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Research Papers

Genetic Algorithm Applied to Geometric Optimization of Isothermal Y-Shaped Cavities

[+] Author and Article Information
Giulio Lorenzini

Dipartimento di Ingegneria Industriale,
Università degli Studi di Parma,
Parco Area delle Scienze 181/A,
Parma 43124, Italy
e-mail: giulio.lorenzini@unipr.it

Cesare Biserni

Dipartimento di Ingegneria Industriale,
Università degli Studi di Bologna,
Viale Risorgimento 2,
Bologna 40136, Italy
e-mail: cesare.biserni@unibo.it

Emanuel da Silva Diaz Estrada

Centro de Ciências Computacionais (C3),
Universidade Federal do Rio Grande (FURG),
Av. Itália, km 8,
Carreiros, Rio Grande-RS 96021-900, Brazil
e-mail: emanuelestrada@furg.br

Elizaldo Domingues Dos Santos

Escola de Engenharia (EE),
Universidade Federal do Rio Grande (FURG),
Av. Itália, km 8,
Carreiros, Rio Grande-RS 96021-900, Brazil
e-mail: elizaldosantos@furg.br

Liércio André Isoldi

Escola de Engenharia (EE),
Universidade Federal do Rio Grande (FURG),
Av. Itália, km 8,
Carreiros, Rio Grande-RS 96021-900, Brazil
e-mail: liercioisoldi@furg

Luiz Alberto Oliveira Rocha

Departamento de Engenharia Mecânica (DEMEC),
Universidade Federal do Rio
Grande do SUL (UFRGS),
Rua Sarmento Leite, 425, Centro,
Porto Alegre-RS 90050-170, Brazil
e-mail: luizrocha@mecanica.ufrgs.br

1Corresponding author.

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received February 18, 2014; final manuscript received April 7, 2014; published online May 12, 2014. Assoc. Editor: Gary Miller.

J. Electron. Packag 136(3), 031011 (May 12, 2014) (9 pages) Paper No: EP-14-1022; doi: 10.1115/1.4027421 History: Received February 18, 2014; Revised April 07, 2014

Constructal design associated with genetic algorithm (GA) is employed to optimize the geometry of an isothermal Y-shaped cavity embedded into a solid conducting wall. The structure has four degrees of freedom (DOF). The main purpose is to minimize the maximum excess of temperature between the solid and the cavity by means of GA and exhaustive search (simulating every geometry combinations). Results showed that GA was well succeeded to find the best shapes which minimize the maximal excess of temperature with a number of simulations strongly lower than that required with exhaustive search, allowing the optimization of cavity under new constraint conditions.

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References

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Lorenzini, G., Biserni, C., Isoldi, L. A., dos Santos, E. D., and Rocha, L. A. O., 2011, “Constructal Design Applied to the Geometric Optimization of Y-Shaped Cavities Embedded in a Conducting Medium,” ASME J. Electron. Packag., 133(40), p. 041008. [CrossRef]
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Figures

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Fig. 1

Domain of the Y-shaped cavity intruded into a two-dimensional conducting body with uniform heat generation

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Fig. 2

GA steps to optimize the isothermal Y-shaped cavity

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Fig. 3

Illustration of some shapes as a function of L1/L0 and tributary angle found with GA

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Fig. 4

Bit array representing two degrees of freedom (L1/L0 and α)

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Fig. 5

Comparison between the GA (symbols) and results of Ref. [17] (lines) for once-minimized dimensionless maximum excess of temperature (θmax)m as a function of L1/L0 for t1/t0 = 4.0 and 11.0

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Fig. 6

Comparison between the GA (symbols) and results of Ref. [17] (lines) for twice dimensionless maximum excess of temperature (θmax)m and optimal shapes as a function of t1/t0

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Fig. 7

Illustration of some optimized shapes, found with GA, as function of the t1/t0 and L1/L0 ratios and tributary angle

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Fig. 8

Bit array representing four degrees of freedom (H/L, t1/t0, L1/L0, and α)

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Fig. 9

The effect of parameter ϕ over (θmax)mmmm for various values of ψ

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Fig. 10

Effect of parameter ϕ over αoooo for various values of ψ

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Fig. 11

Graph of L1/L0 as function ϕ for fractions of ψ = 0.3, 0.4, 0.5, and 0.6

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Fig. 12

Graph of t1/t0 as function ϕ for fractions of ψ = 0.3, 0.4, 0.5, and 0.6

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Fig. 13

Graph of H/L as function ϕ for fractions of ψ = 0.3, 0.4, 0.5, and 0.6

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Fig. 14

Optimal geometries when ψ = 0.3: (a) ϕ = 0.01, (H/L)o = 7, (t1/t0)oo = 140, (L1/L0)ooo = 0.05, αoooo = 1.56, (θmax)mmmm = 0.0124; (b) ϕ = 0.05, (H/L)o = 20, (t1/t0)oo = 18, (L1/L0)ooo = 1, αoooo = 1.56, (θmax)mmmm = 0.0052; (c) ϕ = 0.1, (H/L)o = 7, (t1/t0)oo = 9, (L1/L0)ooo = 1, αoooo = 1.55, (θmax)mmmm = 0.0124; (d) ϕ = 0.2, (H/L)o = 2, (t1/t0)oo = 2, (L1/L0)ooo = 0.01, αoooo = 1.54, (θmax)mmmm = 0.0364

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Fig. 15

Optimal geometries when ψ = 0.5: (a) ϕ = 0.01, (H/L)o = 20, (t1/t0)oo = 18, (L1/L0)ooo = 0.007, αoooo = 1.56, (θmax)mmmm = 0.00516; (b) ϕ = 0.05, (H/L)o = 20, (t1/t0)oo = 50, (L1/L0)ooo = 1, αoooo = 1.56, (θmax)mmmm = 0.0051; (c) ϕ = 0.1, (H/L)o = 20, (t1/t0)oo = 11, (L1/L0)ooo = 0.5, αoooo = 1.56, (θmax)mmmm = 0.0038; (d) ϕ = 0.2, (H/L)o = 15, (t1/t0)oo = 13, (L1/L0)ooo = 1, αoooo = 1.56, (θmax)mmmm = 0.0081

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