Metal and graphite foam are relatively new types of porous materials characterized by having high-solid phase conductivities. In many cooling applications of these materials, including high-power electronics, low-conductivity fluids flow through them, e.g., air. A simple approximate engineering solution for the convection heat transfer inside a two-dimensional rectangular porous media subjected to constant heat flux on one side is presented. The conduction in the fluid is set to zero, and for simplicity, a plug flow is considered. As a result, the non-local-thermal equilibrium equations are significantly simplified and solved. The solid and fluid temperatures decay in what looks like an exponential fashion as the distance from the heated wall increases. The results are in good agreement with one more complex analytical solution in the literature, in the region far from the heated wall only.

1.
Ashby
,
M. F.
,
Evans
,
A. G.
,
Fleck
,
N. A.
,
Gibson
,
L. J.
,
Hutchinson
,
J. W.
, and
Wadley
,
H. N. G.
, 2000,
Metal Foams: A Design Guide
,
Butterworth-Heinemann
,
Woburn, MA
, pp.
181
188
.
2.
Sullines
,
D.
, and
Daryabeige
,
K.
, 2001, “
Effective Thermal Conductivity of High Porosity Open Cell Nickel Foam
,”
Proceedings of the 35th AIAA Thermophysics Conference
, Anaheim, CA, Paper No. 2819, p.
12
.
3.
Vafai
,
K.
, and
Tien
,
C. L.
, 1982, “
Boundary and Inertia Effects on Convective Mass Transfer in Porous Media
,”
Int. J. Heat Mass Transfer
0017-9310,
25
(
8
), pp.
1183
1190
.
4.
Hunt
,
M. L.
, and
Tien
,
C. L.
, 1988, “
Effect of Thermal Dispersion on Forced Convection in Fibrous Media
,”
Int. J. Heat Mass Transfer
0017-9310,
31
(
2
), pp.
301
309
.
5.
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
.
6.
Hwang
,
J. J.
,
Hwang
,
G. J.
,
Yeh
,
R. H.
, and
Chao
,
C. H.
, 2002, “
Measurement of the Interstitial Convection Heat Transfer and Frictional Drag for Flow Across Metal Foam
,”
ASME J. Heat Transfer
0022-1481,
124
, pp.
120
129
.
7.
Kim
,
S. J.
, and
Kim
,
D.
, 1999, “
Forced Convection in Microstructures for Electronic Equipment Cooling
,”
ASME J. Heat Transfer
0022-1481,
121
, pp.
639
645
.
8.
Lee
,
D. Y.
, and
Vafai
,
K.
, 1999, “
Analytical Characterization and Conceptual Assessment of Solid and Fluid Temperature Differentials in Porous Media
,”
Int. J. Heat Mass Transfer
0017-9310,
42
, pp.
423
435
.
9.
Angirasa
,
D.
, 2002, “
Forced Convective Heat Transfer in Metallic Fibrous Materials
,”
ASME J. Heat Transfer
0022-1481,
124
, pp.
739
745
.
10.
Poulikakos
,
D.
, and
Renken
,
K.
, 1987, “
Forced Convection in a Channel Filled With Porous Medium, Including the Effect of Flow Inertia, Variable Porosity, and Brinkman Friction
,”
ASME J. Heat Transfer
0022-1481,
109
, pp.
880
888
.
11.
Kim
,
S. J.
, and
Jang
,
S. P.
, 2002, “
Effects of the Darcy Number, the Prandtl Number and the Reynolds Number on the Local Thermal Non-Equilibrium
,”
Int. J. Heat Mass Transfer
0017-9310,
45
, pp.
3885
3896
.
12.
Vafai
,
K.
, and
Kim
,
S. J.
, 1989, “
Forced Convection in a Channel Filled With a Porous Medium: An Exact Solution
,”
ASME J. Heat Transfer
0022-1481,
111
, pp.
1103
1106
.
13.
Quintard
,
M.
,
Kaviany
,
M.
, and
Whitaker
,
S.
, 1997, “
Two-Medium Treatment of Heat Transfer in Porous Media: Numerical Results for Effective Properties
,”
Adv. Water Resour.
0309-1708,
20
(
2–3
), pp.
77
94
.
14.
Haji-Sheikh
,
A.
, and
Vafai
,
K.
, 2004, “
Analysis of Flow and Heat Transfer in Porous Media Imbedded Inside Various-Shaped Ducts
,
Int. J. Heat Mass Transfer
0017-9310,
47
, pp.
1889
1905
.
15.
Narasimhan
,
A.
,
Lage
,
J.
, and
Nield
,
D. A.
, 2001, “
New Theory for Forced Convection Through Porous Media by Fluids With Temperature-Dependent Viscosity
,”
ASME J. Heat Transfer
0022-1481,
123
, pp.
1045
1051
.
16.
Minkowycz
,
W. J.
, and
Haji-Sheikh
,
A.
, 2006, “
Heat Transfer in Parallel Plates and Circular Porous Passages With Axial Conduction
,”
Int. J. Heat Mass Transfer
0017-9310,
49
(
13–14
), pp.
2381
2390
.
17.
Ingham
,
D. B.
, and
Pop
,
I.
, 1998,
Transport Phenomena in Porous Media
,
Elsevier
,
Oxford
,
p.
103
.
18.
Krishnan
,
S.
,
Murthy
,
J. Y.
, and
Garimella
,
S. V.
, 2004, “
A Two-Temperature Model for the Analysis of Passive Thermal Control System
,”
ASME J. Heat Transfer
0022-1481,
126
, pp.
628
637
.
19.
Amiri
,
A.
, and
Vafai
,
K.
, 1994, “
Analysis of Dispersion Effects and Non-Thermal Equilibrium, Non-Darcian, Variable Porosity Incompressible Flow Through Porous Media
,”
Int. J. Heat Mass Transfer
0017-9310,
37
(
6
), pp.
939
954
.
20.
Hwang
,
G. J.
, and
Chao
,
C. H.
, 1994, “
Heat Transfer Measurement and Analysis for Sintered Porous Channels
,”
ASME J. Heat Transfer
0022-1481,
116
, pp.
456
464
.
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,
27
, pp.
651
664
.
22.
Alazmi
,
B.
, and
Vafai
,
K.
, 2002, “
Constant Wall Heat Flux Boundary Conditions in Porous Media Under Local Thermal Non-Equilibrium Conditions
,”
Int. J. Heat Mass Transfer
0017-9310,
45
, pp.
3071
3087
.
23.
Kim
,
S. J.
, and
Kim
,
D.
, 2001, “
The Thermal Interaction at the Interface Between a Porous Medium and an Impermeable Wall
,”
ASME J. Heat Transfer
0022-1481,
123
, pp.
527
533
.
24.
Deleglise
,
M.
,
Simacek
,
P.
,
Binetruy
,
C.
, and
Advani
,
S.
, 2003, “
Determination of the Thermal Dispersion Coefficient During Radial Filling of a Porous Medium
,”
ASME J. Heat Transfer
0022-1481,
125
, pp.
875
880
.
25.
Noh
,
J. -S.
,
Lee
,
K. B.
, and
Lee
,
C. G.
, 2006, “
Pressure Loss and Forced Convective Heat Transfer in an Annulus Filled With Aluminum Foam
,”
Int. Commun. Heat Mass Transfer
0735-1933,
33
, pp.
434
444
.
You do not currently have access to this content.