This note deals with three main themes. The first is a discussion of the early literature on convection in porous media. The second is a brief overview of current analytical modeling of single-phase convection in saturated porous media and in composite fluid/porous-medium domains. The third is a brief discussion of some pertinent recent studies involving nanofluids, cellular porous materials, bidisperse and tridisperse porous media.

References

References
1.
Horton
,
C. W.
, and
Rogers
,
F. T.
,
1945
, “
Convection Currents in a Porous Medium
,”
J. Appl. Phys.
,
16
, pp.
367
370
.10.1063/1.1707601
2.
Morrison
,
H. L.
,
Rogers
,
F. T.
, and
Horton
,
C. W.
,
1949
, “
Convection Currents in Porous Media. II. Observations of Conditions at the Onset of Convection
,”
J. Appl. Phys.
,
20
, pp.
1027
1029
.10.1063/1.1698267
3.
Rogers
,
F. T.
, and
Morrison
,
H. L.
,
1950
, “
Convection Currents in Porous Media. III. Extended Theory of the Critical Gradient
,”
J. Appl. Phys.
,
21
, pp.
1177
1180
.10.1063/1.1699561
4.
Rogers
,
F. T.
,
Schilberg
,
L. E.
, and
Morrison
,
H. L.
,
1951
, “
Convection Currents in Porous Media. IV. Remarks on the Theory
,”
J. Appl. Phys.
,
22
, pp.
1476
1479
.10.1063/1.1699895
5.
Rogers
,
F. T.
, and
Schilberg
,
L. E.
,
1952
, “
Significance of Flow Patterns for Initial Convection in Porous Media
,”
J. Appl. Phys.
,
23
, pp.
1058
1059
.10.1063/1.1702324
6.
Rogers
,
F. T.
,
1953
, “
Convection Currents in Porous Media. V. Variational Form of the Theory
,”
J. Appl. Phys.
,
4
, pp.
877
880
.10.1063/1.1721396
7.
Lapwood
,
E. R.
,
1948
, “
Convection of a Fluid in a Porous Medium
,”
Proc. Cambridge Philos. Soc.
,
44
, pp.
508
521
.10.1017/S030500410002452X
8.
Wooding
,
R. A.
,
1957
, “
Steady State Free Thermal Convection of Liquid in a Saturated Permeable Medium
,”
J. Fluid Mech.
,
2
, pp.
273
285
.10.1017/S0022112057000129
9.
Wooding
,
R. A.
,
1958
, “
An Experiment on Free Thermal Convection of Water in Saturated Permeable Material
,”
J. Fluid Mech.
,
3
, pp.
582
600
.10.1017/S0022112058000203
10.
Wooding
,
R. A.
,
1960
, “
Rayleigh Instability of a Thermal Boundary Layer in Flow Through a Porous Medium
,”
J. Fluid Mech.
,
9
, pp.
183
192
.10.1017/S0022112060001031
11.
Wooding
,
R. A.
,
1962
, “
Free Convection of Fluid in a Vertical Tube Filled With Porous Material
,”
J. Fluid Mech.
,
13
, pp.
129
144
.10.1017/S0022112062000567
12.
Wooding
,
R. A.
,
1963
, “
Convection in a Saturated Porous Medium at Large Rayleigh Number or Péclet Number
,”
J. Fluid Mech.
,
15
, pp.
527
544
.10.1017/S0022112063000434
13.
Wooding
,
R. A.
,
1964
, “
Mixing Layer Flows in a Saturated Porous Medium
,”
J. Fluid Mech.
,
19
, pp.
103
112
.10.1017/S0022112064000568
14.
Elder
,
J. W.
,
1967
, “
Steady Free Convection in a Porous Medium Heated From Below
,”
J. Fluid Mech.
,
27
, pp.
29
48
.10.1017/S0022112067000023
15.
Elder
,
J. W.
,
1967
, “
Transient Convection in a Porous Medium
,”
J. Fluid Mech.
,
27
, pp.
609
623
.10.1017/S0022112067000576
16.
Gheorghitza
,
S. I.
,
1961
, “
The Marginal Stability in Porous Inhomogeneous Media
,”
Proc. Cambridge Philos. Soc.
,
57
, pp.
871
877
.10.1017/S0305004100036021
17.
McNabb
,
A.
