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Research Papers: Natural and Mixed Convection

Constructal Design of Rectangular Fin Intruded Into Mixed Convective Lid-Driven Cavity Flows

[+] Author and Article Information
G. Lorenzini

Università degli Studi di Parma,
Dipartimento di Ingegneria Industriale,
Parco Area delle Scienze 181/A,
Parma 43124, Italy

B. S. Machado

Department of Mechanical Engineering,
Federal University of Rio Grande do Sul,
Sarmento Leite Street,
Porto Alegre 425, 90.050-170, Brazil

L. A. Isoldi, E. D. dos Santos

School of Engineering,
Federal University of Rio Grande,
Italia Avenue, km 8,
Rio Grande 96201-900, Brazil

L. A. O. Rocha

Department of Mechanical Engineering,
Federal University of Rio Grande do Sul,
Sarmento Leite Street, 425,
Porto Alegre 90.050-170, Brazil
e-mail: giulio.lorenzini@unipr.it

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 22, 2015; final manuscript received February 19, 2016; published online June 7, 2016. Assoc. Editor: Gongnan Xie.

J. Heat Transfer 138(10), 102501 (Jun 07, 2016) (12 pages) Paper No: HT-15-1614; doi: 10.1115/1.4033378 History: Received September 22, 2015; Revised February 19, 2016

The present work shows a numerical study of laminar, steady, and mixed convective flow inside lid-driven square cavity with intruded rectangular fin in its lower surface. The main purpose here is to maximize the heat transfer between the rectangular fin and the surrounding mixed convective flow inside a lid-driven cavity by means of constructal design. The problem is subject to two constraints, the lid-driven cavity and intruded fin areas. The ratio between the fin and cavity areas is kept fixed (ϕ = 0.05). The investigated geometry has one degree-of-freedom (DOF), the fin aspect ratio (H1/L1), which is varied in the range 0.1 ≤ H1/L1 ≤ 10. The aspect ratio of the cavity is maintained fixed (H/L = 1.0). The effect of the fin geometry over the Nusselt number is investigated for several Rayleigh (RaH = 103, 104, 105 and 106) and Reynolds numbers (ReH = 10, 102, 3.0 × 102, 5.0 × 102, 7.0 × 102 and 103). For all simulations, the Prantdl number is fixed (Pr = 0.71). The conservation equations of mass, momentum, and energy are numerically solved with the finite volume method. Results showed that fin geometry (H1/L1) has strong influence over the Nusselt number in the fin. It was also observed that the effect of H1/L1 over Nusselt number changes considerably for different Rayleigh numbers and for the lowest magnitudes of Reynolds numbers, for example, differences of nearly 770% between RaH = 106 and forced convective flow were observed for the lowest Reynolds number studied (ReH = 10).

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Figures

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Fig. 1

Problem domain for lid-driven cavity flow with intruded rectangular fin

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Fig. 2

Flowchart of performed simulations

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Fig. 3

Effect of the ratio H1/L1 over the spatial-averaged Nusselt number (NuH¯) for various Reynolds numbers and RaH = 103

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Fig. 4

Effect of Reynolds number over once maximized spatial-averaged Nusselt number (NuH,max¯) and its respective optimal shape, (H1/L1)opt

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Fig. 5

Effect of Reynolds number over once maximized spatial-averaged Nusselt number (NuH,max¯) for various values of RaH

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Fig. 6

Effect of Reynolds number over once optimized ratio (H1/L1)opt for various values of RaH

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Fig. 7

Local Nusselt number for Pr = 0.71 and RaH = 103: (a) ReH = 10, (H1/L1)opt = 0.6, (b) ReH = 100, (H1/L1)opt = 0.6, (c) ReH = 300, (H1/L1)opt = 0.6, (d) ReH = 500, (H1/L1)opt = 0.6, (e) ReH = 700, (H1/L1)opt = 0.6, and (f) ReH = 1000, (H1/L1)opt = 0.6

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Fig. 8

Dimensionless temperature field for RaH = 103 for different Reynolds number: (a) ReH = 10, (b) ReH = 100, (c) ReH = 300, (d) ReH = 500, (e) ReH = 700, and (f) ReH = 1000

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Fig. 9

Dimensionless velocity field for RaH = 103 for different Reynolds number: (a) ReH = 10, (b) ReH = 100, (c) ReH = 300, (d) ReH = 500, (e) ReH = 700, and (f) ReH = 1000

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Fig. 10

Local Nusselt number for several Reynolds numbers and the corresponding optimal fin aspect ratio: (a) RaH = 103, ReH = 1000, (H1/L1)opt = 0.5, (b) RaH = 104, ReH = 1000, (H1/L1)opt = 0.5, (c) RaH = 105, ReH = 1000, (H1/L1)opt = 0.5, and (d) RaH = 106, ReH = 1000, (H1/L1)opt = 0.5

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Fig. 11

Dimensionless temperature field for optimal aspect ratio (H1/L1)o for different Rayleigh numbers and ReH = 1000: (a) RaH = 103, (b) RaH = 104, (c) RaH = 105, and (d) RaH = 106

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Fig. 12

Dimensionless velocity field for optimal aspect ratio (H1/L1)o for different Rayleigh numbers and ReH = 1000: (a) RaH = 103, (b) RaH = 104, (c) RaH = 105, and (d) RaH = 106

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Fig. 13

Comparison between mixed convection and forced convection cases for different Reynolds number: (a) ReH = 10, (b) ReH = 100, (c) ReH = 300, (d) ReH = 500, (e) ReH = 700, and (f) ReH = 1000

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