0
Research Papers

Constructal Design Applied to the Geometric Optimization of Y-shaped Cavities Embedded in a Conducting Medium

[+] Author and Article Information
G. Lorenzini1

 Dipartimento di Ingegneria Industriale, Università degli Studi di Parma, viale G.P. Usberti no.181/A, 43124 Parma, Italy, giulio.lorenzini@unipr.it

C. Biserni

 Dipartimento di Ingegneria Energetica, Nucleare e del Controllo Ambientale, Alma Mater Studiorum—Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy

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

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

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

1

Corresponding author.

J. Electron. Packag 133(4), 041008 (Dec 09, 2011) (8 pages) doi:10.1115/1.4005296 History: Received May 13, 2011; Revised August 10, 2011; Published December 09, 2011; Online December 09, 2011

In this paper, we rely on the Constructal method to optimize the geometry of a Y-shaped cavity embedded into a solid conducting wall. The structure has four degrees of freedom. The objective is to minimize the global thermal resistance between the solid and the cavity. The optimization procedure has demonstrated that for larger solids, a cavity shaped as T led to a minimization of the global thermal resistance, while the opposite effect is observed for tall solids, where the optimal shapes are reached when the bifurcated branches deeply penetrates the solid in the vertical direction, according to the Constructal principle of “optimal distribution of imperfections”. The three times minimized global thermal resistance of the Y-shaped cavity has been correlated by power laws as a function of its corresponding optimal configurations. Finally, the performance of the Y-shaped intrusion proved to be superior to that of other basic geometries: the optimized global thermal resistances of the Y-shaped cavities obtained for H/L = 1.0, 2.0, and 5.0 were, respectively 66.61%, 55.37%, and 19.05% lower than the optimal T-shaped cavities under the same thermal and geometric conditions. Furthermore, in comparison with the “finger cavity” shaped as C, the Y-shaped cavities increased the thermal performance in 109.12%, 84.45%, 59.32%, and 20.10% for H/L = 0.5, 1.0, 2.0, and 5.0, respectively.

FIGURES IN THIS ARTICLE
<>
Copyright © 2011 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

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

Grahic Jump Location
Figure 2

Optimization of the global thermal resistance as function of α for several values of the ratio L1 /L0

Grahic Jump Location
Figure 3

Illustration of the shapes as a function of the tributary angle: (a) α = 1.10, (b) α = 1.41 (optimal), and (c) α = 1.45

Grahic Jump Location
Figure 4

The behavior of the minimized global thermal resistance (θmax )m as function of L1 /L0 for various rates of t1 /t0

Grahic Jump Location
Figure 5

The behavior of the optimized tributary angle αo for various rates of t1 /t0

Grahic Jump Location
Figure 6

Illustration of some optimized shapes for t1 /t0  = 11.0 as function of the ratio L1 /L0 : (a) L1 /L0  = 0.001, (b) L1 /L0  = 0.007 (optimal), and (c) L1 /L0  = 0.5

Grahic Jump Location
Figure 7

The optimization of the optimized global thermal resistance and optimal shapes as function of the ratio t1 /t0

Grahic Jump Location
Figure 8

The best shapes for the t1 /t0 ratios corresponding to the two extremes and the optimal configuration reached in Fig. 6: (a) t1 /t0  = 2.0, (b) t1 /t0  = 11.0 (optimal), and (c) t1 /t0  = 18.0

Grahic Jump Location
Figure 9

The optimization of the (three times) optimized global thermal resistance and the optimal shape for the tributary angle (α) as function of the ratio H/L

Grahic Jump Location
Figure 10

The optimal (t1 /t0 )o and (L1 /L0 )oo as function of the ratio H/L

Grahic Jump Location
Figure 11

Some shapes calculated in Figs.  89 as a function of the ratio H/L: (a) H/L = 0.5, (b) H/L = 1.0, (c) H/L = 2.0, and (d) H/L = 5.0

Grahic Jump Location
Figure 12

Optimal Y, T and C-shaped cavities for H/L = 1

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In