,
1965
, “
On Convection in a Porous Medium
,”
Proceedings of the 2nd Australasian Conference on Hydraulics and Fluid Mechanics
,
University of Auckland, Auckland, New Zealand
, pp.
C161
C171
.
18.
Prats
,
M.
,
1966
, “
The Effects of Horizontal Fluid Flow on Thermally Induced Convection Currents in Porous Mediums
,”
J. Geophys. Res.
,
71
, pp.
4835
4837
.10.1029/JZ071i020p04835
19.
Katto
,
Y.
, and
Masuoka
,
T.
,
1967
, “
Criterion for the Onset of Convective Flow in a Fluid in a Porous Medium
,”
Int. J. Heat Mass Transfer
,
10
, pp.
297
309
.10.1016/0017-9310(67)90147-0
20.
Nield
,
D. A.
,
1968
, “
Onset of Thermohaline Convection in a Porous Medium
,”
Water Resour. Res.
,
11
, pp.
553
560
.10.1029/WR004i003p00553
21.
Bories
,
S. A.
,
1970
, “
Sur les Mécanismes Fondamentaux de la Convection Naturelle en Milieu Poreux
,” Ph.D. thesis,
University of Toulouse
,
Toulouse, France
.
22.
Combarnous
,
M. A.
,
1970
, “
Convection Naturelle et Convection Mixte en Milieu Poreux
,” Ph.D. thesis,
University of Paris
,
Paris
.
23.
Combarnous
,
M. A.
, and
Bories
,
S. A.
,
1975
, “
Hydrothermal Convection in Saturated Porous Media
,”
Adv. Hydrosci.
,
10
, pp.
231
307
.
24.
Cheng
,
P.
,
1978
, “
Heat Transfer in Geothermal Systems
,”
Adv. Heat Transfer
,
14
, pp.
1
105
.10.1016/S0065-2717(08)70085-6
25.
Shenoy
,
A. V.
,
1994
, “
Non-Newtonian Fluid Heat Transfer in Porous Media
,”
Adv. Heat Transfer
,
24
, pp.
101
190
.10.1016/S0065-2717(08)70233-8
26.
Nield
,
D. A.
, and
Bejan
,
A.
,
2013
,
Convection in Porous Media
,
4th ed.
,
Springer
,
New York
.
27.
Darcy
,
H. P. C.
,
1856
,
Les Fontaines Publiques de la Ville de Dijon
,
Victor Dalmont
,
Paris
.
28.
Muskat
,
M.
,
1937
,
The Flow of Homogeneous Fluids Through Porous Media
,
McGraw-Hill
,
New York
, p.
71
.
29.
Dupuit
,
A. J. E. J.
,
1863
,
Etudes Theoriques et Pratiques sur le Mouvement des Eaux dans les Canaux Découverts et a Travers les Terrains Perméables
,
Victor Dalmont
,
Paris
.
30.
Forchheimer
,
P.
,
1901
, “
Wasserbewegung durch Boden
,”
VDI Z.
,
45
, pp.
1782
1788
.
31.
Lage
,
J. L.
,
1998
, “
The Fundamental Theory of Flow Through Permeable Media From Darcy to Turbulence
,”
Transport Phenomena in Porous Media
,
D. B.
Ingham
, and
I.
Pop
, eds.,
Elsevier Science
,
Oxford
, pp.
1
30
.
32.
Nield
,
D. A.
,
1999
, “
Modeling the Effects of a Magnetic Field or Rotation on Flow in a Porous Medium: Momentum Equation and Anisotropic Permeability Analogy
,”
Int. J. Heat Mass Transfer
,
42
, pp.
3715
3718
.10.1016/S0017-9310(99)00049-6
33.
Hsu
,
C. T.
, and
Cheng
,
P.
,
1990
, “
Thermal Dispersion in a Porous Medium
,”
Int. J. Heat Mass Transfer
,
33
, pp.
1587
1597
.10.1016/0017-9310(90)90015-M
34.
Nield
,
D. A.
,
1991
, “
The Limitations of the Brinkman-Forchheimer Equation in Modelling Flow in a Saturated Porous Medium and at an Interface
,”
Int. J. Heat Fluid Flow
,
2
, pp.
269
272
.10.1016/0142-727X(91)90062-Z
35.
Vadasz
,
P.
