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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

Bejan, A. , 2004, Convection Heat Transfer, 3rd ed., Wiley, Hoboken, NJ.
Kreith, F. , Manglik, R. M. , and Bohn, M. S. , 2011, Principles of Heat Transfer, 7th ed., Cengage, Independence, KY.
Güvenç, A. , and Yüncü, H. , 2001, “ An Experimental Investigation on Performance of Fins on a Horizontal Base in Free Convection Heat Transfer,” Heat Mass Transfer, 37(4), pp. 409–416. [CrossRef]
Yazicioǧlu, B. , and Yüncü, H. , 2007, “ Optimum Fin Spacing of Rectangular Fins on a Vertical Base in Free Convection Heat Transfer,” Heat Mass Transfer, 44(1), pp. 11–21. [CrossRef]
Bejan, A. , 1979, “ A Study of Entropy Generation in Fundamental Convective Heat Transfer,” ASME J. Heat Transfer, 101(4), pp. 718–725. [CrossRef]
Kuhen, T. H. , Kwon, S. S. , and Topadi, A. K. , 1983, “ Similarity Solution for Conjugate Natural Convection Heat Transfer From a Long Vertical Plate Fin,” Int. J. Heat Mass Transfer, 26(11), pp. 1718–1721. [CrossRef]
Abu-Hijleh, B. , Abu-Qudais, M. , and Abu Nada, E. , 1999, “ Numerical Prediction of Entropy Generation Due to Natural Convection From a Horizontal Cylinder,” Energy, 24(4), pp. 327–333. [CrossRef]
Abu-Hijleh, B. A. K. , and Heilen, W. N. , 1999, “ Entropy Generation Due to Laminar Natural Convection Over a Heated Rotating Cylinder,” Int. J. Heat Mass Transfer, 42(22), pp. 4225–4233. [CrossRef]
Baytas, A. C. , 2000, “ Entropy Generation for Natural Convection in an Inclined Porous Cavity,” Int. J. Heat Mass Transfer, 43(12), pp. 2089–2099. [CrossRef]
Abu-Hijleh, B. , 2001, “ Natural Convection and Entropy Generation From a Cylinder With High Conductivity Fins,” Numer. Heat Transfer, Part A, 39(4), pp. 405–432. [CrossRef]
Mahmud, S. , and Islam, A. K. M. S. , 2003, “ Laminar Free Convection and Entropy Generation Inside an Inclined Wavy Enclosure,” Int. J. Therm. Sci., 42(11), pp. 1003–1012. [CrossRef]
Magherbi, M. , Abbassi, H. , and Brahim, A. B. , 2003, “ Entropy Generation at the Onset of Natural Convection,” Int. J. Heat Mass Transfer, 46(18), pp. 3441–3450. [CrossRef]
Mahmud, S. , and Fraser, R. A. , 2004, “ Magnetohydrodynamic Free Convection and Entropy Generation in a Square Porous Cavity,” Int. J. Heat Mass Transfer, 47(14–16), pp. 3245–3256. [CrossRef]
Daǧtekin, I. , Öztop, H. F. , and Şahin, A. Z. , 2005, “ An Analysis of Entropy Generation Through a Circular Duct With Different Shaped Longitudinal Fins for Laminar Flow,” Int. J. Heat Mass Transfer, 48(1), pp. 171–181. [CrossRef]
Andreozzi, A. , Auletta, A. , and Manca, O. , 2006, “ Entropy Generation in Natural Convection in a Symmetrically and Uniformly Heated Vertical Channel,” Int. J. Heat Mass Transfer, 49(17–18), pp. 3221–3228. [CrossRef]
Jery, A. E. , Hidouri, N. , Magherbi, M. , and Brahim, A. B. , 2010, “ Effect of an External Oriented Magnetic Field on Entropy Generation in Natural Convection,” Entropy, 12(6), pp. 1391–1417. [CrossRef]
Dagtekin, I. , Oztop, H. F. , and Bahloul, A. , 2007, “ Entropy Generation for Natural Convection in Γ-Shaped Enclosures,” Int. Commun. Heat Mass Transfer, 34(4), pp. 502–510. [CrossRef]
Famouri, M. , and Hooman, K. , 2008, “ Entropy Generation for Natural Convection by Heated Partitions in a Cavity,” Int. Commun. Heat Mass Transfer, 35(4), pp. 492–502. [CrossRef]
Zahmatkesh, I. , 2008, “ On the Importance of Thermal Boundary Conditions in Heat Transfer and Entropy Generation for Natural Convection Inside a Porous Enclosure,” Int. J. Therm. Sci., 47(3), pp. 339–346. [CrossRef]
Varol, Y. , Oztop, H. F. , and Koca, A. , 2008, “ Entropy Generation Due to Conjugate Natural Convection in Enclosures Bounded by Vertical Solid Walls With Different Thicknesses,” Int. Commun. Heat Mass Transfer, 35(5), pp. 648–656. [CrossRef]
Oliveski, R. D. C. , Macagnan, M. H. , and Copetti, J. B. , 2009, “ Entropy Generation and Natural Convection in Rectangular Cavities,” Appl. Therm. Eng., 29(8–9), pp. 1417–1425. [CrossRef]
