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Research Papers: Natural and Mixed Convection

Entropy Generation in Laminar and Turbulent Natural Convection Heat Transfer From Vertical Cylinder With Annular Fins

[+] Author and Article Information
Jnana Ranjan Senapati

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India
e-mail: jnanabharat270@gmail.com

Sukanta Kumar Dash, Subhransu Roy

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 5, 2016; final manuscript received November 18, 2016; published online January 24, 2017. Assoc. Editor: Jim A. Liburdy.

J. Heat Transfer 139(4), 042501 (Jan 24, 2017) (13 pages) Paper No: HT-16-1441; doi: 10.1115/1.4035355 History: Received July 05, 2016; Revised November 18, 2016

Entropy generation due to natural convection has been calculated for a wide range of Rayleigh number (Ra) in both laminar (104 ≤ Ra ≤ 108) and turbulent (1010 ≤ Ra ≤ 1012) flow regimes, for diameter ratio of 2 ≤ D/d ≤ 5, for an isothermal vertical cylinder fitted with annular fins. In the laminar regime, the entropy generation was predominantly caused by heat transfer (conduction and convection) and the viscous contribution was negligible with respect to heat transfer. But in the turbulent regime, entropy generation due to fluid friction is significant enough although heat transfer entropy generation is still dominant. The results demonstrate that the degree of irreversibility is higher in case of finned configuration when compared with unfinned one. With the deployment of a merit function combining the first and second laws of thermodynamics, we have tried to delineate the thermodynamic performance of finned cylinder with natural convection. So, we have defined the ratio (I/Q)finned/(I/Q)unfinned. The ratio (I/Q)finned/(I/Q)unfinned gets its minimum value at optimum fin spacing where maximum heat transfer occurs in turbulent flow, whereas in laminar flow the ratio (I/Q)finned/(I/Q)unfinned decreases continuously with the increase in number of fins.

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References

Figures

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Fig. 1

Schematic diagram of computational domain (not to scale)

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Fig. 3

Grid arrangement over the finned cylinder in the computational domain

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Fig. 2

Variation of Nusselt number with Rayleigh number for vertical unfinned cylinder: A comparison between the present computation and the experimental correlations: (a) laminar flow and (b) turbulent flow

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Fig. 4

Variation of Nusselt number with computational cells (a) and domain size (b)

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Fig. 7

Variation of heat transfer rate with nondimensional fin spacing for different values of diameter ratio D/d and Ra in laminar flow

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Fig. 8

Variation of heat transfer rate with nondimensional fin spacing for different values of diameter ratio D/d and Ra in turbulent flow

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Fig. 12

Variation of heat transfer irreversibility (a) and fluid friction irreversibility (b) with nondimensional fin spacing, S/d for different values of Ra in laminar flow, with D/d = 5

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Fig. 11

Variation of entropy generation rate with Rayleigh number: (a) laminar range and (b) turbulent range

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Fig. 5

Variation of the ratio (I/Q)finned/(I/Q)unfinned with nondimensional fin spacing, S/d for different values diameter ratio D/d and Ra for laminar flow

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Fig. 6

Variation of the ratio (I/Q)finned/(I/Q)unfinned with nondimensional fin spacing, S/d for different values diameter ratio D/d and Ra for turbulent flow

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Fig. 9

Variation of Nusselt number as a function of Rayleigh number: (a) laminar range and (b) turbulent range

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Fig. 10

Evaluation of local heat transfer coefficient along the fin: (a) laminar range and (b) turbulent range

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Fig. 15

Variation of Bejan number with nondimensional fin spacing, S/d for different values diameter ratio D/d and Ra for turbulent flow

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Fig. 13

Variation of heat transfer irreversibility with nondimensional fin spacing, S/d for different values of Ra in turbulent flow, with D/d = 5

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Fig. 16

Plots of velocity vector with varying fin spacing in laminar range for D/d = 5 and Ra = 1.773 × 107

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Fig. 17

Plots of velocity vector with varying fin spacing in turbulent range for D/d = 5 and Ra = 1.773 × 1011

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Fig. 18

Contours of static temperature with varying fin spacing in laminar flow for D/d = 5 and Ra = 1.773 × 107

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Fig. 19

Contours of static temperature with varying fin spacing in turbulent flow for D/d = 5 and Ra = 1.773 × 1011

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Fig. 14

Variation of fluid friction irreversibility with nondimensional fin spacing, S/d for different values of Ra in turbulent flow, with D/d = 5

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Fig. 20

Contours of entropy generation rate per unit volume with varying fin spacing, S/d at D/d = 5 and Ra = 1.773 × 107

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Fig. 21

Contours of entropy generation rate per unit volume with varying fin spacing, S/d at D/d = 5 and Ra = 1.773 × 1011

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