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Research Papers: Forced Convection

Constructal Design of Convective Y-Shaped Cavities by Means of Genetic Algorithm

[+] Author and Article Information
G. 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

C. Biserni

Dipartimento di Ingegneria Industriale,
Università degli Studi di Bologna,
Viale Risorgimento 2,
Bologna 40136, Italy

E. D. Estrada

Centro de Ciências Computacionais,
Universidade Federal do Rio Grande,
Italia Avenue km 8,
Rio Grande, RS 96201-900, Brazil

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

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

L. A. O. Rocha

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

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 20, 2013; final manuscript received March 11, 2014; published online April 10, 2014. Editor: Terry Simon.

J. Heat Transfer 136(7), 071702 (Apr 10, 2014) (10 pages) Paper No: HT-13-1497; doi: 10.1115/1.4027195 History: Received September 20, 2013; Revised March 11, 2014

In the present work constructal design is employed to optimize the geometry of a convective, Y-shaped cavity that intrudes into a solid conducting wall. The main purpose is to investigate the influence of the dimensionless heat transfer parameter a over the optimal geometries of the cavity, i.e., the ones that minimize the maximum excess of temperature (or reduce the thermal resistance of the solid domain). The search for the best geometry has been performed with the help of a genetic algorithm (GA). For square solids (H/L = 1.0) the results obtained with an exhaustive search (which is based on solution of all possible geometries) were adopted to validate the GA method, while for H/L ≠ 1.0 GA is used to find the best geometry for all degrees of freedom investigated here: H/L, t1/t0, L1/L0, and α (four times optimized). The results demonstrate that there is no universal optimal shape that minimizes the thermal field for all values of a investigated. Moreover, the temperature distribution along the solid domain becomes more homogeneous with an increase of a, until a limit where the configuration of “optimal distribution of imperfections” is achieved and the shape tends to remain fixed. Finally, it has been highlighted that the GA method proved to be very effective in the search for the best shapes with the number of required simulations much lower (8 times for the most difficult situation) than that necessary for exhaustive search.

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References

Figures

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Fig. 1

Y-shaped cavity cooled by convection into a two-dimensional conducting body with uniform heat generation

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Fig. 3

Optimization of the maximum excess of temperature as function of α for several values of the ratio L1/L0: (a) a = 0.1 and (b) a = 10.0

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Fig. 4

The behavior of the once minimized maximum excess of temperature (θmax)m as a function of L1/L0 for various values of parameter a

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Fig. 5

The behavior of the of the once optimized tributary angle αo as function of L1/L0 for various values of parameter a

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Fig. 7

Illustration of some optimized shapes calculated in Fig. 5: (a) a = 0.1, (b) a = 1.0, (c) a = 10.0, and (d) a = ∞

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Fig. 6

The effect of the parameter a over the twice minimized maximum excess of temperature (θmax)mm and over the cavity optimal shapes: αoo and (L1/L0)o

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Fig. 2

Flow chart illustrating the optimization process

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Fig. 11

The behavior of the twice minimized maximum excess of temperature (θmax)mm and the optimal shapes as a function of t1/t0 for a = 10.0

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Fig. 12

The effect of the parameter a over the three times minimized maximum excess of temperature (θmax)mmm and over the optimal shapes for H/L = 1.0

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Fig. 13

Some optimal shapes calculated in Fig. 11: (a) a = 0.1, (b) a = 1.0, (c) a = 10.0, and (d) a = ∞

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Fig. 14

The optimal shapes obtained with G.A. for fourth minimized maximum excess of temperature (θmax)mmmm and for various values of parameter a: (a) a = 0.1, (b) a = 1.0, and (c) a = 10.0

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Fig. 8

The behavior of the twice minimized maximum excess of temperature (θmax)mm as a function of the ratio t1/t0 for various values of parameter a

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Fig. 9

The behavior of the twice minimized maximum excess of temperature (θmax)mm and the respective optimal shapes as a function of t1/t0 for a = 0.1

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Fig. 10

The behavior of the twice minimized maximum excess of temperature (θmax)mm and the respective optimal shapes as a function of t1/t0 for a = 1.0

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