,
1999
, “
Note and Discussion on J. L. Aurialt's Letter Comments on the Paper ‘Local and Global Transitions to Chaos and Hysteresis in a Porous Layer Heated From Below’ by P. Vadasz
,”
Transp. Porous Media
,
37
, pp.
251
254
.10.1023/A:1006609826737
36.
Joseph
,
D. D.
,
Nield
,
D. A.
, and
Papanicolaou
,
G.
,
1982
, “
Nonlinear Equation Governing Flow in a Saturated Porous Medium
,”
Water Resour. Res.
,
18
, pp.
1049
1052
.10.1029/WR018i004p01049
37.
Joseph
,
D. D.
,
Nield
,
D. A.
, and
Papanicolaou
,
G.
,
1983
, “
Correction to ‘Nonlinear Equation Governing Flow in a Saturated Porous Medium’ by D. D. Joseph et al.
,”
Water Resour. Res.
,
19
, p.
591
.10.1029/WR019i002p00591
38.
Nield
,
D. A.
,
1994
, “
Modelling High Speed Flow of an Incompressible Fluid in a Saturated Porous Medium
,”
Transp. Porous Media
,
14
, pp.
85
88
.10.1007/BF00617029
39.
Nield
,
D. A.
,
2001
, “
Resolution of a Paradox Involving Viscous Dissipation and Nonlinear Drag in a Porous Medium
,”
Transp. Porous Media
,
41
, pp.
349
357
.10.1023/A:1006636605498
40.
Nield
,
D. A.
,
2001
, “
Alternative Models of Turbulence in a Porous Medium, and Related Matters
,”
ASME J. Fluids Eng.
,
123
(4), pp.
928
931
.10.1115/1.1413246
41.
Lage
,
J. L.
,
1992
, “
Effect of the Convective Inertia Term on Bénard Convection in a Porous Medium
,”
Numer. Heat Transfer, Part A
,
22
, pp.
469
485
.10.1080/10407789208944778
42.
Brinkman
,
H. C.
,
1947
, “
A Calculation of the Viscous Force Exerted by a Flowing Fluid on a Dense Swarm of Particles
,”
Appl. Sci. Res., Sect. A
,
1
, pp.
27
34
.10.1007/BF02120313
43.
Bear
,
J.
, and
Bachmat
,
Y.
,
1990
,
Introduction to Modeling of Transport Phenomena in Porous Media
,
Kluwer Academic
,
Dordrecht, The Netherlands
, p.
174
.
44.
Whitaker
,
S.
,
1999
,
The Method of Volume Averaging
,
Kluwer
,
Dordrecht, The Netherlands
, p.
173
.
45.
Givler
,
R. C.
, and
Altobelli
,
S. A.
,
1994
, “
A Determination of the Effective Viscosity for the Brinkman-Forchheimer Flow Model
,”
J. Fluid Mech.
,
258
, pp.
355
370
.10.1017/S0022112094003368
46.
Ward
,
J. C.
,
1964
, “
Turbulent Flow in Porous Media
,”
J. Hydraul.
,
90
(
HY5
), pp.
1
12
.
47.
Lage
,
J. L.
,
Antohe
,
B. V.
, and
Nield
,
D. A.
,
1997
, “
Two Types of Nonlinear Pressure-Drop Versus Flow-Rate Relation Observed for Saturated Porous Media
,”
ASME J. Fluids Eng.
,
119
(3), pp.
700
706
.10.1115/1.2819301
48.
Mei
,
C. C.
, and
Auriault
,
J. L.
,
1991
, “
The Effect of Weak Inertia on Flow Through a Porous Medium
,”
J. Fluid Mech.
,
222
, pp.
647
663
.10.1017/S0022112091001258
49.
Lage
,
J. L.
, and
Antohe
,
B. V.
,
2000
, “
Darcy's Experiments and the Deviation to Nonlinear Flow Regime
,”
ASME J. Fluids Eng.
,
122
(3), pp.
619
625
.10.1115/1.1287722
50.
Ergun
,
S.
,
1952
, “
Fluid Flow Through Packed Columns
,”
Chem. Eng. Prog.
,
48
, pp.
89
94
.
51.
Nield
,
D. A.
,
2001
, “
Some Pitfalls in the Modelling of Convective Flows in Porous Media
,”
Transp. Porous Media
,
41
, pp.
597
601
.10.1023/A:1010741519401
52.
Kaviany
,
M.
