The thermal response of porous foam filled with a solid material was theoretically investigated under unsteady heat conduction with a sinusoidally changing boundary temperature. The local thermal nonequilibrium (LTNE) effect between the porous foam and the infill was obvious, and the two-equation model is employed for the unsteady heat conduction in porous-solid system. The temperature difference, which was defined as the time average of the absolute value of the difference between the temperatures of the porous solid and the infill, was proposed for quantitatively describing the LTNE effect in porous media. The LTNE phenomenon for unsteady heat conduction in porous media is influenced by the fluctuation period of the thermal boundary, foam morphology, and the thermal diffusivities of the porous solid and the infill. The LTNE effect of unsteady porous-media heat conduction was evident in the region near the thermal disturbance boundary. The maximum temperature difference was found on the curve of temperature difference versus fluctuation period, which means that the thermal response characteristics of porous composites resonate with periodically changing thermal disturbance. The fluctuation period corresponding to the maximum temperature difference has positive correlations with thermal diffusion resistance for unsteady porous-media heat conduction.

References

1.
Lu
,
T. J.
,
He
,
D. P.
,
Chen
,
C. Q.
,
Zhao
,
C. Y.
,
Fang
,
D. N.
, and
Wang
,
X. L.
,
2006
, “
The Multi-Functionality of Ultra-Light Porous Metals and Their Applications
,”
Adv. Mech.
,
36
(
4
), pp.
517
535
.
2.
Xu
,
H. J.
,
Qu
,
Z. G.
, and
Tao
,
W. Q.
,
2011
, “
Thermal Transport Analysis in Parallel-Plate Channel Filled With Open-Celled Metallic Foams
,”
Int. Commun. Heat Mass Transfer
,
38
(
7
), pp.
868
873
.
3.
Wang
,
F.
,
Shuai
,
Y.
,
Tan
,
H.
, and
Yu
,
C.
,
2013
, “
Thermal Performance Analysis of Porous Media Receiver With Concentrated Solar Irradiation
,”
Int. J. Heat Mass Transfer
,
62
, pp.
247
254
.
4.
Xu
,
H. J.
,
Qu
,
Z. G.
, and
Tao
,
W. Q.
,
2011
, “
Analytical Solution of Forced Convective Heat Transfer in Tubes Partially Filled With Metallic Foam Using the Two-Equation Model
,”
Int. J. Heat Mass Transfer
,
54
(
17–18
), pp.
3846
3855
.
5.
Li
,
W. Q.
,
Qu
,
Z. G.
,
He
,
Y. L.
, and
Tao
,
W. Q.
,
2012
, “
Experimental and Numerical Studies on Melting Phase Change Heat Transfer in Open-Cell Metallic Foams Filled With Paraffin
,”
Appl. Therm. Eng.
,
37
, pp.
1
9
.
6.
Wang
,
F.
,
Shuai
,
Y.
,
Wang
,
Z.
,
Leng
,
Y.
, and
Tan
,
H.
,
2014
, “
Thermal and Chemical Reaction Performance Analyses of Steam Methane Reforming in Porous Media Solar Thermochemical Reactor
,”
Int. J. Hydrogen Energy
,
39
(
2
), pp.
718
730
.
7.
Zhao
,
C. Y.
,
2012
, “
Review on Thermal Transport in High Porosity Cellular Metal Foams With Open Cells
,”
Int. J. Heat Mass Transfer
,
55
(
13–14
), pp.
3618
3632
.
8.
Yang
,
K.
, and
Vafai
,
K.
,
2011
, “
Transient Aspects of Heat Flux Bifurcation in Porous Media: An Exact Solution
,”
ASME J. Heat Transfer
,
133
(
5
), p.
052602
.
9.
Zhao
,
C. Y.
,
Kim
,
T.
,
Lu
,
T. J.
, and
Hodson
,
H. P.
,
2001
, “
Thermal Transport Phenomena in Porvair Metal Foams and Sintered Beds
,” University of Cambridge, Final Report.
10.
Xu
,
H. J.
,
Qu
,
Z. G.
, and
Tao
,
W. Q.
,
2014
, “
Numerical Investigation on Self-Coupling Heat Transfer in a Counter-Flow Double-Pipe Heat Exchanger Filled With Metallic Foams
,”
Appl. Therm. Eng.
,
66
(
1–2
), pp.
43
54
.
11.
Li
,
Y. H.
,
Tao
,
W. Q.
,
Sun
,
D. L.
, and
Zhao
,
C. Y.
,
2008
, “
Numerical Simulation of Convective Heat Transfer in Metal Foam Filled Pipes
,”
J. Xi'an Jiaotong Univ.
,
42
(
3
), pp.
261
264
.
12.
Xu
,
H. J.
,
Gong
,
L.
,
Huang
,
S. B.
, and
Xu
,
M. H.
,
2014
, “
Non-Equilibrium Heat Transfer in Metal-Foam Solar Collector With No-Slip Boundary Condition
,”
Int. J. Heat Mass Transfer
,
76
, pp.
357
365
.
13.
Lu
,
T. J.
,
Stone
,
H. A.
, and
Ashby
,
M. F.
,
1998
, “
Heat Transfer in Open-Cell Metal Foams
,”
Acta Mater.
,
46
(
10
), pp.
3619
3635
.
14.
Quintard
,
M.
, and
Whitaker
,
S.
