of the two cylinders in the cold enclosure. The Prandtl number Pr was taken to be 0.7 corresponding to that of air. This study investigated the effects of the locations of the two cylinders in the enclosure on the heat transfer and laminar fluid flow, when they move vertically along the centerline of the left and right halves of the enclosure. The bifurcation of natural convection from the steady to the unsteady state depended on the Rayleigh number (Ra) and the dimensionless vertical distance from the square cylinder center to the circular cylinder center (δ) of the two cylinders. When 103⩽Ra⩽105, the flow and thermal fields eventually reached steady state. However, the state of flow and thermal fields became unsteady for 0⩽δ⩽0.1 at Ra = 106. The dependence of the Nusselt number on Ra and δ was also evaluated.