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Research Papers: Heat Transfer Enhancement

Constructal Design of Complex Assembly of Fins

[+] Author and Article Information
Giulio Lorenzini1

Department of Industrial Engineering, University of Parma, Parco Area delle Scienze No. 181/A, 43124 Parma, Italygiulio.lorenzini@unipr.it

Roberta Lima Corrêa

Program of Postgraduation in Computational Modeling, Universidade Federal do Rio Grande, Caixa Postal 474, Rio Grande, Rio Grande do Sul 96201-900, Brazilluizrocha@furg.br

Elizaldo Domingues dos Santos

School of Engineering, Universidade Federal do Rio Grande, Caixa Postal 474, Rio Grande, Rio Grande do Sul 96201-900, Brazilelizaldosantos@furg.br

Luiz Alberto Oliveira Rocha

Department of Mechanical Engineering, Universidade Federal do Rio Grande do Sul, Rua Sarmento Leite, 425 Porto Alegre, RS, 90050-170, Brazilluizrocha@mecanica.ufrgs.br

1

Corresponding author.

J. Heat Transfer 133(8), 081902 (May 02, 2011) (7 pages) doi:10.1115/1.4003710 History: Received December 07, 2010; Revised February 03, 2011; Published May 02, 2011

Constructal design is a method that conducts the designer toward flow (e.g., heat flux) architectures that have greater global performance. This numerical work uses this method to seek for the best geometry of a complex assembly of fins, i.e., an assembly where there is a cavity between the two branches of the T-Y-assembly of fins and two additional extended surfaces. The global thermal resistance of the assembly is minimized four times by geometric optimization subject to the following constraints: the total volume, the volume of fin material, the volume of the cavity, and the volume of the two additional extended surfaces. Larger amount of fin material improves the performance of the assembly of fins. The three times optimized global thermal resistance of the complex assembly of fins performs 32% better than the best T-Y-configuration under the same thermal and geometric conditions. The three times minimized global thermal resistance of the complex assembly of fins was correlated by power laws as a function of its corresponding optimal configurations.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Complex assembly of fins

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Figure 2

The optimization of the global thermal resistance as a function of the ratio H0/L0 for several values of the ratio H1/L1

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Figure 3

The optimization of the once minimized global thermal resistance and the corresponding once minimized ratio (H0/L0)o as a function of the ratio H1/L1

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Figure 4

The best shapes for the H1/L1 ratios corresponding to the two extremes and the optimal configuration reached in Fig. 3: (a) H1/L1=0.01, (b) H1/L1=0.058 (optimal), and (c) H1/L1=0.2

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Figure 5

The optimization of the twice optimized global thermal resistance and optimal shapes as a function of the ratio H2/L2

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Figure 6

The best complex assembly of fins shown in Fig. 5 and the best T-Y-shaped assembly of fins (16) (H/L=1, a=0.1, ϕ=0.1, and ϕ=0.05)

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Figure 7

The fourth optimization of the global thermal resistance and optimal shapes of the complex assembly of fins as a function of the ratio H/L for ϕ1=0.2

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Figure 8

Some shapes calculated in Fig. 7 as a function of the ratio H/L: (a) H/L=0.5, (b) H/L=1.0, (c) H/L=1.7 (optimal), and (d) H/L=2.0

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Figure 9

The fourth optimization as a function of the ratio H/L for several values of ϕ1

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Figure 10

The best shapes calculated in Fig. 9 as a function of ϕ1

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Figure 11

The optimal (H0/L0)ooo as a function of the ratio H/L for several values of ϕ1

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Figure 12

The optimal (H1/L1)oo as a function of the ratio H/L for several values of ϕ1

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Figure 13

The optimal (H2/L2)o as a function of the ratio H/L for several values of ϕ1

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