In this paper, we present our recent experimental results on buoyancy-induced convection in aluminum metal foams of different pore densities [corresponding to 5, 10, 20, and 40 pores per in. (PPI)] and porosities (0.89–0.96). The results show that compared to a heated surface, the heat transfer coefficients in these heat sinks are five to six times higher. However, when compared to commercially available heat sinks of similar dimensions, the enhancement is found to be marginal. The experimental results also show that for a given pore size, the heat transfer rate increases with porosity, suggesting the dominant role played by conduction in enhancing heat transfer. On the other hand, if the porosity is held constant, the heat transfer rate is found to be lower at higher pore densities. This can be attributed to the higher permeability with the larger pores, which allows higher entrainment of air through the porous medium. New empirical correlations are proposed for the estimation of Nusselt number in terms of Rayleigh and Darcy numbers. We also report our results on novel finned metal foam heat sinks in natural convection. Experiments were conducted on aluminum foams of 90% porosity with 5 and 20 PPI with one, two, and four aluminum fins inserted in the foam. All of these heat sinks were fabricated in-house. The results show that the finned metal foam heat sinks are superior in thermal performance compared to the normal metal foam and conventional finned heat sinks. The heat transfer increases with an increase in the number of fins. However, the relative enhancement is found to decrease with each additional fin. The indication is that there exists an optimum number of fins beyond which the enhancement in heat transfer, due to increased surface area, is offset by the retarding effect of overlapping thermal boundary layers. Similar to normal metal foams, the 5 PPI samples are found to give higher values of $h$ compared to the 20 PPI samples due to higher permeability of the porous medium. Future work is planned to arrive at the optimal heat sink configuration for even larger enhancement in heat transfer.

1.
Horton
,
C. W.
, and
Rogers
,
F. T.
, 1945, “
Convection Currents in Porous Media
,”
J. Appl. Phys.
0021-8979,
16
, pp.
367
370
.
2.
Lapwood
,
E. R.
, 1948, “
Convection of a Fluid in a Porous Medium
,”
Proc. Cambridge Philos. Soc.
0068-6735,
44
, pp.
508
521
.
3.
Kaviany
,
M.
, 1991,
Principles of Heat Transfer in Porous Media
,
Springer
, New York.
4.
,
V.
,
Kulacki
,
F. A.
, and
Keyhani
,
M.
, 1985, “
Natural Convection in Porous Media
,”
J. Fluid Mech.
0022-1120,
150
, pp.
89
119
.
5.
Cheng
,
P.
, 1978, “
Heat Transfer in Geothermal Systems
,”
0065-2717,
4
, pp.
1
105
.
6.
Nield
,
D. A.
, and
Bejan
,
A.
, 1992,
Convection in Porous Media
,
Springer
, New York.
7.
Beckermann
,
C.
,
Viskanta
,
R.
, and
,
S.
, 1986, “
A Numerical Study of Non-Darcian Natural Convection in a Vertical Enclosure Filled With a Porous Medium
,”
Numer. Heat Transfer
0149-5720,
10
, pp.
557
570
.
8.
Lauriat
,
G.
, and
,
V.
, 1987, “
Natural Convection in a Vertical Porous Cavity: A Numerical Study of Brinkman-Extended Darcy Formulation in Natural Convection in Porous Media
,”
ASME J. Heat Transfer
0022-1481,
109
, pp.
688
696
.
9.
Poulikakos
,
D.
, and
Bejan
,
A.
, 1985, “
The Departure form Darcy Flow in Natural Convection in a Vertical Porous Layer
,”
Phys. Fluids
0031-9171,
28
, pp.
3477
3484
.
10.
,
V.
, and
Tuntomo
,
A.
, 1987, “
Inertia Effects on Natural Convection in a Vertical Porous Cavity
,”
Numer. Heat Transfer
0149-5720,
11
, pp.
295
320
.
11.
Tong
,
T. W.
, and
Subramanian
,
E.
, 1985, “
A Boundary Layer Analysis for Natural Convection in a Porous Enclosure: Use of Brinkman-Extended Darcy Model
,”
Int. J. Heat Mass Transfer
0017-9310,
28
, pp.
