Effect of pitch-to-diameter ratio on the natural convection heat transfer of two vertically aligned horizontal cylinders Myeong-Seon Chae, Bum-Jin Chung n Department of Nuclear and Energy Engineering, Applied Radiological Science Research Institute, Jeju National University, #102 Jejudaehakno, Jeju 690-756, Republic of Korea article info Article history: Received 18 April 2011 Received in revised form 13 July 2011 Accepted 15 July 2011 Available online 22 July 2011 Keywords: Double cylinders Electrochemistry Heat transfer Mass transfer Natural convection Visualization abstract Natural convection heat transfer experiments were conducted for two parallel horizontal cylinders using various pitch-to-diameter ratios (P/D) from 1.02 to 9 for the Prandtl numbers between 2014 and 8334 and Rayleigh numbers between 7.3  10 7 and 4.5  10 10 . Based upon analogy concept, mass transfer rate were measured instead of heat transfer rates by measuring the limiting current of the cathodic deposition of copper from acidified copper sulfate solution. The mass transfer rates for the lower cylinders were unaffected by the presence of the upper cylinders, and agreed well with the prediction from existing heat transfer correlations developed from a single horizontal cylinder. The Nusselt number ratios of the upper to lower cylinders increased with P/D. The ratios were less than 1 at P/D values less than about 1.5 for laminar flows, but the ratios were almost 1 at a P/D very close to 1 for turbulent flows. The variation of the ratios with P/D becomes steep with higher Prandtl numbers, which is confirmed by numerical simulations using the FLUENT program. The plating pattern that appeared on the surface of the cylinder revealed local mixed convection heat transfer. The area covered by thin lines, denoting the flow separation on top of the upper cylinder, increased for laminar but decreased for turbulent flow due to the laminarization phenomena in turbulent mixed convection. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction Natural convection from two horizontal cylinders is either laminar or turbulent, depending on the Rayleigh number. The heat transfer of the lower cylinder is unaffected by the presence of the upper cylinder and is the same as that of a single cylinder (Smith and Wragg, 1974). However, the heat transfer of the upper cylinder is affected by the flow developed from the lower cylinder, due to preheating and velocity effects (Yuncu and Batta, 1994). With a small pitch-to-diameter ratio (P/D), the heat transfer coefficients of the upper cylinder decrease due to the preheating effect from the lower cylinder. With larger P/D values, the upper cylinder is exposed to the increased forced convection flow induced by the lower cylinder. The fluid arriving at the upper cylinder is added to the velocity, and the upper cylinder is then situated in what appears to be a forced convection flow. Thus, the upper cylinder is under a mixed convection condition. There have been several experimental and numerical studies devoted to this topic (D’Orazio and Fontana, 2010; Gorman et al., 2009; Corcione, 2007, 2005; Chouikh et al., 1999; Sadegh and Asheghi, 1994; Yuncu and Batta, 1994; Sparrow and Niethammer, 1981; Smith and Wragg, 1974; Liberman and Gebhart, 1969). However, most of them were restricted to laminar natural convec- tion of two horizontal cylinders, while less attention has been paid to turbulent natural convection. This is because turbulent flows occur only around large cylinders, and experiments using such cylinders are difficult to realize within a laboratory framework. For example, Toshiyuki et al. used the test chamber of 2.7 m long, 2 m wide, and 2.3 m high in order to suppress the disturbance of air as it exerts serious influences on the transition of flows around cylinders. The steady state was achieved about 4 and 15 h after heating for the cylinders of 200 and 1200 mm diameter (Toshiyuki et al., 2003). In this study, the heat transfer affected by varying the P/D of two vertically aligned horizontal cylinders was investigated. Experiments were performed by varying the P/D from 1.02 to 9 for Prandtl numbers 2014 to 8334 and Rayleigh numbers from 7.3  10 7 to 4.5  10 10 . Using an analogy concept, mass transfer was measured instead of heat transfer, and a cupric acid–copper sulfate (H 2 SO 4 –CuSO 4 ) electroplating system was adopted as the mass transfer system. The diameters of the cathodes were 9.5, 12, 35, and 67 mm, which correspond to Rayleigh numbers of 7.3  10 7 to 4.5  10 10 , covering both laminar and turbulent conditions. The P/D values were varied from 1.1 to 9 for laminar and from 1.02 to 2 for turbulent conditions. Numerical simulations using FLUENT 6.2 were performed to investigate the effect of large Prandtl numbers on the experiment. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ces Chemical Engineering Science 0009-2509/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2011.07.021 n Corresponding author. Tel.: þ82 64 754 3644; fax: þ82 64 757 9276. E-mail addresses: bjchung@jejunu.ac.kr, bjchung123@naver.com (B.-J. Chung). Chemical Engineering Science 66 (2011) 5321–5329