Abstract

A unified integral solution procedure has been proposed to analyze all possible Darcian local thermal nonequilibrium (LTNE) free, forced, and mixed convective boundary layer flows, commonly encountered in porous media engineering applications. The heated body may be arbitrarily shaped, and its temperature may vary over the surface. The integral energy equation for the solid phase yields an algebraic equation between the dimensionless fluid thermal boundary layer thickness and its ratio to the solid-phase counterpart, while the integral energy equation for the fluid phase reduces to a first order ordinary differential equation in terms of the dimensionless fluid thermal boundary layer thickness. This set of the equations for determining the local Nusselt number of our primary interest proved to be valid for all possible Darcian cases of LTNE free, forced, and mixed convective boundary layer flows over an arbitrarily shaped nonisothermal body in a fluid saturated porous medium. Asymptotic expressions for the cases of arbitrary shapes were also obtained analytically for both leading edge and far downstream regions. The results are found to agree well with available direct numerical integration results. Furthermore, the regime map has been constructed to show the boundary layer transition point from the LTNE to equilibrium. The proposed unified method is found quite useful when designing thermal engineering systems associated with fluid saturated porous media.

References

References
1.
Nield
,
D. A.
, and
Bejan
,
A.
,
1992
,
Convection in Porous Media
,
Springer Verlag
,
New York
.
2.
Carbonnel
,
R. G.
, and
Whitaker
,
S.
,
1984
, “
Heat and Mass Transfer in Porous Media
,”
Fundamentals of Transport Phenomena in Porous Media
, J.
Bear
and M. Y.
Corapcioglu
,
eds.,
Martinus Nijhoff
,
Dordrecht, The Netherlands
, pp.
121
198
.
3.
Vafai
,
K.
, and
Sozen
,
M.
,
1990
, “
Analysis of Energy and Momentum Transport for Fluid Flow Through a Porous Bed
,”
ASME J. Heat Transfer
,
112
(
3
), pp.
690
699
.10.1115/1.2910442
4.
Quintard
,
M.
, and
Whitaker
,
S.
,
1993
, “
One and Two Equation Models for Transient Diffusion Processes in Two-Phase Systems
,”
Adv. Heat Transfer
,
23
, pp.
369
465
.10.1016/S0065-2717(08)70009-1
5.
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
.10.1016/0017-9310(95)00028-8
6.
Quintard
,
M.
,
1998
, “
Modelling Local Non-Equilibrium Heat Transfer in Porous Media
,”
11th International Heat Transfer Conference
, Vol.
1
, Kyongyu, South Korea, Aug. 23–28, pp.
279
285
.
7.
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
,
37
(
6
), pp.
939
954
.10.1016/0017-9310(94)90219-4
8.
Jiang
,
P. X.
,
Ren
,
Z. P.
,
Wang
,
B. X.
, and
Wang
,
Z.
,
1996
, “
Forced Convective Heat Transfer in a Plate Channel Filled With Solid Particles
,”
J. Therm. Sci.
,
5
(
1
), pp.
43
53
.10.1007/BF02663732
9.
Jiang
,
P. X.
, and
Ren
,
Z. P.
,
2001
, “
Numerical Investigation of Forced Convection Heat Transfer in Porous Media Using a Thermal Non-Equilibrium Model
,”
Int. J. Heat Fluid Flow
,
22
(
1
), pp.
102
110
.10.1016/S0142-727X(00)00066-7
10.
Peterson
,
G. P.
, and
Chang
,
C. S.
,
1998
, “
Two-Phase Heat Dissipation Utilizing Porous-Channels of High-Conductivity Materials
,”
ASME J. Heat Transfer
,
120
(
1
), pp.
243
252
.10.1115/1.2830048
11.
Spiga
,
M.
, and
Morini
,
G. L.
,
1999
, “
Transient Response of Non-Thermal Equilibrium Packed Beds
,”
Int. J. Eng. Sci.
,
37
(
2
), pp.
179
188
.10.1016/S0020-7225(98)00061-5
12.
Hsu
,
C. T.
,
2000
, “
Heat Conduction in Porous Media
,”
Handbook of Porous Media
,
K.
Vafai
, ed.,
Marcel Dekker
,
New York
, pp.
170
200
.
13.
Hsu
,
C. T.
,
Cheng
,
P.
, and
Wong
,
K. W.
,
1995
, “
A Lumped Parameter Model for Stagnant Thermal Conductivity of Spatially Periodic Porous Media
,”
ASME J. Heat Transfer
,
117
(
2
), pp.
264
269
.10.1115/1.2822515
14.
Nakayama
,
A.
,
Kuwahara
,
F.
,
Sugiyama
,
N.
, and
Xu
,
G.
,
2001
, “
A Two Energy Equation Model for Conduction and Convection in Porous Media
