Natural convection in a square enclosure with four circular cylinders positioned at different rectangular locations

A numerical study was carried out to investigate natural convection heat transfer induced by a temperature difference between a cold outer square enclosure and four hot inner circular cylinders placed in a rectangular array. A two-dimensional solution for natural convection in an enclosure with four cylinders was obtained using an accurate and efficient immersed boundary method. The immersed boundary method based on the finite volume method was used to handle four inner cylinders placed equal distance away from each other within an enclosure moving along the diagonal centerlines for different Rayleigh numbers in the range 103 ⩽ Ra ⩽ 106. This study investigated the effects of the location of the cylinders in the enclosure on the heat transfer and fluid flow, when they moved along the diagonal centerlines of the enclosure. For all the cases considered in the present study, the flow and thermal fields eventually reached steady state in the range of 103 ⩽ Ra ⩽ 104. However, for 105 ⩽ Ra ⩽ 106, the flow and thermal fields became unsteady depending on the cylinders position. Also, the symmetry about the vertical centerline was affected by the cylinders position as well. The distribution of the instantaneous, time-averaged local and surface-averaged Nusselt number as a function of the Rayleigh number and the distance between inner cylinders was also presented.