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.

References

References
1.
Bejan
,
A.
, 1997,
Advanced Engineering Thermodynamics
,
2nd ed.
,
Wiley
,
New York
.
2.
Bejan
,
A.
, 2000,
Shape and Structure, from Engineering to Nature
,
Cambridge University
,
Cambridge, UK
.
3.
Bejan
,
A.
, and
Lorente
,
S.
, 2008,
Design with Constructal Theory
,
Wiley
,
Hoboken
.
4.
Bejan
,
A.
, and
Marden
,
J. H.
, 2009, “
The Constructal Unification of Biological and Geophysical Design
,”
Phys. Life Rev.
,
6
, pp.
85
102
.
5.
Bejan
,
A.
, and
Lorente
,
S.
, 2006, “
Constructal Theory of Generation of Configuration in Nature and Engineering
,”
J. Appl. Phys.
,
100
,
041301
.
6.
Beyene
,
A.
, and
Peffley
,
J.
, 2009, “
Constructal Theory, Adaptive Motion, and Their Theoretical Application to Low-Speed Turbine Design
,”
J. Energy Eng. ASCE
,
135
(
4
), pp.
112
118
.
7.
Kang
,
D.-H.
,
Lorente
,
S.
, and
Bejan
,
A.
, 2010, “
Constructal Dentritic Configuration for the Radiation Heating of a Solid Stream
,”
J. Appl. Phys.
107
,
114910
.
8.
Kim
,
Y.
,
Lorente
,
S.
, and
Bejan
,
A.
, 2010, “
Constructal Multi-Tube Configuration for Natural and Forced Convection in Cross-Flow
,”
Int. J. Heat Mass Transfer
,
53
, pp.
5121
5128
.
9.
Kim
,
Y.
,
Lorente
,
S.
, and
Bejan
,
A.
, 2011, “
Steam Generator Structure: Continuous Model and Constructal Design
,”
Int. J. Energy Res.
,
35
, pp.
336
345
.
10.
Azad
,
A. V.
, and
Amidpour
,
M.
, 2011, “
Economic Optimization of Shell and Tube Heat Exchanger based on Constructal Theory
,”
Energy
36
, pp.
1087
1096
.
11.
Kraus
,
A. D.
, 1999, “
Developments in the Analysis of Finned Arrays
,” (Donald Q. Kern Award Lecture, National Heat Transfer Conference, Baltimore, MD, Aug. 11, 1997) Int. J. Transp. Phenom.,
1
, pp.
141
164
.
12.
Aziz
,
A.
, 1992, “
Optimum Dimensions of Extended Surfaces Operating in a Convective Environment
,”
Appl. Mech. Rev.
,
45
(
5
), pp.
155
173
.
13.
Bello-Ochende
,
T.
,
Mejer
,
J. P.
, and
Bejan
,
A.
, 2010, “
Constructal Multi-Scale Pin Fins
,”
Int. J. Heat Mass Transfer
,
53
, pp.
2773
2779
.
14.
Falter
,
H. D.
, and
Thompson
,
E.
, 1996, “
Performance of Hypervapotron Beamstopping Elements at Jet
,”
Fusion Technol.
,
29
, pp.
584
594
.
15.
Biserni
,
C.
, and
Lorenzini
,
G.
, 2002, “
Experimental Tests on Subcooled Boiling Heat Transfer Under Forced Convection Conditions
,”
J. Eng. Phys. Thermophys.
,
11
, pp.
73
81
.
16.
Lorenzini
,
G.
, and
Biserni
,
C.
, 2003, “
A Vapotron Effect Application for Electronic Equipment Cooling
,”
J. Electron. Packag.
,
125
, pp.
475
479
.
17.
Biserni
,
C.
,
Rocha
,
L. A. O.
, and
Bejan
,
A.
, 2004, “
Inverted Fins: Geometric Optimization of the Intrusion Into a Conducting Wall
,”
Int. J. Heat Mass Transfer
,
47
, pp.
2577
2586
.
18.
Rocha
,
L. A. O.
,
Lorenzini
,
E.
, and
Biserni
,
C.
, 2005, “
Geometric Optimization of Shapes on the Basis of Bejan’s Constructal Theory
,”
Int. Commun. Heat Mass Transfer
,
32
, pp.
1281
1288
.
19.
Xie
,
Z.
,
Chen
,
L.
, and
Sun
,
F.
, 2010, “
Geometry Optimization of T-Shaped Cavities According to Constructal Theory
,”
Math. Comput. Modell.
52
, pp.
1538
1546
.
20.
Biserni
,
C.
,
Rocha
,
L. A. O.
,
Stanescu
,
G.
, and
Lorenzini
,
E.
, 2007, “
Constructal H-shaped Cavities According to Bejan’s Theory
,”
Int. J. Heat Mass Transfer
,
50
, pp.
2132
2138
.
21.
Marques
,
C. H.
,
Rocha
,
L. A. O.
, and
dos Santos
,
E. D.
, 2009, “
Constructal Design Applied to the Optimization of Heat Transfer in a Solid Conducting Wall
,” 3rd Southern Conference on Computational Modeling,
IEEE Computer Society
, Rio Grande, pp.
7
11
.
22.
Lorenzini
,
G.
, and
Rocha
,
L. A. O.
, 2006, “
Constructal Design of Y-shaped Assembly of Fins
,”
Int. J. Heat Mass Transfer
,
49
, pp.
4552
4557
.
23.
Xie
,
Z. H.
,
Chen
,
L. G.
, and
Sun
,
F. R.
, 2010, “
Constructal Optimization of Twice Y-shaped Assemblies of Fins by Taking Maximum Thermal Resistance Minimization as Objective
,”
Sci. China, Ser. E: Technol. Sci.
,
53
, pp.
2756
2764
.
24.
MATLAB
, 2000,
User’s Guide, Version 6.0.088, Release 12
,
The Mathworks Inc.
,
Natick, MA
.
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