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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

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/D20. 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

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Figures

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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)

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Fig. 2

Variation of average Nusselt number Nu with the domain height

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Fig. 3

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

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Fig. 4

Variation of Nusselt number Nu with the computational cells

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Fig. 5

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

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Fig. 6

Temperature contour for various Ra at L/D = 5

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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

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Fig. 8

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

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Fig. 9

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

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Fig. 10

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

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Fig. 11

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

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Fig. 12

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

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Fig. 13

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

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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

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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

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Fig. 16

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

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