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Research Papers: Natural and Mixed Convection

# Numerical Analysis of Natural Convection Heat Transfer From a Vertical Hollow Cylinder Suspended in Air

[+] Author and Article Information
Swastik Acharya

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur 721 302, India
e-mail: swastik.acharya8@gmail.com

Sumit Agrawal

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur 721 302, India
e-mail: sumit89agr@gmail.com

Sukanta K. Dash

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur 721 302, India

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 30, 2017; final manuscript received September 13, 2017; published online January 30, 2018. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 140(5), 052501 (Jan 30, 2018) (12 pages) Paper No: HT-17-1177; doi: 10.1115/1.4038478 History: Received March 30, 2017; Revised September 13, 2017

## Abstract

Natural convection heat transfer from a vertical hollow cylinder suspended in air has been analyzed numerically by varying the Rayleigh number (Ra) in the laminar (104 ≤ Ra ≤ 108) regime. The simulations have been carried out by changing the ratio of length to pipe diameter (L/D) in the range of 0.05 $≤$ L/D$≤20$. Full conservation equations have been solved numerically for a vertical hollow cylinder suspended in air using algebraic multigrid solver of fluent 13.0. The flow and the temperature field around the vertical hollow cylinder have been observed through velocity vectors and temperature contours for small and large L/D. It has been found that the average Nusselt number (Nu) for vertical hollow cylinder suspended in air increases with the increase in Rayleigh number (Ra) and the Nu for both the inner and the outer surface also increases with Ra. However, with the increase in L/D, average Nu for the outer surface increases almost linearly, whereas the average Nu for the inner surface decreases and attains asymptotic value at higher L/D for low Ra. In this study, the effect of parameters like L/D and Ra on Nu is analyzed, and a correlation for average Nusselt number has been developed for the laminar regime. These correlations are accurate to the level of $±6%.$

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## References

Bar-Cohen, A. , Iyengar, M. , and Benjaafar, S. , 2001, “Design for Manufacturability of Natural Convection Cooled Heat Sinks,” Int. J. Transp. Phenom., 4(1), pp. 43–57.
Xin, R. C. , and Ebadian, M. A. , 1996, “Natural Convection Heat Transfer From Helicoidal Pipes,” J. Thermophys. Heat Transfer, 10(2), pp. 297–302.
McGlen, R. J. , Jachuck, R. , and Lin, S. , 2004, “Integrated Thermal Management Techniques for High Power Electronic Devices,” Appl. Therm. Eng., 24(8–9), pp. 1143–1156.
Churchill, S. W. , and Chu, H. H. S. , 1975, “Correlating Equations for Laminar Free Convection From a Horizontal Cylinder,” Int. J. Heat Mass Transfer, 18(9), pp. 1049–1053.
Churchill, S. W. , 1973, “A Comprehensive Correlating Equation for Laminar, Assisting, Forced and Free Convection,” AIChE J., 23(1), pp. 10–16.
Kuehn, T. , and Goldstein, R. , 1980, “Numerical Solution to the Navier–Stokes Equations for Laminar Natural Convection About a Horizontal Isothermal Circular Cylinder,” Int. J. Heat Mass Transfer, 23(7), pp. 971–979.
Gebhart, B. , Jaluria, Y. , Mahajan, R. I. , and Sammakia, B. , 1988, Buoyancy-Inducted Flows and Transport, Hemisphere, New York.
Ozisik, M. N. , 1985, Heat Transfer a Basic Approach, McGraw-Hill, Boston, MA.
Holman, J. P. , 2010, Heat Transfer, 10th ed., McGraw-Hill Higher Education, New York.
Popiel, C. , Wojtkowiak, J. , and Bober, K. , 2007, “Laminar Free Convective Heat Transfer From Isothermal Vertical Slender Cylinder,” Exp. Therm. Fluid Sci., 32(2), pp. 607–613.
LeFevre, E. J. , and Ede, A. J. , 1956, “Laminar Free Convection From the Outer Surface of a Vertical Circular Cylinder,” Ninth International Congress for Applied Mechanics, Brussels, Belgium, Sept. 5–13, pp. 175–183.
Minkowycz, W. , and Sparrow, E. , 1974, “Local Non Similar Solutions for Natural Convection on a Vertical Cylinder,” ASME J. Heat Transfer, 96(2), pp. 178–183.
Fujii, T. , and Uehara, H. , 1970, “Laminar Natural-Convective Heat Transfer From the Outer Surface of a Vertical Cylinder,” Int. J. Heat Mass Transfer, 13(3), pp. 607–615.
Kuiken, H. K. , 1998, “Axisymmetric Free Convection Boundary-Layer Flow Past Bodies,” Int. J. Heat Mass Transfer, 11(7), pp. 1141–1153.
Day, J. C. , Zemler, M. K. , Tarum, M. J. , and Boetcher, S. K. S. , 2013, “Laminar Natural Convection From Isothermal Vertical Cylinders; Revisiting the Classical Subject,” ASME J. Heat Transfer, 135(2), p. 022505.
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. , 2017, “Natural Convection Heat Transfer From Perforated Hollow Cylinder With Inline and Staggered Holes,” ASME J. Heat Transfer, 140(3), p. 032501.
Gray, D. D. , and Giorgini, A. , 1976, “The Validity of the Boussinesq Approximation for Liquids and Gases,” Int. J. Heat Mass Transfer, 19(5), pp. 545–551.
ANSYS, 2006, “Release 13.0, User Manual,” ANSYS Inc., Canonsburg, PA.

## Figures

Fig. 1

(a) Three-dimensional (3D) view of a vertical hollow cylinder suspended in air and (b) schematic diagram of computational domain showing a vertical hollow cylinder in cross-sectional view (2D axisymmetric geometry)

Fig. 2

Variation of average Nusselt number Nu with the domain height

Fig. 3

Grid arrangement in the domain (a) and a blown-up view of cells near the wall (b)

Fig. 4

Variation of Nusselt number Nu with the computational cells

Fig. 5

Variation of Nusselt number with Rayleigh number: a comparison between the present computation and the experimental correlations for vertical solid cylinder

Fig. 6

Temperature contour for various Ra at L/D = 5

Fig. 7

Variation of mass flow rate of air entering the cylinder as a function of Ra and L/D: (a) dimensional and (b) nondimensional

Fig. 8

Variation of heat transfer rate as a function of Ra and L/D

Fig. 9

Variation of Nu with Ra as a function of L/D

Fig. 10

Thermal plume around a vertical hollow cylinder for various L/D at Ra = 107

Fig. 11

Variation of dimensional and nondimensional mass flow rates through the cylinder as a function of Ra and L/D

Fig. 12

Heat loss from the inner and outer surfaces of the cylinder as a function of L/D and Ra

Fig. 13

Variation of Nu as a function of L/D and Ra

Fig. 14

Velocity vector around a vertical hollow cylinder for L/D = 5, Ra: (a) 104, (b) 105, (c) 106, (d) 107, and (e) 108

Fig. 15

Velocity vector around a vertical hollow cylinder for Ra = 107, L/D: (a) 1, (b) 2.5, (c) 5, (d) 10, (e) 15, and (f) 20

Fig. 16

A comparison between predicted and the computed value: (a) Nu and (b) mass flow rate

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