The aim of this paper is to consider, by means of the numerical investigation, the geometric optimization of a cavity that intrudes into a solid with internal heat generation. The objective is to minimize the maximal dimensionless excess of temperature between the solid and the cavity. The cavity is rectangular, with fixed volume and variable aspect ratio. The cavity shape is optimized for two sets of boundary conditions: isothermal cavity and cavity cooled by convection heat transfer. The optimal cavity is the one that penetrates almost completely the conducting wall and proved to be practically independent of the boundary thermal conditions, for the external ratio of the solid wall smaller than 2. As for the convective cavity, it is worthy to know that for values of H/L greater than 2, the best shape is no longer the one that penetrates completely into the solid wall, but the one that presents the largest cavity aspect ratio H0/L0. Finally, when compared with the optimal cavity ratio calculated for the isothermal C-shaped square cavity, the cavities cooled by convection highlight almost the same optimal shape for values of the dimensionless group λ ≤ 0.01. Both cavities, isothermal and cooled by convection, also present similar optimal shapes for ϕ0 < 0.3 and ϕ0 > 0.7. However, in the range 0.3 ≤ ϕ0 ≤ 0.7, the ratio (H0/L0)opt calculated for the cavities cooled by convection is greater than the one presented by isothermal cavities. This difference is approximately 17% when λ = 0.1 and ϕ0 = 0.7, and 20% for λ = 1 and ϕ0 = 0.5.
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Departamento de Engenharia Mecânica,
Rua Sarmento Leite,
425, Porto Alegre,
Rio Grande do Sul 90.050-170,
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September 2013
Research-Article
Geometric Optimization of C-Shaped Cavities According to Bejan's Theory: General Review and Comparative Study
G. Lorenzini,
G. Lorenzini
Dipartimento di Ingegneria Industriale,
Parco Area delle Scienze 181/A,
43124 Parma,
Università degli Sudi di Parma
,Parco Area delle Scienze 181/A,
43124 Parma,
Italy
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C. Biserni,
C. Biserni
Dipartimento di Ingegneria Industriale,
Viale Risorgimento 2,
40136 Bologna,
Università degli Studi di Bologna
,Viale Risorgimento 2,
40136 Bologna,
Italy
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L. A. O. Rocha
Departamento de Engenharia Mecânica,
Rua Sarmento Leite,
425, Porto Alegre,
Rio Grande do Sul 90.050-170,
L. A. O. Rocha
Universidade Federal do Rio Grande do Sul
,Departamento de Engenharia Mecânica,
Rua Sarmento Leite,
425, Porto Alegre,
Rio Grande do Sul 90.050-170,
Brazil
Search for other works by this author on:
G. Lorenzini
Dipartimento di Ingegneria Industriale,
Parco Area delle Scienze 181/A,
43124 Parma,
Università degli Sudi di Parma
,Parco Area delle Scienze 181/A,
43124 Parma,
Italy
C. Biserni
Dipartimento di Ingegneria Industriale,
Viale Risorgimento 2,
40136 Bologna,
Università degli Studi di Bologna
,Viale Risorgimento 2,
40136 Bologna,
Italy
L. A. O. Rocha
Universidade Federal do Rio Grande do Sul
,Departamento de Engenharia Mecânica,
Rua Sarmento Leite,
425, Porto Alegre,
Rio Grande do Sul 90.050-170,
Brazil
Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received February 18, 2013; final manuscript received March 22, 2013; published online June 4, 2013. Assoc. Editor: Gary Miller.
J. Electron. Packag. Sep 2013, 135(3): 031007 (7 pages)
Published Online: June 4, 2013
Article history
Received:
February 18, 2013
Revision Received:
March 22, 2013
Citation
Lorenzini, G., Biserni, C., and Rocha, L. A. O. (June 4, 2013). "Geometric Optimization of C-Shaped Cavities According to Bejan's Theory: General Review and Comparative Study." ASME. J. Electron. Packag. September 2013; 135(3): 031007. https://doi.org/10.1115/1.4024113
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