This investigation addresses the thermogeometric performance of a two-square cavity system contrasted against a two-isosceles triangular cavity system, with an exactly equal heating segment and comparable cooling segment. When one square cavity is cut diagonally in half, it results in a pair of isosceles triangular cavities. The isosceles triangular cavity on the left is heated from the left vertical wall, the top wall is insulated, and the inclined wall is cold; the so-called HIC triangular cavity. The isosceles triangular cavity on the right is heated from the right vertical wall, the bottom wall is insulated, and the inclined wall is cold; the so-called HCI triangular cavity. It may be speculated that the two-isosceles triangular cavity system may find application in the miniaturization of electronic packaging severely constrained by space and/or weight. The finite volume method, accounting for temperature-dependent thermophysical properties of air, is employed to perform the computational analysis. Representative height-based Rayleigh numbers assume values up to 106 to avoid oscillations that occur at a Rayleigh number between RaH=2×106 and 2.2×106. Numerical results are reported for the velocity field, the temperature field, and the local and the mean convective coefficient along the heated vertical wall. Under a dominant conduction condition for RaH=103, the heat flux across the derived two-isosceles triangular system is 334% higher than its counterpart across the original two-square system. In contrast, for a dominant convection condition for RaH=106, this margin diminishes to 20%, but still constitutes a significant improvement. For the design of two-triangular cavity systems, a NuH correlation equation has been constructed yielding a maximum error of 2% at RaH=104.

1.
Ostrach
,
S.
, 1972,
Advances in Heat Transfer
,
6th ed.
,
Academic
,
San Diego, CA
, pp.
161
174
.
2.
Catton
,
I.
, 1978, “
Natural Convection in Enclosures
,”
Proceedings of the 6th International Heat Transfer Conference
, Toronto, Canada.
3.
Hoogendoorn
,
C. J.
, 1986, “
Natural Convection in Enclosures
,”
Proceedings of the 8th International Heat Transfer Conference
, San Francisco, CA.
4.
Yang
,
K. T.
, 1987, “
Natural Convection in Enclosures
,”
Handbook of Single-Phase Heat Transfer
,
S.
Kakac
et al.
, ed.,
Wiley
,
New York
, Chap. 13.
5.
Raithby
,
G. D.
, and
Hollands
,
K. G. T.
, 1998, “
Natural Convection
,”
Handbook of Heat Transfer
,
W. M.
Rohsenow
et al.
, ed.,
3rd. ed.
,
McGraw–Hill
,
New York
, Chap. 4.
6.
Charmchi
,
M.
, and
Martin
,
J. G.
, 1999, “
Natural Convection Heat Transfer
,”
Handbook of Applied Thermal Design
,
E. C.
Guyer
, ed.,
Taylor and Francis
,
Philadelphia, PA
.
7.
Jaluria
,
Y.
, 2003, “
Natural Convection
,”
Heat Transfer Handbook
,
A.
Bejan
and
A. D.
Kraus
, eds.,
Wiley
,
New York
.
8.
Flack
,
R. D.
, 1980, “
The Experimental Measurement of Natural Convection Heat Transfer in Triangular Enclosures Heated or Cooled from Below
,”
ASME J. Heat Transfer
0022-1481,
102
, pp.
770
772
.
9.
Akinsete
,
V. A.
, and
Coleman
,
T. A.
, 1982, “
Heat Transfer by Steady Laminar Free Convection in Triangular Enclosures
,”
Int. J. Heat Mass Transfer
0017-9310,
25
, pp.
991
998
.
10.
Poulikakos
,
D.
, and
Bejan
,
A.
, 1983, “
The Fluid Mechanics of an Attic Space
,”
J. Fluid Mech.
0022-1120,
131
, pp.
251
269
.
11.
Karyakin
,
Y. E.
,
Sokovishin
,
A.
, and
Martynenko
,
O. G.
, 1988, “
Transient Natural Convection in Triangular Enclosures
,”
Int. J. Heat Mass Transfer
0017-9310,
31
, pp.
1759
1766
.
12.
Del Campo
,
E. M.
,
Sen
,
M.