563
571
.
12.
Beji
,
H.
, and
Gobin
,
D.
, 1987, “
Influence du Terme de Brinkman dans le Modele de Darcy Modifie
,”
Colloque Maghrebin sur les Modeles Numeriques de l’Ingenieur
,
Alger
, N
ew York
.
13.
David
,
E.
,
Lauriat
,
G.
, and
Cheng
,
P.
, 1991, “
A Numerical Solution of Variable Porosity Effects on Natural Convection in Packed-Sphere Cavity
,”
ASME J. Heat Transfer
0022-1481,
113
, pp.
391
399
.
14.
Cheng
,
P.
,
Ali
,
C. L.
, and
Verma
,
A. K.
, 1981, “
An Experimental Study of Non-Darcian Effects in Free Convection in a Saturated Porous Medium
,”
Lett. Heat Mass Transfer
0094-4548,
8
, pp.
261
165
.
15.
Beji
,
H.
, and
Gobin
,
D.
, 1992, “
Influence of Thermal Dispersion on Natural Convection Heat Transfer in Porous Media
,”
Numer. Heat Transfer, Part A
1040-7782,
22
, pp.
487
500
.
16.
Hong
,
J. T.
, and
Tien
,
C. L.
, 1987, “
Analysis of Thermal Dispersion Effects on Vertical-Plate Natural Convection in Porous Media
,”
Int. J. Heat Mass Transfer
0017-9310,
30
, pp.
143
150
.
17.
,
J. G.
, and
Catton
,
I.
, 1988, “
Dispersion in Cellular Convection in Porous Layers
,”
Int. J. Heat Mass Transfer
0017-9310,
31
, pp.
1081
1091
.
18.
Hsu
,
C. T.
, and
Cheng
,
P.
, 1990, “
Thermal Dispersion in a Porous Medium
,”
Int. J. Heat Mass Transfer
0017-9310,
33
, pp.
1587
1597
.
19.
Inaba
,
H.
,
Sugawara
,
M.
, and
Blumenberg
,
J.
, 1988, “
Natural Convection Heat Transfer in an Inclined Porous Layer
,”
Int. J. Heat Mass Transfer
0017-9310,
31
, pp.
1365
1372
.
20.
Amiri
,
A.
, and
Vafai
,
K.
, 1994, “
Analysis of Dispersion Effects and Local Thermal Nonequilibrium, Non-Darcian Variable Porosity Incompressible Flow Through Porous Media
,”
Int. J. Heat Mass Transfer
0017-9310,
37
, pp.
939
954
.
21.
Amiri
,
A.
,
Vafai
,
K.
, and
Kuzay
,
T. M.
, 1995, “
Effects of Boundary Conditions on Non-Darcian Heat Transfer Through Porous Media and Experimental Comparisons
,”
Numer. Heat Transfer, Part A
1040-7782, Part A,
27
, pp.
651
664
.
22.
Vafai
,
K.
, and
Sozen
,
M.
, 1990, “
Analysis of Energy and Momentum Transport for Fluid Flow Through a Porous Bed
,”
ASME J. Heat Transfer
0022-1481,
112
, pp.
690
699
.
23.
Calmidi
,
V. V.
, and
Mahajan
,
R. L.
, 2000, “
Forced Convection in High Porosity Metal Foams
,”
ASME J. Heat Transfer
0022-1481,
122
, pp.
557
565
.
24.
Phanikumar
,
M. S.
, and
Mahajan
,
R. L.
, 2002, “
Non-Darcy Natural Convection in High Porosity Metal Foams
,”
Int. J. Heat Mass Transfer
0017-9310,
45
, pp.
3781
3793
.
25.
Zhao
,
C. Y
,
Lu
,
T. J.
, and
Hodson
,
H. P.
, 2005, “
Natural Convection in Metal Foams with Open Cells
,”
Int. J. Heat Mass Transfer
0017-9310,
48
, pp.
2452
2463
.
26.
Taylor
,
T. R.
, 1980,
An Introduction to Error Analysis—The Study of Uncertainties in Physical Measurements
,
University Science Books
, Mill Valley, CA.
