Natural convection around a pair of hot and cold horizontal microtubes at low Rayleigh numbers
Introduction
Natural convection is a common but complex phenomenon of fluid flow driven by a kind of internal body force, such as the buoyancy in the gravity field, and it is still an interesting topic in many scientific areas. Recent reviews on natural convection cover various aspects representing the up-to-date achievement, which are meaningful for many industry applications [1], [2]. This paper reports a numerical modeling of natural convection between two parallelized horizontal microtubes enclosed in a relative large rectangular channel. To our knowledge, there is no previous work that directly related to this configuration. In order to give an evaluation of the numerical simulation in the present paper, a simple experimental loop was set up and made a comparison with the obtained numerical results except that the rectangular channel in the numerical simulation was replaced by a cylinder.
Section snippets
Mathematical model and configuration descriptions
The geometry configuration of the problem is as shown in Fig. 1. The hot and cold microtubes were placed in the middle of a 20d × 20d sized square, where d is the diameter of the microtube, and the distance between the two microtubes or tube spacing is 1.5d. All the solid boundaries were given as no slip boundary. The hot and cold tubes were at constant temperatures, and given by 2 and 1, respectively. The enclosure wall was adiabatic, and its initial temperature was given by the averaged hot
Numerical results and discussions
While the Rayleigh number is given as zero, it is corresponding to the case of heat conduction. The calculated mean Nusselt numbers for both the hot and cold tubes are approximate to 1.02, which is close to unity of the pure heat conduction state in an infinite large space. Fig. 4 shows the temperature and velocity profiles at various Rayleigh numbers while the hot and cold tubes are side by side. It shows that there is only one vortex clockwise surrounding the tube pair at very low Rayleigh
Comparison with the experimental results
An experimental loop was set up in order to make a comparison with the obtained numerical results. The experimental system includes a test section, a cold and a hot water loop, a flow rate control system and a data acquisition system.
In the test section, a plexiglass circular pipe was used as the tube shell, which is 300 mm in length, and the inner diameter and thickness are respectively 20 mm and 2.5 mm. Two stainless steel microtubes are circulated respectively with cold and hot water, both
Conclusions
The natural convection of a parallelized hot and cold tube pair in a rectangular enclosure was numerically studied in a range of Ra < 1400. The results show that the vortex structure of fluid flow is more complicated with increasing Rayleigh number than that of a free convection for a horizontal cylinder. The arrangement of hot tube right over cold tube could have the most complicated vortex structure at relative large Rayleigh number (Ra ≈ 103), and its averaged Nusselt number is the lowest
Acknowledgements
The work was supported by National Program on Key Basic Research Project fund under contract 2011CB707203 and NSF of China under grant No. 40972160.
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