To investigate the feasibility of the use of foams with an interconnected spherical pore structure in heat transfer applications, models for heat transfer and pressure drop for this type of porous materials are developed. Numerical simulations are carried out for laminar multidirectional thermofluid flow in an idealized pore geometry of foams with a wide range of geometry parameters. Semiheuristic models for pressure drop and heat transfer are developed from the results of simulations. A simplified solid-body drag equation with an extended high inertia term is used to develop the hydraulic model. A heat transfer model with a nonzero asymptotic term for very low Reynolds numbers is also developed. To provide hydraulic and heat transfer models suitable for a wide range of porosity, only a general form of the length-scale as a function of pore structure is defined a priori, where the parameters of the function were determined as part of the modeling process. The proposed ideal models are compared to the available experimental results, and the source of differences between experimental results and the ideal models is recognized and then calibrated for real graphitic foam. The thermal model is used together with volume-averaged energy equations to calculate the thermal dispersion in graphitic foam. The results of the calculations show that the linear models for thermal dispersion available in literature are oversimplified for predicting thermal dispersion in this type of porous material.

1.
Klett
,
W.
,
Hardy
,
R.
,
Romine
,
E.
,
Walls
,
C.
, and
Burchell
,
T.
, 2000, “
High-Thermal Conductivity, Mesophase-Pitch-Derived Carbon Foam: Effect of Precursor on Structure and Properties
,”
Carbon
0008-6223,
38
, pp.
953
973
.
2.
Gallego
,
C.
, and
Klett
,
W.
, 2003, “
Carbon Foams for Thermal Managements
,”
Carbon
0008-6223,
41
, pp.
1461
1466
.
3.
Yu
,
Q.
,
Thompson
,
B. E.
, and
Straatman
,
A. G.
, 2006, “
A Unit Cube-Based Model for Heat Transfer and Fluid Flow in Porous Carbon Foam
,”
ASME J. Heat Transfer
0022-1481,
128
, pp.
352
360
.
4.
Straatman
,
A. G.
,
Gallego
,
N. C.
,
Thompson
,
B. E.
, and
Hangan
,
H.
, 2006, “
Thermal Characterization of Porous Carbon Foam—Convection in Parallel Flow
,”
Int. J. Heat Mass Transfer
0017-9310,
49
, pp.
1991
1998
.
5.
Straatman
,
A. G.
,
Gallego
,
N. C.
,
Yu
,
Q.
,
Betchen
,
L.
, and
Thompson
,
B. E.
, 2007, “
Forced Convection Heat Transfer and Hydraulic Losses in Graphitic Foam
,”
ASME J. Heat Transfer
0022-1481,
129
(
9
), pp.
1237
1245
.
6.
Betchen
,
L.
,
Straatman
,
A. G.
, and
Thompson
,
B. E.
, 2006, “
A Nonequilibrium Finite-Volume Model for Conjugate Fluid/Porous/Solid Domains
,”
Numer. Heat Transfer, Part A
1040-7782,
49
, pp.
543
565
.
7.
Calmidi
,
V.
, and
Mahajan
,
R.
, 1999, “
The Effective Thermal Conductivity of High Porosity Fibrous Metal Foam
,”
ASME J. Heat Transfer
0022-1481,
121
, pp.
466
471
.
8.
Calmidi
,
V.
, and
Mahajan
,
R.
, 2000, “
Forced Convection in High Porosity Metal Foams
,”
ASME J. Heat Transfer
0022-1481,
122
, pp.
557
565
.
9.
Karimian
,
S. A. M.
, and
Straatman
,
A. G.
, 2008, “
CFD Study of the Hydraulic and Thermal Behavior of Spherical-Void-Phase Porous Materials
,”
Int. J. Heat Fluid Flow
,
29
(
1
), pp.
292
305
. 0142-727X
10.
Karimian
,
S. A. M.
, 2006. “
Computational Modeling of the Flow and Heat Transfer in an Idealized Porous Metal
,” Ph.D. thesis, The University of Western Ontario, London, ON, Canada.
11.
Karimian
,
S. A. M.
, and
Straatman
,
A. G.
, 2006, “
Discretization and Parallel Performance of an Unstructured Finite Volume Navier–Stokes Solver
,”
Int. J. Numer. Methods Fluids
0271-2091,
52
(
6
), pp.
591
615
.
12.
Balay
,
S.
,
Buschelman
,
K.
,
Eijkhout
,
V.
,
Gropp
,
W. D.
,
Kaushik
,
D.
,
Knepley
,
M. G.
,
McInnes
,
L. C.
,
Smith
,
B. F.
, and
Zhang
,
H.
, 2004, PETSc Users Manual, Revision 2.1.5, Argonne National Laboratory, Technical Report No. ANL-95/11.
13.
Khosla
,
P. K.
, and
Rubin
,
S. G.
, 1974, “
A Diagonally Dominant Second-Order Accurate Implicit Scheme
,”
Comput. Fluids
0045-7930,
2
, pp.
207
209
.
14.
Karimian
,
S. A. M.
, and
Straatman
,
A. G.
, 2007, “
A Thermal Periodic Boundary Condition for Heating and Cooling Processes
,”
Int. J. Heat Fluid Flow
,
28
, pp.
329
339
. 0142-727X
16.
Kaviany
,
M.
, 1999,
Principles of Heat Transfer in Porous Media
, 2nd ed.,
Springer
,
New York
.
17.
Fourie
,
J. G.
, and
Du Plessis
,
J. P.
, 2002, “
Pressure Drop Modeling in Cellular Metallic Foams
,”
Chem. Eng. Sci.
0009-2509,
57
, pp.
2781
2789
.
18.
Incropera
,
F. P.
, and
DeWitt
,
D. P.
, 2002,
Fundamentals of Heat and Mass Transfer
, 5th ed.,
Wiley
,
New York
.
19.
Nakayama
,
A.
,
Kuwahara
,
F.
, and
Kodama
,
Y.
, 2006, “
An Equation for Thermal Dispersion Flux Transport and Its Mathematical Modeling for Heat and Fluid Flow in a Porous Medium
,”
J. Fluid Mech.
,
563
, pp.
81
96
. 0022-1120
You do not currently have access to this content.