,
1995
,
Principles of Heat Transfer in Porous Media
,
2nd ed.
,
Springer
,
New York
, Sec. 2.7.s.
53.
Macdonald
,
I. F.
,
El-Sayed
,
M. S.
,
Mow
,
K.
, and
Dullien
,
F. A. L.
,
1979
, “
Flow Through Porous Media—Ergun Equation Revisited
,”
Ind. Eng. Chem. Fundam.
,
18
, pp.
199
208
.10.1021/i160071a001
54.
Dybbs
,
A.
, and
Edwards
,
R. V.
,
1984
,
A New Look at Porous Media Fluid Mechanics— Darcy to Turbulent
,
J.
Bear
, and
Y.
Corapcioglu
, eds.,
Martinus Nijhoff
,
Dordrecht, The Netherlands
, pp.
199
256
.
55.
Beavers
,
G. S.
, and
Joseph
,
D. D.
,
1967
, “
Boundary Conditions at a Naturally Permeable Wall
,”
J. Fluid Mech.
,
30
, pp.
197
207
.10.1017/S0022112067001375
56.
Sahraoui
,
M.
, and
Kaviany
,
M.
,
1992
, “
Slip and No-Slip Velocity Boundary Conditions at the Interface of Porous, Plain Media
,”
Int. J. Heat Mass Transfer
,
35
, pp.
927
943
.10.1016/0017-9310(92)90258-T
57.
Chen
,
F.
, and
Chen
,
C. F.
,
1992
, “
Convection in Superposed Fluid and Porous Layers
,”
J. Fluid Mech.
,
234
, pp.
97
119
.10.1017/S0022112092000715
58.
Nield
,
D. A.
,
1997
, “
Discussion of a Discussion by F. Chen and C. F. Chen
,”
ASME J. Heat Trans.
,
119
(1)
, pp.
193
194
.10.1115/1.2824090
59.
Gartling
,
D. K.
,
Hickox
,
C. E.
, and
Givler
,
R. C.
,
1996
, “
Simulation of Coupled Viscous and Porous Flow Problems
,”
Comput. Fluid Dyn. J.
,
7
, pp.
23
48
.10.1080/10618569608940751
60.
Ochoa-Tapia
,
J. A.
, and
Whitaker
,
S.
,
1995
, “
Momentum Transfer at the Boundary Between a Porous Medium and a Homogeneous Fluid— I. Theoretical Development
,”
Int. J. Heat Mass Transfer
,
38
, pp.
2635
2646
.10.1016/0017-9310(94)00346-W
61.
Ochoa-Tapia
,
J. A.
, and
Whitaker
,
S.
,
1995
, “
Momentum Transfer at the Boundary Between a Porous Medium and a Homogeneous Fluid— II. Comparison With Experiment
,”
Int. J. Heat Mass Transfer
,
38
, pp.
2647
2655
.10.1016/0017-9310(94)00347-X
62.
Kuznetsov
,
A. V.
,
1996
, “
Analytical Investigation of the Fluid Flow in the Interface Region Between a Porous Medium and a Clear Fluid in Channels Partially Filled With a Porous Medium
,”
Appl. Sci. Res.
,
56
, pp.
53
57
.10.1007/BF02282922
63.
Kuznetsov
,
A. V.
,
1997
, “
Influence of the Stress Jump Condition at the Porous-Medium/Clear-Fluid Interface on a Flow at a Porous Wall
,”
Int. Commun. Heat Mass Transfer
,
24
, pp.
401
410
.10.1016/S0735-1933(97)00025-0
64.
Kuznetsov
,
A. V.
,
2003
, “
Limitation of the Single-Domain Numerical Approach: Comparisons of Analytical and Numerical Solutions for a Forced Convection Heat Transfer Problem in a Composite Duct
,”
Comp. Assist. Mech. Eng. Sci.
,
10
, pp.
33
43
.
65.
Salinger
,
A. G.
,
Aris
,
R.
, and
Derby
,
J. J.
,
1994
, “
Finite Element Formulations for Large-Scale Coupled Flows in Adjacent Porous and Open Fluid Domains
,”
Int. J. Numer. Methods Fluids
,
18
, pp.
1185
1209
.10.1002/fld.1650181205
66.
Alazmi
,
B.
, and
Vafai
,
K.