Varol, Y. , Oztop, H. F. , and Pop, I. , 2009, “ Entropy Generation Due to Natural Convection in Non-Uniformly Heated Porous Isosceles Triangular Enclosures at Different Positions,” Int. J. Heat Mass Transfer, 52(5–6), pp. 1193–1205. [CrossRef]
García, J. C. C. , and Treviño, C. T. , 2010, “ Natural Convection and Entropy Generation in a Small Aspect Ratio Cavity,” Mecánica Comput., XXIX, pp. 3281–3289. http://www.cimec.org.ar/ojs/index.php/mc/article/viewFile/3232/3155
Mukhopadhyay, A. , 2010, “ Analysis of Entropy Generation Due to Natural Convection in Square Enclosures With Multiple Discrete Heat Sources,” Int. Commun. Heat Mass Transfer, 37(7), pp. 867–872. [CrossRef]
Shahi, M. , Mahmoudi, A. H. , and Raouf, A. H. , 2011, “ Entropy Generation Due to Natural Convection Cooling of a Nanofluid,” Int. Commun. Heat Mass Transfer, 38(7), pp. 972–983. [CrossRef]
Kaluri, R. S. , and Basak, T. , 2011, “ Analysis of Entropy Generation for Distributed Heating in Processing of Materials by Thermal Convection,” Int. J. Heat Mass Transfer, 54(11–12), pp. 2578–2594. [CrossRef]
Kaluri, R. S. , and Basak, T. , 2011, “ Entropy Generation Due to Natural Convection in Discretely Heated Porous Square Cavities,” Energy, 36(8), pp. 5065–5080. [CrossRef]
Bouabid, M. , Magherbi, M. , Hidouri, N. , and Brahim, A. B. , 2011, “ Entropy Generation at Natural Convection in an Inclined Rectangular Cavity,” Entropy, 13(12), pp. 1020–1033. [CrossRef]
Sheikhzadeh, G. A. , Nikfar, M. , and Fattahi, A. , 2012, “ Numerical Study of Natural Convection and Entropy Generation of Cu-Water Nanofluid Around an Obstacle in a Cavity,” J. Mech. Sci. Technol., 26(10), pp. 3347–3356. [CrossRef]
Basak, T. , Kaluri, R. S. , and Balakrishnan, A. R. , 2012, “ Entropy Generation During Natural Convection in a Porous Cavity: Effect of Thermal Boundary Conditions,” Numer. Heat Transfer, Part A, 62(4), pp. 336–364. [CrossRef]
Basak, T. , Gunda, P. , and Anandalakshmi, R. , 2012, “ Analysis of Entropy Generation During Natural Convection in Porous Right-Angled Triangular Cavities With Various Thermal Boundary Conditions,” Int. J. Heat Mass Transfer, 55(17–18), pp. 4521–4535. [CrossRef]
Singh, A. K. , Roy, S. , and Basak, T. , 2012, “ Analysis of Entropy Generation Due to Natural Convection in Tilted Square Cavities,” Ind. Eng. Chem. Res., 51(40), pp. 13300–13318. [CrossRef]
Esmaeilpour, M. , and Abdollahzadeh, M. , 2012, “ Free Convection and Entropy Generation of Nanofluid Inside an Enclosure With Different Patterns of Vertical Wavy Walls,” Int. J. Therm. Sci., 52, pp. 127–136. [CrossRef]
Mchirgui, A. , Hidouri, N. , Magherbi, M. , and Ben Brahim, A. , 2013, “ Entropy Generation for Natural Convection in a Darcy–Brinkman Porous Cavity,” Int. Sch. Sci. Res. Innovation, 7(4), pp. 600–604. http://waset.org/publications/8320/entropy-generation-for-natural-convection-in-a-darcy-brinkman-porous-cavity
Pati, S. , Som, S. K. , and Chakraborty, S. , 2013, “ Thermodynamic Performance of Microscale Swirling Flows With Interfacial Slip,” Int. J. Heat Mass Transfer, 57(1), pp. 397–401. [CrossRef]
Salari, M. , Rezvani, A. , Mohammadtabar, A. , and Mohammadtabar, M. , 2014, “ Numerical Study of Entropy Generation for Natural Convection in Rectangular Cavity With Circular Corners,” Heat Transfer Eng., 36(2), pp. 186–199. [CrossRef]
Naas, T. T. , Lasbet, Y. , and Kezrane, C. , 2015, “ Entropy Generation Analyze Due to the Steady Natural Convection of Newtonian Fluid in a Square Enclosure,” International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 9(4), pp. 582–586. http://www.waset.org/publications/10001025
Selimefendigil, F. , Öztop, H. , and Abu-Hamdeh, N. , 2016, “ Natural Convection and Entropy Generation in Nanofluid Filled Entrapped Trapezoidal Cavities Under the Influence of Magnetic Field,” Entropy, 18(2), p. 43. [CrossRef]
Herwig, H. , and Kock, F. , 2006, “ Direct and Indirect Methods of Calculating Entropy Generation Rates in Turbulent Convective Heat Transfer Problems,” Heat Mass Transfer, 43(3), pp. 207–215. [CrossRef]
Shuja, S. Z. , Yilbas, B. S. , and Budair, M. O. , 2001, “ Local Entropy Generation in an Impinging Jet: Minimum Entropy Concept Evaluating Various Turbulence Models,” Comput. Methods Appl. Mech. Eng., 190(28), pp. 3623–3644. [CrossRef]