,”
Int. J. Heat Mass Transfer
,
44
(
22
), pp.
4375
4379
.10.1016/S0017-9310(01)00069-2
15.
Yang
,
C.
,
Kuwahara
,
F.
,
Liu
,
W.
, and
Nakayama
,
A.
,
2011
, “
Thermal Non-Equilibrium Forced Convective Flow in an Annulus Filled With a Porous Medium
,”
Open Transp. Phenom. J.
,
3
(
1
), pp.
31
39
.10.2174/1877729501103010031
16.
Yang
,
C.
,
Ando
,
K.
, and
Nakayama
,
A.
,
2011
, “
A Local Thermal Non-Equilibrium Analysis of Fully Developed Forced Convective Flow in a Tube Filled With a Porous Medium
,”
Transp. Porous Media
,
89
(
2
), pp.
237
249
.10.1007/s11242-011-9766-1
17.
Kuwahara
,
F.
,
Yang
,
C.
,
Ando
,
K.
, and
Nakayama
,
A.
,
2011
, “
Exact Solutions for a Thermal Nonequilibrium Model of Fluid Saturated Porous Media Based on an Effective Porosity
,”
ASME J. Heat Transfer
,
133
(
11
), p.
12602
.10.1115/1.4004354
18.
Zhang
,
W.
,
Bai
,
X.
,
Bao
,
M.
, and
Nakayama
,
A.
,
2018
, “
Heat Transfer Performance Evaluation Based on Local Thermal Non-Equilibrium for Air Forced Convection in Channels Filled With Metal Foam and Spherical Particles
,”
Appl. Therm. Eng.
,
145
, pp.
735
742
.10.1016/j.applthermaleng.2018.09.097
19.
Heinze
,
T.
, and
Hamidi
,
S.
,
2017
, “
Heat Transfer and Parameterization in Local Thermal Nonequilibrium for Dual Porosity Continua
,”
Appl. Therm. Eng.
,
114
, pp.
645
652
.10.1016/j.applthermaleng.2016.12.015
20.
Xu
,
Z. G.
,
Qin
,
J.
,
Zhou
,
X.
, and
Xu
,
H. J.
,
2018
, “
Forced Convective Heat Transfer of Tubes Sintered With Partially-Filled Gradient Metal Foams (GMFs) Considering Local Thermal Nonequilibrium Effect
,”
Appl. Therm. Eng.
,
137
, pp.
101
111
.10.1016/j.applthermaleng.2018.03.074
21.
Rees
,
D. A. S.
, and
Pop
,
I.
,
2000
, “
Vertical Free Convective Boundary-Layer Flow in a Porous Medium Using a Thermal Non-Equilibrium Model
,”
J. Porous Media
,
3
(
1
), pp.
31
44
.10.1615/JPorMedia.v3.i1.30
22.
Rees
,
D. A. S.
,
2003
, “
Vertical Free Convective Boundary-Layer Flow in a Porous Medium Using a Thermal Nonequilibrium Model: Elliptical Effects
,”
Z. Angew. Math. Phys.
,
54
(
3
), pp.
437
448
.10.1007/s00033-003-0032-4
23.
Celli
,
M.
,
Rees
,
D. A. S.
, and
Barletta
,
A.
,
2010
, “
The Effect of Local Thermal Non-Equilibrium on Forced Convection Boundary Layer Flow From a Heated Surface in Porous Media
,”
Int. J. Heat Mass Transfer
,
53
(
17–18
), pp.
3533
3539
.10.1016/j.ijheatmasstransfer.2010.04.014
24.
Cebeci
,
T.
, and
Bradshaw
,
P.
,
1984
,
Physical and Computational Aspects of Convective Heat Transfer
,
Springer
,
New York
.
25.
Nakayama
,
A.
,
Ando
,
K.
,
Yang
,
C.
,
Sano
,
Y.
,
Kuwahara
,
F.
, and
Liu
,
J.
,
2009
, “
A Study on Interstitial Heat Transfer in Consolidated and Unconsolidated Porous Media
,”
Heat Mass Transfer
,
45
(
11
), pp.
1365
1372
.10.1007/s00231-009-0513-x
26.
Yang
,
C.
, and
Nakayama
,
A.
,
2010
, “
A Synthesis of Tortuosity and Dispersion in Effective Thermal Conductivity of Porous Media
,”
Int. J. Heat Mass Transfer
,
53
(
15–16
), pp.
3222
3230
.10.1016/j.ijheatmasstransfer.2010.03.004
27.
Nakayama
,
A.
,
1995
,
PC-Aided Numerical Heat Transfer and Convective Flow
,
CRC Press
,
Boca Raton, FL
.
28.
Cheng
,
P.
,
1982
, “
Mixed Convection About a Horizontal Cylinder and a Sphere in a Fluid Saturated Porous Medium
,”
Int. J. Heat Mass Transfer
,
25
(
8
), pp.
1245
1247
.10.1016/0017-9310(82)90219-8
29.
Merkin
,
J. H.
,
1978
, “
Free Convection Boundary Layers in a Saturated Porous Medium With Lateral Mass Flux
,”
Int. J. Heat Mass Transfer
,
21
(
12
), pp.
1499
1504
.10.1016/0017-9310(78)90006-6
30.
Masuoka
,
T.
,
1968
, “
Free Convection Heat Transfer From a Vertical Surface to a Porous Medium
,”
Trans. Jpn. Soc. Mech. Eng.
,
34
(
259
), pp.
491
500
.10.1299/kikai1938.34.491
31.
Cheng
,
P.
, and
Minkowycz
,
W. J.
,
1977
, “
Free Convection About a Vertical Flat Plate Embedded in a Porous Medium With Application to Heat Transfer From a Dike
,”
J. Geophys. Res.
,
82
(
14
), pp.
2040
2044
.10.1029/JB082i014p02040
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