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Research Papers: Natural and Mixed Convection

Natural Convection Heat Transfer From Perforated Hollow Cylinder With Inline and Staggered Holes

[+] 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

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 February 21, 2017; final manuscript received July 24, 2017; published online October 10, 2017. Assoc. Editor: Antonio Barletta.

J. Heat Transfer 140(3), 032501 (Oct 10, 2017) (14 pages) Paper No: HT-17-1095; doi: 10.1115/1.4037875 History: Received February 21, 2017; Revised July 24, 2017

The continuity, momentum, and the energy conservation equation for air around a hollow cylinder with inline or staggered holes have been solved in three dimensions to assess the buoyancy driven flow and temperature field around the cylinder. From the thermal field, the average surface Nu could be computed for hollow cylinders with inline or staggered holes and the heat loss from the cylinder could be compared with that of a hollow cylinder without holes. Interesting flow and thermal plume around the hollow cylinder with holes could be seen, which could help to explain why there is more heat loss from a cylinder with staggered holes compared to a cylinder with inline holes at lower Ra of 105, whereas for higher Ra of 106 or more, there exists an optimum d/D where the heat loss from the perforated cylinder has a maximum value and thereafter it reduces. There are interesting comparisons on Nu for the hollow cylinder with inline or staggered holes and new correlations for Nu versus many different pertinent input parameters have been developed for many cases, which can be used practically in industry for designing perforated cylinder with heat loss.

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Figures

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Fig. 1

(a) Cylinder with staggered holes for θ = 45 deg (front view, X = 4) and (b) cylinder with inline holes for θ = 45 deg (front view, X = 4)

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Fig. 2

(a) Top view of the hollow cylinder with inline holes, (b) top view of hollow cylinder with staggered holes (a schematic representation), and (c) isometric view of cylinder showing hole arrangements (inline and staggered) and X

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Fig. 3

Influence of domain height on average Nu for a perforated hollow cylinder in air

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Fig. 4

(a) Cell arrangement for perforated hollow cylinder in air, (b) cross-sectional view, and (c) blown-up view near the cylinder wall

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Fig. 5

Average Nu for a hollow perforated cylinder in air as a function of number of cells

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Fig. 6

Average Nu for a (a) long solid cylinder in air and (b) a sphere in air, a comparison with experimental correlation

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Fig. 7

Average surface Nu variation as a function of d/D, P/D, and Ra for (a) L/D = 20, (b) L/D = 10, and (c) L/D = 2 for inline holes with θ = 180 deg

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Fig. 8

Velocity vector around hollow cylinder for inline holes with θ = 180 deg at L/D = 5, d/D = 0.1, Ra = 106: (a) P/D = 0.5, (b) P/D = 1 and thermal plume around the cylinder for, (c) P/D = 0.5, and (d) P/D = 1

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Fig. 9

Velocity vector around hollow cylinder for inline holes with θ = 180 deg at L/D = 5, d/D = 0.333, Ra = 106: (a) P/D = 0.5, (b) P/D = 1 and thermal plume around the cylinder for, (c) P/D = 0.5, and (d) P/D = 1

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Fig. 10

Variation of Nu as a function of number of pair of inline holes at θ = 180 deg: (a) d/D = 0.167, (b) d/D = 0.333 (Rayleigh number 104), (c) d/D = 0.167, and (d) d/D = 0.333 (Rayleigh number 107)

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Fig. 11

Velocity vector around hollow cylinder for inline holes with d/D = 0.333, Ra = 107: (a) X = 1, L/D = 5, (b) X = 1, L/D = 2, (c) X = 3, L/D = 5, and (d) X = 3, L/D = 2

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Fig. 12

Thermal plume around the cylinder for inline holes with d/D = 0.333, Ra = 107: (a) X = 1, L/D = 5, (b) X = 1, L/D = 2, (c) X = 3, L/D = 5, and (d) X = 3, L/D = 2

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Fig. 13

Variation of Nu as a function of number of pair of staggered holes at θ = 45 deg: (a) d/D = 0.167, (b) d/D = 0.333 (Rayleigh number 104), (c) d/D = 0.167, and (d) d/D = 0.333 (Rayleigh number 107)

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Fig. 14

Variation of Nu as a function L/D for inline (θ = 180) and staggered holes (θ = 30, 45, 90), P/D = 1: (a) d/D = 0.167 and (b) d/D = 0.333

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Fig. 15

Thermal plume around the cylinder with inline holes for d/D = 0.333, P/D = 1, Ra = 106: (a) L/D = 10, (b) L/D = 5, (c) L/D = 2, (d) L/D = 5, Ra = 104, and (e) L/D = 5, Ra = 107

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Fig. 16

variation of Nu as a function d/D at P/D = 1, L/D = 5: (a) θ = 90 deg and (b) θ = 45 deg

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Fig. 17

Thermal plume around the cylinder for L/D = 5, d/D = 0.333, P/D = 1, Ra = 106: (a) inline holes with longitudinal cross section, (b) inline holes with midtransverse cross section on, (c) staggered holes with θ = 45 deg longitudinal cross section, and (d) staggered holes with θ = 45 deg with midtransverse cross section

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Fig. 18

Ratio of heat transfer from hollow cylinder with holes to hollow cylinder without holes for θ = 180 (inline holes) as a function of d/D at P/D = 0.5 with Rayleigh number (a) 104, (b) 106, (c) 107 and at P/D = 1 with Rayleigh number, (d) 104, (e) 106, and (f) 107

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Fig. 19

Ratio of heat transfer from hollow cylinder with holes to hollow cylinder without holes for staggered holes at θ = 30 deg as a function of d/D at P/D = 0.5 with Rayleigh number (a) 104, (b) 106, (c) 107 and at P/D = 1 with Rayleigh number, (d) 104, (e) 106, and (f) 107

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Fig. 20

A comparison of predicted Nu with that of the computed value for a hollow cylinder with inline holes for θ = 180

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