Chen, S. , and Krafczyk, M. , 2009, “ Entropy Generation in Turbulent Natural Convection Due to Internal Heat Generation,” Int. J. Therm. Sci., 48(10), pp. 1978–1987. [CrossRef]
Şahin, A. Z. , 2000, “ Entropy Generation in Turbulent Liquid Flow Through a Smooth Duct Subjected to Constant Wall Temperature,” Int. J. Heat Mass Transfer, 43(8), pp. 1469–1478. [CrossRef]
Sahin, A. Z. , 2002, “ Entropy Generation and Pumping Power in a Turbulent Fluid Flow Through a Smooth Pipe Subjected to Constant Heat Flux,” Exergy Int. J., 2(4), pp. 314–321. [CrossRef]
Tandiroglu, A. , 2007, “ Effect of Flow Geometry Parameters on Transient Entropy Generation for Turbulent Flow in Circular Tube With Baffle Inserts,” Energy Convers. Manag., 48(3), pp. 898–906. [CrossRef]
Kock, F. , and Herwig, H. , 2004, “ Local Entropy Production in Turbulent Shear Flows: A High-Reynolds Number Model With Wall Functions,” Int. J. Heat Mass Transfer, 47(10–11), pp. 2205–2215. [CrossRef]
Kock, F. , and Herwig, H. , 2005, “ Entropy Production Calculation for Turbulent Shear Flows and Their Implementation in CFD Codes,” Int. J. Heat Fluid Flow., 26(4), pp. 672–680. [CrossRef]
Singh, B. , and Dash, S. K. , 2015, “ Natural Convection Heat Transfer From a Finned Sphere,” Int. J. Heat Mass Transfer, 81, pp. 305–324. [CrossRef]
Senapati, J. R. , Dash, S. K. , and Roy, S. , 2016, “ 3D Numerical Study of the Effect of Eccentricity on Heat Transfer Characteristics Over Horizontal Cylinder Fitted With Annular Fins,” Int. J. Therm. Sci., 108, pp. 28–39. [CrossRef]
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. [CrossRef]
Launder, B. E. , and Spalding, D. B. , 1972, Lectures in Mathematical Models of Turbulence, Academic Press, New York.
Launder, B. E. , and Spalding, D. B. , 1974, “ The Numerical Computation of Turbulent Flows,” Comput. Methods Appl. Mech. Eng., 3(2), pp. 269–289. [CrossRef]
Senapati, J. R. , Dash, S. K. , and Roy, S. , 2016, “ Numerical Investigation of Natural Convection Heat Transfer Over Annular Finned Horizontal Cylinder,” Int. J. Heat Mass Transfer, 96, pp. 330–345. [CrossRef]
Gebhart, B. , Jaluria, Y. , Mahajan, R. L. , and Sammakia, B. , 1988, Buoyancy-Induced Flows and Transport, Hemisphere, New York.
Minkowycz, W. , and Sparrow, E. , 1974, “ Local Nonsimilar Solutions for Natural Convection on a Vertical Cylinder,” ASME J. Heat Transfer, 96(2), pp. 178–183. [CrossRef]
Churchill, S. W. , 1977, “ A Comprehensive Correlating Equation for Laminar, Assisting, Forced and Free Convection,” AIChE J., 23(1), pp. 10–16. [CrossRef]
McAdams, W. H. , 1954, Heat Transmission, 3rd ed., McGraw-Hill, New York.
Eckert, E. R. G. , and Jackson, T. W. , 1951, “ Analysis of Turbulent Free-Convection Boundary Layer on Flat Plate,” U.S. National Advisory Committee for Aeronautics, Report No. NACA-TR-1015. https://ntrs.nasa.gov/search.jsp?R=19930092070
Nag, P. K. , 2007, Heat and Mass Tranfer, 2nd ed., Tata McGraw-Hill, Delhi, India.

Figures

Grahic Jump Location
Fig. 1

Schematic diagram of computational domain (not to scale)

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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. 3

Grid arrangement over the finned cylinder in the computational domain

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Fig. 4

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

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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. 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. 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. 11

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

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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. 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. 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. 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. 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. 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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