The natural or free convection in a polygonal duct with a heated core is solved by eigenfunction expansion and boundary collocation. The optimal sizes of the core for maximum flow or maximum energy transport are determined.

References

1.
Nield
,
D. A.
, and
Bejan
,
A.
, 2006,
Convection in Porous Media
, 3rd ed.,
Springer
,
New York
.
2.
Prasad
,
V.
,
Kulacki
,
F. A.
, and
Kulkarni
,
A. V.
, 1986, “
Free Convection in a Vertical, Porous Annulus With Constant Heat Flux on the Inner Wall-Experimental Results
,”
Int. J. Heat Mass Transfer
,
29
, pp.
713
723
.
3.
Kou
,
H. S.
, and
Lu
,
K. T.
, 1993, “
Combined Boundary and Inertia Effects for Fully Developed Mixed Convection in a Vertical Channel Embedded in a Porous Media
,”
Int. Commun. Heat Mass Transfer
,
20
, pp.
333
345
.
4.
Al-Nimr
,
M. A.
, and
Alkam
,
M. K.
, 2000, “
Basic Fluid Flow Problems in Porous Media
,”
J. Porous Media
3
, pp.
45
59
.
5.
Al-Nimr
,
M. A.
, and
El-Shaarawi
,
M. A. I.
, 1995, “
Analytical Solution for Transient Laminar Fully Developed Free Convection in Vertical Channels
,”
Heat Mass Transfer
,
30
, pp.
241
248
.
6.
Al-Nimr
,
M. A.
, and
Haddad
,
O. M.
, 1999, “
Fully Developed Free Convection in Open-Ended Vertical Channels Partially Filled With Porous Material
,”
J. Porous Media
2
, pp.
179
189
.
7.
Parang
,
M.
, and
Keyhani
,
M.
, 1987, “
Boundary Effects in Laminar Mixed Convection Flow Through an Annular Porous Medium
,”
ASME Trans. J. Heat Transfer
,
109
, pp.
1039
1041
.
8.
Hasnaoui
,
M.
,
Vasseur
,
P.
,
Bilgen
,
E.
, and
Robillard
,
L.
, 1995, “
Analytical and Numerical Study of Natural Convection Heat Transfer in a Vertical Porous Annulus
,”
Chem. Eng. Commun.
,
136
, pp.
77
94
.
9.
Al-Nimr
,
M. A.
, 1995, “
Fully Developed Free Convection in Open Ended Vertical Concentric Porous Annuli
,”
Int. J. Heat Mass Transfer
,
38
, pp.
1
12
.
10.
Du
,
J. H.
, and
Wang
,
B. X.
, 1999, “
Mixed Convection in Porous Media Between Vertical Concentric Cylinders
,”
Heat Trans. Asian Res.
,
28
, pp.
95
101
.
11.
Jha
,
B. K.
, 2005, “
Free Convection Flow Through an Annular Porous Medium
,”
Heat Mass Trans.
,
41
, pp.
675
679
.
12.
Wang
,
C. Y.
, 2010, “
Optimization of Natural Convection in Open Vertical Ducts With Heated Cores
,”
J. Thermophys. Heat Transfer
,
24
, pp.
669
672
.
13.
Hadim
,
H. A.
, and
Chen
,
G.
, 1994, “
Non-Darcy Mixed Convection in a Vertical Porous Channel with Asymmetric Heating
,”
J. Thermophys. Heat Transfer
,
8
, pp.
805
808
.
14.
Al-Nimr
,
M. A.
, and
Alkam
,
M.
, 1997, “
Unsteady Non-Darcian Forced Convection Analysis in an Annulus Partly Filled With Porous Material
,”
ASME Trans. J. Heat Trans.
,
119
, pp.
799
804
.
You do not currently have access to this content.