, and
Ramos
,
E.
, 1988, “
Analysis of Laminar Natural Convection in a Triangular Enclosure
,”
Numer. Heat Transfer
0149-5720,
13
, pp.
353
372
.
13.
Salmun
,
H.
, 1995, “
Convection Patterns in a Triangular Domain
,”
Int. J. Heat Mass Transfer
0017-9310,
38
, pp.
351
362
.
14.
Holtzmann
,
G. A.
,
Hill
,
R. W.
, and
Ball
,
K. S.
, 2000, “
Laminar Natural Convection in Isosceles Triangular Enclosures Heated From Below and Symmetrically Cooled From Above
,”
ASME J. Heat Transfer
0022-1481,
122
, pp.
485
491
.
15.
Asan
,
H.
, and
Namli
,
L.
, 2000, “
Laminar Natural Convection in a Pitched Roof of Triangular Cross Section: Summer Day Boundary Conditions
,”
Energy Build.
0378-7788,
33
, pp.
69
73
.
16.
Haese
,
P. M.
, and
Teubner
,
M. D.
, 2002, “
Heat Exchange in an Attic Space
,”
Int. J. Heat Mass Transfer
0017-9310,
45
, pp.
4925
4936
.
17.
Ridouane
,
E. H.
, and
Campo
,
A.
, 2005, “
Experimental-Based Correlations for the Characterization of Free Convection of Air Inside Isosceles Triangular Cavities With Variable Apex Angles
,”
Exp. Heat Transfer
0891-6152,
18
, pp.
81
86
.
18.
Simons
,
R. E.
,
Antonnetti
,
V. W.
,
Nakayawa
,
W.
, and
Oktay
,
S.
, 1997, “
Heat Transfer in Electronic Packages
,”
Microelectronics Packaging Handbook
,
R. R.
Tummala
,
et al.
, ed.,
2nd ed.
,
Chapman and Hall
,
New York
, pp.
1
-315–1-
403
.
19.
Bar-Cohen
,
A.
,
Watwe
,
A. A.
, and
Prasher
,
R. S.
, 2003, “
Heat Transfer in Electronic Equipment
,”
Heat Transfer Handbook
,
A.
Bejan
and
A. D.
Kraus
, eds.,
Wiley
,
New York
, Chap. 13.
20.
Elicer-Cortés
,
J. C.
,
Kim-Son
,
D.
, and
Coutanceau
,
J.
, 1990, “
Transfert de Chaleur dans un Diedre a Geometrie Variable
,”
Int. Commun. Heat Mass Transfer
0735-1933,
17
, pp.
759
769
.
21.
Elicer-Cortés
,
J. C.
, and
Kim-Son
,
D.
, 1993, “
Natural Convection in a Dihedral Enclosure: Influence of the Angle and the Wall Temperatures on the Thermal Field
,”
Exp. Heat Transfer
0891-6152,
6
, pp.
205
213
.
22.
Ridouane
,
E. H.
, and
Campo
,
A.
, 2005, “
Natural Convection Patterns in a Set of Right-Angled Triangular Cavities With Heated Vertical Sides and Cooled Hypotenuses
,”
ASME J. Heat Transfer
0022-1481,
127
, pp.
1181
1186
.
23.
LeQuéré
,
P.
, and
Alziari de Roquefort
,
T.
, 1986, “
Transition to Unsteady Natural Convection of Air in Vertical Differentially Heated Cavities: Influence of Thermal Boundary Conditions on the Horizontal Walls
,”
Proceedings of the 8th International Heat Transfer Conference
, San Francisco, CA.
24.
Briggs
,
D. G.
, and
Jones
,
D. N.
, 1985, “
Two-Dimensional Periodic Natural Convection in an Enclosure of Aspect Ratio One
,”
ASME J. Heat Transfer
0022-1481,
107
, pp.
850
854
.
25.
De Vahl Davis
,
G.
, 1983, “
Natural Convection of Air in a Square Cavity: A Benchmark Numerical Solution
,”
Int. J. Numer. Methods Fluids
0271-2091,
11
, pp.
249
264
.
You do not currently have access to this content.