27.
Boomsma
,
K.
, and
Poulikakos
,
D.
, 2001, “
On the Effective Thermal Conductivity of a Three-Dimensionally Structured Fluid-Saturated Metal Foam
,”
Int. J. Heat Mass Transfer
0017-9310,
44
, pp.
827
836
.
28.
Bhattacharya
,
A.
,
Calmidi
,
V. V.
, and
Mahajan
,
R. L.
, 2002, “
Thermophysical Properties of High Porosity Metal Foams
,”
Int. J. Heat Mass Transfer
0017-9310,
45
, pp.
1017
1031
.
29.
Evans
,
G. H.
, and
Plumb
,
O. A.
, 1978, “
Natural Convection from a Vertical Isothermal Surface Embedded in a Saturated Porous Medium
,” AIAA-ASME Thermophysics and Heat Transfer Conference, Paper 78-HT-55, Palo Alto, CA.
30.
Hsu
,
C. T.
, and
Cheng
,
P.
, 1985, “
The Brinkman Model for Natural Convection About a Semi-infinite Vertical Plate in a Porous Medium
,”
Int. J. Heat Mass Transfer
0017-9310,
28
, pp.
683
697
.
31.
Kim
,
S. J.
, and
Vafai
,
K.
, 1989, “
Analysis of Natural Convection about a Vertical Plate Embedded in a Porous Medium
,”
Int. J. Heat Mass Transfer
0017-9310,
32
, pp.
665
677
.
32.
Plumb
,
O. A.
, and
Huenefeld
,
J. C.
, 1981, “
Non-Darcy Natural Convection from Heated Surfaces in Saturated Porous Media
,”
Int. J. Heat Mass Transfer
0017-9310,
24
, pp.
765
768
.
33.
Bejan
,
A.
, and
Poulikakos
,
D.
, 1984, “
The Non-Darcy Regime for Vertical Boundary Layer Natural Convection in a Porous Medium
,”
Int. J. Heat Mass Transfer
0017-9310,
27
, pp.
717
722
.
34.
Kaviany
,
M.
, and
Mittal
,
M.
, 1987, “
Natural Convection Heat Transfer from a Vertical Plate to High Permeability Porous Media: An Experiment and an Approximate Solution
,”
Int. J. Heat Mass Transfer
0017-9310,
30
, pp.
967
978
.
35.
Goldstein
,
R. J.
,
Sparrow
,
E. M.
, and
Jones
,
D. C.
, 1973, “
Natural Convection Mass Transfer Adjacent to Horizontal Plates
,”
Int. J. Heat Mass Transfer
0017-9310,
16
, pp.
1025
1035
.
36.
Calmidi
,
V. V.
, 1998, “
Transport Phenomena in High Porosity Metal Foams
,” Ph.D. thesis, University of Colorado.
37.
Bhattacharya
,
A.
, and
Mahajan
,
R. L.
, 2000, “
Finned Metal Foam Heat Sinks for Electronics Cooling in Forced Convection
,”
ASME J. Electron. Packag.
1043-7398,
124
, pp.
155
163
.
38.
Aavid Inc.
, www.aavid.comwww.aavid.com, Website Information on their Heat Sink Part, No. 65530, Sep. 29, 2000.
39.
Bar-Cohen
,
A.
, and
Rosenhow
,
W. M.
, 1984, “
Thermally Optimum Spacing of Vertical Natural Convection Cooled Parallel Plate
,”
ASME J. Heat Transfer
0022-1481,
106
, pp.
116
123
.
40.
Van De Pol
,
D. W.
, and
Tierney
,
J. K.
, 1973, “
Free Convection Nusselt Number for Vertical U-Shaped Channel
,”
ASME J. Heat Transfer
0022-1481,
95
, pp.
542
543
.
41.
Sahraoui
,
M.
, and
Refai-Ahmed
,
G.
, 1999, “
Flat Plate Fin Heat Sinks in Natural Convection Telecommunication Modules
,”
Adv. Electron. Circuit Packag.
0065-2520,
26
(
1
), pp.
521
527
.
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