,
2001
, “
Analysis of Fluid Flow and Heat Transfer Interfacial Conditions Between a Porous Medium and a Fluid Layer
,”
Int. J. Heat Mass Transfer
,
44
, pp.
1735
1749
.10.1016/S0017-9310(00)00217-9
67.
Fadda
,
D.
,
1996
, “
Free Surface Flow With Heat Transfer in Clear and Porous Media
,” Ph.D. thesis,
Southern Methodist University
,
Dallas, TX
.
68.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2009
, “
The Effect of a Transition Layer Between a Fluid and a Porous Medium: Shear Flow in a Channel
,”
Transp. Porous Media
,
78
, pp.
477
487
.10.1007/s11242-009-9342-0
69.
Jäger
,
W.
, and
Mikelič
,
A.
,
2009
, “
Modeling Effective Interface Laws for Transport Phenomena Between an Unconfined Fluid and a Porous Medium Using Homogenization
,”
Transp. Porous Media
,
78
, pp.
489
508
.10.1007/s11242-009-9354-9
70.
Auriault
,
J. L.
,
2010
, “
About the Beavers and Joseph Boundary Condition
,”
Transp. Porous Media
,
83
, pp.
257
266
.10.1007/s11242-009-9435-9
71.
Jäger
,
W.
, and
Mikelič
,
A.
,
2010
, “
Letter to the Editor: Comments on ‘About the Beavers and Joseph Boundary Condition’
,”
Transp. Porous Media
,
83
, pp.
267
268
.10.1007/s11242-010-9560-5
72.
Auriault
,
J. L.
,
2010
, “
Reply to the Comments on ‘About the Beavers and Joseph Boundary Condition’
,”
Transp. Porous Media
,
83
, pp.
269
270
.10.1007/s11242-010-9581-0
73.
Chandesris
,
M.
, and
Jamet
,
D.
,
2006
, “
Boundary Conditions at a Planar Fluid-Porous Interface for a Poiseuille Flow
,”
Int. J. Heat Mass Transfer
,
49
, pp.
2137
2150
.10.1016/j.ijheatmasstransfer.2005.12.010
74.
Chandesris
,
M.
, and
Jamet
,
D.
,
2007
, “
Boundary Conditions at a Fluid-Porous Interface: An A Priori Estimation of the Stress Jump Boundary Conditions
,”
Int. J. Heat Mass Transfer
,
50
, pp.
3422
3436
.10.1016/j.ijheatmasstransfer.2007.01.053
75.
Chandesris
,
M.
, and
Jamet
,
D.
,
2009
, “
Derivation of Jump Conditions for the Turbulence k-ε Model at a Fluid/Porous Interface
,”
Int. J. Heat Fluid Flow
,
30
, pp.
306
318
.10.1016/j.ijheatfluidflow.2009.01.008
76.
Chandesris
,
M.
, and
Jamet
,
D.
,
2009
, “
Jump Conditions and Surface-Excess Quantities at a Fluid/Porous Interface: A Multiple Scale Approach
,”
Transp. Porous Media
,
78
, pp.
419
428
.10.1007/s11242-008-9302-0
77.
Jamet
,
D.
, and
Chandesris
,
M.
,
2009
, “
On the Intrinsic Nature of Jump Coefficients at the Interface Between a Porous Medium and a Free Fluid Region
,”
Int. J. Heat Mass Transfer
,
52
, pp.
289
300
.10.1016/j.ijheatmasstransfer.2008.04.072
78.
Zhang
,
X. Y.
, and
Nepf
,
H. M.
,
2011
, “
Exchange Flow Between Open Water and Floating Vegetation
,”
Exp. Fluid Mech.
,
11
, pp.
531
546
.10.1007/s10652-011-9213-4
79.
Toutant
,
A.
,
Chandesris
,
M.
, and
Jamet
,
D.
,
2009
, “
Jump Conditions for Filtered Quantities at an Under-Resolved Discontinuous Interface. Part I: Theoretical Development
,”
Int. J. Multiphase Flow
,
35
, pp.
1100
1118
.10.1016/j.ijmultiphaseflow.2009.07.009
80.
Jamet
,
D.
,
Chandesris
,
M.
, and
Goyeau
,
B.
,
2009
, “
On the Equivalence of the Discontinuous One- and Two-Domain Approaches for the Modeling of Transport Phenomena at the Fluid/Porous Interface
,”
Transp. