Using a thermal resistance approach, forced convection heat transfer through metal foam heat exchangers is studied theoretically. The complex microstructure of metal foams is modeled as a matrix of interconnected solid ligaments forming simple cubic arrays of cylinders. The geometrical parameters are evaluated from existing correlations in the literature with the exception of ligament diameter which is calculated from a compact relationship offered in the present study. The proposed, simple but accurate, thermal resistance model considers: the conduction inside the solid ligaments, the interfacial convection heat transfer, and convection heat transfer to (or from) the solid bounding walls. The present model makes it possible to conduct a parametric study. Based on the generated results, it is observed that the heat transfer rate from the heated plate has a direct relationship with the foam pore per inch (PPI) and solidity. Furthermore, it is noted that increasing the height of the metal foam layer augments the overall heat transfer rate; however, the increment is not linear. Results obtained from the proposed model were successfully compared with experimental data found in the literature for rectangular and tubular metal foam heat exchangers.

References

1.
Tamayol
,
A.
, and
Bahrami
,
M.
, 2009, “
Analytical Determination of Viscous Permeability of Fibrous Porous Media
,”
Int. J. Heat Mass Transfer
,
52
(
9–10
), pp.
2407
2414
.
2.
Mahjoob
,
S.
, and
Vafai
,
K.
, 2008, “
A Synthesis of Fluid and Thermal Transport Models for Metal Foam Heat Exchangers
,”
Int. J. Heat Mass Transfer
,
51
(
15–16
), pp.
3701
3711
.
3.
Calmidi
,
V. V.
, and
Mahajan
,
R. L.
, 1999, “
The Effective Thermal Conductivity of High Porosity Fibrous Metal Foams
,”
J. Heat Transfer
,
121
(
2
), pp.
466
471
.
4.
Bhattacharya
,
A.
,
Calmidi
,
V. V.
, and
Mahajan
,
R. L.
, 2002, “
Thermophysical Properties of High Porosity Metal Foams
,”
Int. J. Heat Mass Transfer
,
45
(
5
), pp.
1017
1031
.
5.
Wang
,
M.
, and
Pan
,
N.
, 2008, “
Modeling and Prediction of the Effective Thermal Conductivity of Random Open-Cell Porous Foams
,”
Int. J. Heat Mass Transfer
,
51
(
5–6
), pp.
1325
1331
.
6.
Sadeghi
,
E.
,
Djilali
,
N.
, and
Bahrami
,
M.
, 2009, “
Thermal Conductivity and Thermal Contact Resistance of Metal Foams
,”
ASME Summer Heat Transfer Conference
,
San Francisco, USA
.
7.
Dukhan
,
N.
, 2006, “
Correlations for the Pressure Drop for Flow Through Metal Foam
,”
Exp. Fluids
,
41
(
4
), pp.
665
672
.
8.
Dukhan
,
N.
,
Picon-Feliciano
,
R.
, and
Alvarez-Hernandez
,
A. R.
, 2006, “
Air Flow Through Compressed and Uncompressed Aluminum Foam: Measurements and Correlations
,”
J. Fluids Eng.
,
128
(
5
), pp.
1004
1012
.
9.
Calmidi
,
V. V.
, and
Mahajan
,
R. L.
, 2000, “
Forced Convection in High Porosity Metal Foams
,”
J. Heat Transfer
,
122
(
3
), pp.
557
565
.
10.
Boomsma
,
K.
, and
Poulikakos
,
D.
, 2002, “
The Effects of Compression and Pore Size Variations on the Liquid Flow Characteristics in Metal Foams
,”
J. Fluids Eng.
,
124
(
1
), pp.
263
272
.
11.
Tamayol
,
A.
, and
Bahrami
,
M.
, 2011, “
Transverse Permeability of Fibrous Porous Media
,”
Phys. Rev. E
,
84
, p.
046314
.
12.
Khayargoli
,
P.
,
Loya
,
V.
,
Lefebvre
,
L. P.
, and
Medraj
,
M.
, 2004, “
The Impact of Microstructure on the Permeability of Metalfoams
,” CSME Forum 2004, pp.
220
228
.
13.
Bonnet
,
J. P.
,
Topin
,
F.
, and
Tadrist
,
L.
, 2008, “
Flow Laws in Metal Foams: Compressibility and Pore Size Effects
,”
Transp. Porous Media
,
73
(
2
), pp.
233
254
.
14.
Tadrist
,
L.
,
Miscevic
,
M.
,
Rahli
,
O.
, and
Topin
,
F.
, 2004, “
About the Use of Fibrous Materials in Compact Heat Exchangers
,”
Exp. Therm. Fluid Sci.
,
28
(
2–3
), pp.
193
199
.
15.
Plessis
,
P. D.
,
Montillet
,
A.
,
Comiti
,
J.
, and
Legrand
,
J.
, 1994, “
Pressure Drop Prediction for Flow Through High Porosity Metallic Foams
,”
Chem. Eng. Sci.
,
49
(
21
), pp.
3545
3553
.
16.
Tamayol
,
A.
, and
Bahrami
,
M.
, 2011, “
In-Plane Gas Permeability of Proton Exchange Membrane Fuel Cell Gas Diffusion Layers
,”
J. Power Sources
,
196
(
7
), pp.
3559
3564
.
17.
Hunt
,
M. L.
, and
Tien
,
C. L.
, 1988, “
Effects of Thermal Dispersion on Forced Convection in Fibrous Media
,”
Int. J. Heat Mass Transfer
,
31
(
2
), pp.
301
309
.
18.