,
1995
, “
Local Thermal Equilibrium for Transient Heat Conduction: Theory and Comparison With Numerical Experiments
,”
Int. J. Heat Mass Transfer
,
38
(
15
), pp.
2779
2796
.
15.
Xu
,
H. J.
,
Qu
,
Z. G.
,
Lu
,
T. J.
,
He
,
Y. L.
, and
Tao
,
W. Q.
,
2011
, “
Thermal Modeling of Forced Convection in a Parallel-Plate Channel Partially Filled With Metallic Foams
,”
ASME J. Heat Transfer
,
133
(
9
), p.
092603
.
16.
Krishnan
,
S.
,
Murthy
,
J. Y.
, and
Garimella
,
S. V.
,
2004
, “
A Two-Temperature Model for Solid-Liquid Phase Change in Metal Foams
,”
ASME J. Heat Transfer
,
127
(
9
), pp.
995
1004
.
17.
Hsu
,
C. T.
,
1999
, “
A Closure Model for Transient Heat Conduction in Porous Media
,”
ASME J. Heat Transfer
,
121
(
3
), pp.
733
739
.
18.
Harris
,
K. T.
,”
Haji-Sheikh
,
A.
, and
Nnanna
,
A. G. A.
,
2001
, “
Phase-Change Phenomena in Porous Media—A Non-Local Thermal Equilibrium Model
,”
Int. J. Heat Mass Transfer
,
44
(
8
), pp.
1619
1625
.
19.
Moyne
,
C.
,
1997
, “
Two-Equation Model for a Diffusive Process in Porous Media Using the Volume Averaging Method With an Unsteady-State Closure
,”
Adv. Water Resour.
,
20
(
2–3
), pp.
63
76
.
20.
Minkowycz
,
W. J.
,
Haji-Sheikh
,
A.
, and
Vafai
,
K.
,
1999
, “
On Departure From Local Thermal Equilibrium in Porous Media Due to a Rapidly Changing Heat Source: The Sparrow Number
,”
Int. J. Heat Mass Transfer
,
42
(
18
), pp.
3373
3385
.
21.
Li
,
Z. S.
,
Jiang
,
R. Q.
, and
Li
,
Z. P.
,
2001
, “
Non-Fourier Analysis of Periodical Vibration Temperature Field
,”
J. Harbin Eng. Univ.
,
22
(
3
), pp.
25
28
.
22.
Bai
,
M. L.
, and
Dong
,
W. J.
,
2003
, “
Research on Gridding Plot Rule of Finite Element Computation for Periodic Transient Heat Transfer
,”
J. Therm. Sci. Technol.
,
2
(
1
), pp.
38
41
.
23.
Wu
,
F.
,
Wang
,
G.
, and
Ma
,
X. X.
,
2013
, “
Numerical Investigation of Natural Convection in a Square Enclosure Filled With Porous Medium on Sinusoidal Thermal Boundary Condition
,”
Chin. J. Comput. Mech.
,
30
(
3
), pp.
381
386
.
24.
Yang
,
Q. S.
, and
Rong
,
B. R.
,
1996
,
Advanced Heat Transfer
,
Shanghai Jiaotong University Press
,
Shanghai
.
25.
Nield
,
D. A.
, and
Bejan
,
A.
,
2006
,
Convection in Porous Media
, 3rd ed.,
Springer
,
New York
.
26.
Fourie
,
J. G.
, and
DuPlessis
,
J. P.
,
2003
, “
A Two-Equation Model for Heat Conduction in Porous Media (I: Theory)
,”
Transp. Porous Media
,
53
(
2
), pp.
145
161
.
27.
Vadasz
,
P.
,
2007
, “
On the Paradox of Heat Conduction in Porous Media Subject to Lack of Local Thermal Equilibrium
,”
Int. J. Heat Mass Transfer
,
50
(
21–22
), pp.
4131
4140
.
28.
Vadasz
,
P.
,
2005
, “
Explicit Conditions for Local Thermal Equilibrium in Porous Media Heat Conduction
,”
Transp. Porous Media
,
59
(
3
), pp.
341
355
.
29.
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
,
44
(
4
), pp.
827
836
.
30.
Li
,
W. Q.
,
Qu
,
Z. G.
, and
Tao
,
W. Q.
,
2013
, “
Numerical Study of Solid-Liquid Phase Change in Metallic Foam
,”
J. Eng. Thermophys.
,
34
(
1
), pp.
141
144
.
31.
Gao
,
D. Y.
, and
Chen
,
Z. Q.
,
2011
, “
Lattice Boltzmann Simulation of Conduction Melting of Phase Change Materials in Metal Foams
,”
J. Therm. Sci. Technol.
,
10
(
1
), pp.
6
11
.
32.
Tao
,
W. Q.
,
2001
,
Numerical Heat Transfer
,
Xi'an Jiaotong University Press
,
Xi'an
.
33.
Ozisik
,
M. N.
,
1993
,
Heat Conduction
,
Wiley
,
New York
.
34.
Hu
,
Z. M.
,
Zeng
,
L. K.
,
Wu
,
J. Q.
, and
Liu
,
Z. Q.
,
1997
, “
Numerical Simulation of Unsteady Heat Transfer in Kiln Wall With Periodically Variational Boundary Conditions
,”
Bull. Chin. Ceram. Soc.
,
4
, pp.
4
9
.
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