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Research Papers

Constructal Design Associated to Genetic Algorithm of Asymmetric V-Shaped Pathways

[+] Author and Article Information
Emanuel da S. D. Estrada, Tadeu M. Fagundes

Department of Mechanical Engineering,
Universidade Federal do Rio Grande do Sul,
Rua Sarmento Leite, 425,
Porto Alegre, RS 90050-170, Brazil

Liércio A. Isoldi, Elizaldo D. dos Santos

School of Engineering,
Universidade Federal do Rio Grande,
Italia Avenue km 8,
Rio Grande, RS 96201-900, Brazil

Gongnan Xie

School of Mechanical Engineering,
Northwestern Polytechnical University,
Xi'an 710129, China

Luiz A. O. Rocha

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

1Corresponding author.

Manuscript received May 4, 2014; final manuscript received January 28, 2015; published online March 17, 2015. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 137(6), 061010 (Jun 01, 2015) (7 pages) Paper No: HT-14-1292; doi: 10.1115/1.4029868 History: Received May 04, 2014; Revised January 28, 2015; Online March 17, 2015

This work relies on constructal design to perform the geometric optimization of the V-shaped pathways of highly conductive materials (inserts) that remove a constant heat generation rate from a body and deliver it to isothermal heat sinks. It is shown numerically that the global thermal resistance of the V-shaped pathway can be minimized by geometric optimization subject to total volume and V-shaped pathways material constraints. Constructal design and genetic algorithm (GA) optimization showed the emergence of an optimal architecture that minimizes the global thermal resistance: an optimal external shape for the assembly of pathways and optimal geometry features for the V-shaped pathway. Parametric study was performed to show the behavior of the minimized global thermal resistance as function of the volume fraction of the V-shaped pathways. First achieved results for ϕ = 0.3 indicated that when freedom is given to the geometry, the thermal performance is improved. Afterward, the employment of GA with constructal design allowed the achievement of the optimal shapes of V-shaped pathways for different volume fractions (0.2 ≤ ϕ ≤ 0.4). It was not realized the occurrence of one universal optimal shape for the several values of ϕ investigated, i.e., the optimal design was dependent on the degrees of freedom and the parameter ϕ and it is reached according to constructal principle of optimal distribution of imperfections.

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Figures

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Fig. 1

V-shaped high conductivity pathway

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Fig. 2

Temperature distribution of the V-shaped high conductivity pathway, when ϕ = 0.3, D˜0=0.2, D1/D0 = D2/D0 = 1, H/L = 0.5, and θmax=2.767

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Fig. 3

The effect of H/L and ϕ in the maximum dimensionless temperature θmax

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Fig. 4

The minimum maximal dimensionless temperature θmax,minand the corresponding optimal ratio (H/L)oas function of the volume fraction ϕ

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Fig. 5

Optimization of the minimum maximal dimensionless temperature θmax,minfor several values of the ratio D2/D0 as function of the ratio H/L

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Fig. 6

Summarized values of the minimum maximal dimensionless temperature and the once optimized ratio (H/L)o as function of the ratio D2/D0

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Fig. 7

Trend of the two times optimized θmax,mm and (H/L)oo as function of the ratio D1/D0

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Fig. 8

Trend of the three times optimized ratio (H/L)ooo and the other important optimized corresponding ratios as function ϕ

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Fig. 9

The best shapes of Figs. 3, 6, 7, and 8 when ϕ = 0.3. (a) D˜0=0.2, D1/D0 = 1, D2/D0 = 1, (H/L)o = 0.5, and θmax,m = 2.7670, (b) D˜0=0.2, D1/D0 = 1, (D2/D0)o = 1.9, (H/L)oo = 0.56, and θmax,mm = 2.6323, (c) D˜0=0.2, (D1/D0)o = 0.08, (D2/D0)oo = 3.7, (H/L)ooo = 0.96, and θmax,mmm = 2.5631, and (d) (D˜0)o=0.45, (D1/D0)oo = 0.48, (D2/D0)ooo = 0.55, (H/L)oooo = 0.46, and θmax,mmmm = 2.4575.

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Fig. 10

The optimal four degrees of freedom as function of ϕ

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Fig. 11

The best shapes of Fig. 10 as function of ϕ. (a) ϕ = 0.2, (D˜0)o=0.2, (D1/D0)oo = 0.48, (D2/D0)ooo = 1, (H/L)oooo = 0.5282, and θmax,mmmm = 4.2309, (b) ϕ = 0.25, (D˜0)o=0.4, (D1/D0)oo = 0.4, (D2/D0)ooo = 0.5, (H/L)oooo = 0.46, and θmax,mmmm = 3.1288, (c) ϕ = 0.35, (D˜0)o=0.55, (D1/D0)oo = 0.48, (D2/D0)ooo = 0.55, (H/L)oooo = 0.4497, and θmax,mmmm = 1.9945, and (d) ϕ = 0.40, (D˜0)o=0.2, (D1/D0)oo = 0.1, (D2/D0)ooo = 5, (H/L)oooo = 1.1774, and θmax,mmmm = 1.6263.

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