Hwang
,
J. J.
,
Hwang
,
G. J.
,
Yeh
,
R. H.
, and
Chao
,
C. H.
, 2002, “
Measurement of Interstitial Convective Heat Transfer and Frictional Drag for Flow Across Metal Foams
,”
J. Heat Transfer
,
124
(
1
), pp.
120
129
.
19.
Dukhan
,
N.
,
Picon-Feliciano
,
R.
, and
Alvarez-Hernandez
,
A. R.
, 2006, “
Heat Transfer Analysis in Metal Foams With Low-Conductivity Fluids
,”
J. Heat Transfer
,
128
(
8
), pp.
784
792
.
20.
Albanakis
,
C.
,
Missirlis
,
D.
,
Michailidis
,
N.
,
Yakinthos
,
K.
,
Goulas
,
A.
,
Omar
,
H.
,
Tsipas
,
D.
, and
Granier
,
B.
, 2009, “
Experimental Analysis of the Pressure Drop and Heat Transfer Through Metal Foams Used as Volumetric Receivers Under Concentrated Solar Radiation
,”
Exp. Therm. Fluid Sci.
,
33
(
2
), pp.
246
252
.
21.
Kim
,
S. Y.
,
Paek
,
J. W.
, and
Kang
,
B. H.
, 2003, “
Thermal Performance of Aluminum-Foam Heat Sinks by Forced Air Cooling
,”
Compon. Packag.ng Technol.
,
26
(
1
), pp.
262
267
.
22.
Dukhan
,
N.
, and
Chen
,
K. C.
, 2007, “
Heat Transfer Measurements in Metal Foam Subjected to Constant Heat Flux
,”
Exp. Therm. Fluid Sci.
,
32
(
2
), pp.
624
631
.
23.
Garrity
,
P. T.
,
Klausner
,
J. F.
, and
Mei
,
R.
, 2010, “
Performance of Aluminum and Carbon Foams for Air Side Heat Transfer Augmentation
,”
J. Heat Transfer
,
132
(
12
), p.
121901
.
24.
Cavallini
,
A.
,
Mancin
,
S.
,
Rossetto
,
L.
, and
Zilio
,
C.
, 2010, “
Air Flow in Aluminum Foam: Heat Transfer and Pressure Drops Measurements
,”
Exp. Heat Transfer
,
23
(
1
), pp.
94
105
.
25.
Dukhan
,
N.
,
Quinones-Ramos
,
P. D.
,
Cruz-Ruiz
,
E.
,
Velez-Reyes
,
M.
, and
Scott
,
E. P.
, 2005, “
One-Dimensional Heat Transfer Analysis in Open-Cell 10-PPI Metal Foam
,”
Int. J. Heat Mass Transfer
,
48
(
25–26
), pp.
5112
5120
.
26.
Ghosh
,
I.
, 2009, “
Heat Transfer Correlation for High-Porosity Open-Cell Foam
,”
Int. J. Heat Mass Transfer
,
52
(
5–6
), pp.
1488
1494
.
27.
Odabaee
,
M.
, and
Hooman
,
K.
, 2010, “
Application of Metal Foams in Air-Cooled Condensers for Geothermal Power Plants: An Optimization Study
,”
Int. Commun. Heat Mass Transfer
,
38
(
7
), pp.
838
843
.
28.
Odabaee
,
M.
,
Hooman
,
K.
, and
Gurgenci
,
H.
, 2011, “
Metal Foam Heat Exchangers for Heat Transfer Augmentation From a Cylinder in Cross-Flow
,”
Transp. Porous Media
,
86
(
3
), pp.
911
923
.
29.
Hooman
,
K.
, 2010, “
Dry Cooling Towers as Condensers for Geothermal Power Plants
,”
Int. Commun. Heat Mass Transfer
,
37
(
9
), pp.
1215
1220
.
30.
Ejlali
,
A.
,
Ejlali
,
A.
,
Hooman
,
K.
, and
Gurgenci
,
H.
, 2009, “
Application of High Porosity Metal Foams as Air-Cooled Heat Exchangers to High Heat Load Removal Systems
,”
Int. Commun. Heat Mass Transfer
,
36
(
7
), pp.
674
679
.
31.
Hooman
,
K.
, 2010, “
QGECE Research on Heat Exchangers and Air-Cooled Condensers
,”
Australian Geothermal Energy ConferenceAdelaide
,
Australia
.
32.
Hooman
,
K.
, and
Gurgenci
,
H.
, 2010, “
Porous Medium Modeling of Air-Cooled Condensers
,”
Transp. Porous Media
,
84
(
2
), pp.
257
273
.
33.
T’Joen
,
C.
,
De Jaeger
,
P.
,
Huisseune
,
H.
,
Van Herzeele
,
S.
,
Vorst
,
N.
, and
De Paepe
,
M.
, 2010, “
Thermo-Hydraulic Study of a Single Row Heat Exchanger Consisting of Metal Foam Covered Round Tubes
,”
Int. J. Heat Mass Transfer
,
53
(
15–16
), pp.
3262
3274
.
34.
Hooman
,
K.
, and
Merrikh
,
A.
, 2010, “
Theoretical Analysis of Natural Convection in an Enclosure Filled With Disconnected Conducting Square Solid Blocks
,”
Transp. Porous Media
,
85
(
2
), pp.
641
651
.
35.
Incropera
,
F. P.
, and
Witt
,
D. P. D.
, 1996,
Fundamentals of Heat and Mass Transfer
,
John Wiley & Sons
,
New York
.
You do not currently have access to this content.