A Numerical Study of Natural Convection in a Square Enclosure with a Circular Cylinder at Different Vertical Locations

Abstract

Numerical calculations are carried out for natural convection induced by a temperature difference between a cold outer square enclosure and a hot inner circular cylinder. A two-dimensional solution for unsteady natural convection is obtained, using the immersed boundary method (IBM) to model an inner circular cylinder based on the finite volume method for different Rayleigh numbers varying over the range of 10 3-10 6. The study goes further to investigate the effect of the inner cylinder location on the heat transfer and fluid flow. The location of the inner circular cylinder is changed vertically along the center-line of square enclosure. The number, size and formation of the cell strongly depend on the Rayleigh number and the position of the inner circular cylinder. The changes in heat transfer quantities have also been presented.

Numerical Simulation of Natural Convection From a Pair of Hot Cylinders in a Cold Square Enclosure in Different Boundary Conditions

“…As shown in Table 2, the current result compares well with the numerical results of other studies, including Khozeymehnejad and Mirbozorgi (2012) and Kim et al (2008). The small differences among these results could be attributed to the different numerical approaches which have been implemented in each study.…”

“…Effects of position and size of the cylinder as well as boundary conditions were studied by the third group. Kim et al (2008) investigated the effects of Rayleigh number and vertical position of a hot circular cylinder in a cold square enclosure on the rate of heat transfer. Lee et al (2010) investigated the effects of horizontal position and diameter of a circular cylinder on the rate of heat transfer.…”

Comparison of Natural Convection around a Circular Cylinder with a Square Cylinder Inside a Square Enclosure

“…In order to valid the results of the developed numerical code, a natural convection problem with low temperature for enclosure and high temperature for inner circular cylinder was examined.The wall surface-averaged Nusselt number of enclosure for this test case were co mpared with the benchmark values by Kim et al [2] as shown in Table 2. The comparison is carried out using the following dimensionless parameters: Pr=0.7, Ra = 10 4 -10 6 and δ=0.…”

“…St ream funct ionvorticity fo rmu lation of the Nav ier-Stokes equations was solved numerically using fin ite-difference method. Kim et al [2], perfo rmed numerical simu lation of natural convection induced by a temperature difference between a cold outer square enclosure and a hot inner circu lar cy linder. The imme rsed boundary method (IBM ) was used to model an inner circular cylinder only at AR=0.2 in this paper.…”

Simulation of Mixed Convective Heat Transfer using Lattice Boltzmann Method

“…Most of these studies were concerned with the case of a circular cylinder inside a square enclosure. Excellent reviews of this topic were written by Kim et al (2008) and Angeli et al (2008). In contrast to the overwhelming number of publications on natural convective heat transfer from a heated circular cylinder, the mixed convective heat transfer problem from a heated body has not been investigated to the same extent, although it plays a dominant role in many engineering applications such as the cooling of electronic equipment, nuclear and chemical reactors, thermal storage system, etc.…”