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Research Papers: Natural and Mixed Convection

# Numerical Investigation of Natural Convection Heat Transfer From a Stack of Horizontal Cylinders

[+] Author and Article Information
Subhasisa Rath

School of Energy Science and Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, West Bengal, India
e-mail: subhasisa.rath@gmail.com

Sukanta Kumar Dash

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, West Bengal, India
e-mail: sdash@mech.iitkgp.ernet.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 22, 2017; final manuscript received July 13, 2018; published online October 8, 2018. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 141(1), 012501 (Oct 08, 2018) (10 pages) Paper No: HT-17-1560; doi: 10.1115/1.4040954 History: Received September 22, 2017; Revised July 13, 2018

## Abstract

Natural convection heat transfer from horizontal solid cylinders has been studied numerically by varying the Rayleigh number in the range of $(104≤Ra≤108)$ and $(1010≤Ra≤1013)$ for both laminar and turbulent flows, respectively. The computations were carried out for three different geometries of three, six, and ten cylinders in a stack arranged in a triangular manner having same characteristic length scale. The present numerical investigation on natural convention is able to capture a very interesting flow pattern and temperature field over the stack of horizontal cylinders which has never been reported in the literature so far. Visualization of plume structure over the horizontal cylinders has also been obtained pictorially in the present work. From the numerical results, it has been observed that the total heat transfer is marginally higher for three-cylinder stack in the laminar range. In contrast, for turbulent flow, starting from Ra = 1010, heat transfer for six-cylinder case is higher but when Ra exceeds 5 × 1011, heat transfer for ten cylinders stack is marginally higher. The average surface Nusselt number is higher for the stack of three cylinders compared to six- and ten-cylinder cases for all range of Ra in both laminar and turbulent regimes. A correlation for the average Nusselt number has also been developed as a function of Rayleigh number which may be useful for researchers and industrial purposes.

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## References

Paykoq, E. , Yiincii, H. , and Bezzazo, M. , 1991, “ Laminar Natural Convective Heat Transfer Over Two Vertically Spaced Isothermal Horizontal Cylinders,” Exp. Therm. Fluid Sci., 4(3), pp. 362–368.
Bejan, A. , Fowler, A. J. , and Stanescu, G. , 1995, “ The Optimal Spacing Between Horizontal Cylinders in a Fixed Volume Cooled by Natural Convection,” Int. J. Heat Mass Transfer, 38(11), pp. 2047–2055.
Cianfrini, C. , Corcione, M. , and Habib, E. , 2006, “ Free Convection Heat Transfer From a Horizontal Cylinder Affected by a Downstream Parallel Cylinder of Different Diameter,” Int. J. Therm. Sci., 45(9), pp. 923–931.
Chae, M. , and Chung, B. , 2011, “ Effect of Pitch-to-Diameter Ratio on the Natural Convection Heat Transfer of Two Vertically Aligned Horizontal Cylinders,” Chem. Eng. Sci., 66(21), pp. 5321–5329.
Park, Y. G. , Sik, H. , and Yeong, M. , 2012, “ International Journal of Heat and Mass Transfer Natural Convection in Square Enclosure With Hot and Cold Cylinders at Different Vertical Locations,” Int. J. Heat Mass Transfer, 55(25–26), pp. 7911–7925.
Heo, J. , Chae, M. , and Chung, B. , 2013, “ Influences of Vertical and Horizontal Pitches on the Natural Convection of Two Staggered Cylinders,” Int. J. Heat Mass Transfer, 57(1), pp. 1–8.
Iyi, D. , and Hasan, R. , 2015, “ Natural Convection Flow and Heat Transfer in an Enclosure Containing Staggered Arrangement of Blockages,” Procedia Eng., 105, pp. 176–183.
Park, Y. G. , Ha, M. Y. , and Park, J. , 2015, “ Natural Convection in a Square Enclosure With Four Circular Cylinders Positioned at Different Rectangular Locations,” Int. J. Heat Mass Transfer, 81, pp. 490–511.
Pelletier, Q. , Murray, D. B. , and Persoons, T. , 2016, “ Unsteady Natural Convection Heat Transfer From a Pair of Vertically Aligned Horizontal Cylinders,” Int. J. Heat Mass Transfer, 95, pp. 693–708.
Liu, J. , Liu, H. , Zhen, Q. , and Lu, W. , 2017, “ Numerical Investigation of the Laminar Natural Convection Heat Transfer From Two Horizontally Attached Horizontal Cylinders,” Int. J. Heat Mass Transfer, 104, pp. 517–532.
Liu, J. , Liu, H. , Zhen, Q. , and Lu, W. , 2017, “ Laminar Natural Convection Heat Transfer From a Pair of Attached Horizontal Cylinders Set in a Vertical Array,” Appl. Therm. Eng., 115, pp. 1004–1019.
Acharya, S. , and Dash, S. K. , 2017, “ Natural Convection Heat Transfer From a Short or Long, Solid or Hollow Horizontal Cylinder Suspended in Air or Placed on Ground,” ASME J. Heat Transfer, 139(7), p. 072501.
Acharya, S. , and Dash, S. K. , 2018, “ Natural Convection Heat Transfer From Perforated Hollow Cylinder With Inline and Staggered Holes,” ASME J. Heat Transfer, 140(3), p. 032501.
Churchill, S. W. , and Chu, H. H. S. , 1975, “ Correlating Equations for Laminar and Turbulent Free Convection From a Horizontal Cylinder,” Int. J. Heat Mass Transfer, 18(9), pp. 1049–1053.
Senapati, J. R. , Dash, S. K. , and Roy, S. , 2017, “ Numerical Investigation of Natural Convection Heat Transfer From Vertical Cylinder With Annular Fins,” Int. J. Therm. Sci., 111, pp. 146–159.
Launder, B. E. , and Spalding, D. B. , 1974, “ The Numerical Computation of Turbulent Flows,” Comput. Methods Appl. Mech. Eng., 3(2), pp. 269–289.
ANSYS, 2013, ANSYS Fluent, Release 15.0, User Manual, ANSYS, Canonsburg, PA.

## Figures

Fig. 1

Stacks of horizontal cylinders lying in the bay for cooling2 (Reprinted with permission of Hebei Tobee Group Co., Limited)

Fig. 2

Schematic diagram of the physical problem: (a) three-cylinders, (b) six-cylinders, and (c) ten-cylinders

Fig. 3

Variation of Nu with domain size: (a) laminar and (b) turbulent flows

Fig. 4

Schematic representation of computational grids with blown up view

Fig. 5

Variation of Nu with computational cells: (a) laminar and (b) turbulent flows

Fig. 6

Variation of Nu with Ra for a single cylinder, a comparison with experimental correlation

Fig. 7

Variation of Q with Ra: (a) laminar and (b) turbulent flows

Fig. 8

Variation of Nu with Ra: (a) laminar and (b) turbulent flows

Fig. 9

Contours of static temperature with varying Ra: (a) three-cylinders (Laminar), (b) three-cylinders (Turbulent), (c) six-cylinders (Laminar), (d) six-cylinders (Turbulent), (e) ten-cylinders (Laminar), and (f) ten-cylinders (Turbulent)

Fig. 10

Plot of velocity vectors for (a) laminar flow (Ra = 105) and (b) turbulent flow (Ra = 1010) around the stacks of three, six, and ten cylinders

Fig. 11

Predicted and computed values of Nu for laminar and turbulent flows for different stacks of horizontal cylinders

## Errata

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