Natural convection in a square enclosure with two hot inner cylinders, Part II: The effect of two elliptical cylinders with various aspect ratios in a vertical array

In this study, two-dimensional numerical simulations were conducted for the natural convection in a cold square enclosure with a vertical array of two hot elliptical cylinders at Rayleigh numbers of 10(4) <= Ra <= 10(6). We observed the effect of the aspect ratios of the elliptical cylinders in the range of 0.25 <= AR <= 4.00. The immersed boundary method (IBM), which is based on the finite volume method (FVM), was used to capture the virtual wall boundary of the cylinders. The transition of the flow regime from steady state to unsteady state depends on the aspect ratio at Ra = 10(6). At low Rayleigh numbers of Ra = 10(4) and Ra =10(5), the time- and surface-averaged Nusselt numbers for the enclosure walls increase with the AR of the upper elliptical cylinder. At a relatively high Rayleigh number of Ra = 10(6), the time- and surface-averaged Nusselt numbers of the enclosure walls increase by 3.9% at the upper elliptical cylinder at AR = 0.50 and at the lower elliptical cylinder at AR = 2.00 compared to two circular cylinders. (C) 2019 Elsevier Ltd. All rights reserved.