Constructal Design of Cavities Inserted Into a Cylindrical Solid Body

[+] 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

Luiz Alberto Oliveira Rocha

 Departamento de Engenharia Mecânica, Universidade Federal do Rio Grande do Sul, Rua Sarmento Leite, 425, Porto Alegre, RS 90050-170, Brazil

Cesare Biserni

 Department of Energetic Nuclear and Environmental Control Engineering, University of Bologna, Viale Risorgimento no. 2, 40136 Bologna, Italycesare.biserni@unibo.it

Elizaldo Domingues dos Santos, Liércio André Isoldi

 School of Engineering, Universidade Federal do Rio Grande, Cx.P. 474, Rio Grande, RS 96201-900, Brazilelizaldosantos@furg.br


Corresponding author.

J. Heat Transfer 134(7), 071301 (May 24, 2012) (6 pages) doi:10.1115/1.4006103 History: Received August 18, 2011; Revised November 11, 2011; Published May 24, 2012; Online May 24, 2012

This paper considers the numerical optimization of the shape of cavities that intrude into a cylindrical solid body. The objective is to minimize the global thermal resistance between the solid body and the cavities. Internal heat generating is distributed uniformly throughout the solid body. The cavities are isothermal, while the solid body has adiabatic conditions on the outer surface. The total volume is fixed. The cavities are rectangular, with fixed volume and variable aspect ratio. The number of cavities of the conducting body, N, is a design parameter. The optimized geometry and performance are reported graphically as functions of the ratio between the volume of the cavities and the total volume, φ0, and N. The paper shows an example of the application of optimal distribution of imperfections principle. The results indicate that the optimal distribution of the hot spots is affected not only by the complexity of the configuration (larger N) but also by the area of cavities fraction φ0 .

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Examples of isothermal rectangular cavities inserted to a cylindrical body

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Figure 2

Two-dimensional isothermal rectangular cavities inserted into a cylindrical body

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Figure 3

Optimization of the aspect ratio H0 /L0 of the cavities when N = 4 for several values of the aspect ratio φ0

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Figure 4

The behavior of the optimized aspect ratio (H0 /L0 )opt and the minimal global thermal resistance as function of φ0

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Figure 5

The smallest, the best, and the highest studied aspect ratio shapes (N = 4 and φ0=0.1). Left: H0/L0=0.1, θmax=0.0423; center: (H0/L0)opt=0.149, θmax,min=0.0415; right: H0/L0=0.5, θmax=0.0535

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Figure 6

The best shapes calculated in Fig. 4 for several values of φ0 when N = 4. Left: φ0=0.02, (H0/L0)opt=0.023, θmax,min=0.0473; center: φ0=0.05, (H0L0)opt=0.06, θmax,min=0.0454; right: φ0=0.15, (H0L0)opt=0.31, θmax,min=0.037

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Figure 7

The effect of the number of cavities and φ0 in the minimal global thermal resistance

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Figure 8

The effect of the number of cavities and φ0 in the optimal aspect ratio of the cavities

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Figure 9

The optimal shapes as function the number of cavities when φ0=0.1

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Figure 10

The best shapes as function of several number of cavities and φ0. Upper row: φ0=0.02; center row: φ0=0.05; lower row: φ0=0.15



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