The present investigation deals with the numerical computation of laminar natural convection in a gamma of right-angled triangular cavities filled with air. The vertical walls are heated and the inclined walls are cooled while the upper connecting walls are insulated from the ambient air. The defining apex angle $α$ is located at the lower vertex formed between the vertical and inclined walls. This unique kind of cavity may find application in the miniaturization of electronic packaging severely constrained by space and/or weight. The finite volume method is used to perform the computational analysis encompassing a collection of apex angles $α$ compressed in the interval that extends from 5° to 63°. The height-based Rayleigh number, being unaffected by the apex angle $α$, ranges from a low $103$ to a high $106$. Numerical results are reported for the velocity field, the temperature field and the mean convective coefficient along the heated vertical wall. Overall, the matching between the numerically predicted temperatures and the experimental measurements of air at different elevations inside a slim cavity is of ordinary quality. For purposes of engineering design, a $Nu¯H$ correlation equation was constructed and also a figure-of-merit ratio between the $Nu¯H$ and the cross sectional area $A$ of the cavity was proposed.

1.
Raithby
,
G. D.
, and
Hollands
,
K. G. T.
, 1998,
Handbook of Heat Transfer
, 3rd. ed.,
Mc-Graw–Hill
, New York, Chap. 4.
2.
Jaluria
,
Y.
, 2003,
Heat Transfer Handbook
,
Wiley
, New York, Chap. 7.
3.
Oktay
,
S.
, 1982, “
Departure from Natural Convection in Low Temperature Boiling Heat Transfer in Cooling Microelectronic LSI Devices
,”
Proc. Int. Heat Transfer Conference
, Paper No. PB 17, pp.
113
118
.
4.
Simons
,
R. E.
,
Antonnetti
,
V. W.
,
Nakayawa
,
W.
, and
Oktay
,
S.
, 1997,
Microelectronics Packaging Handbook
, 2nd. ed., pp.
1
315
to
1
403
,
Chapman and Hall
, New York.
5.
Bar-Cohen
,
A.
,
Watwe
,
A. A.
, and
Prasher
,
R. S.
, 2003,
Heat Transfer Handbook
,
Wiley
, New York, Chap. 13.
6.
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
.
7.
Poulikakos
,
D.
, and
Bejan
,
A.
, 1983, “
The Fluid Mechanics of an Attic Space
,”
J. Fluid Mech.
0022-1120,
131
, pp.
251
269
.
8.
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
.
9.
Salmun
,
H.
, 1995, “
Convection Patterns in a Triangular Domain
,”
Int. J. Heat Mass Transfer
0017-9310,
38
, pp.
351
362
.
10.
Asan
,
H.
, and
Namli
,
L.
, 2000, “
Laminar Natural Convection in a Pitched Roof of Triangular Cross Section: Summer Day Boundary Condition
,”
Energy Build.
0378-7788,
33
, pp.
69
73
.
11.
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
.
12.
Elicer-Cortés
,
J. C.
,
Kim-Son
,
D.
, and
Coutanceau
,
J.
, 1990, “
Transfert de Chaleur dans un Diedre a Geometrie Variable
,”
Int. Comm. Heat Mass Transfer
0735-1933,
17
, pp.
759
769
.
13.
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
,
205
213
.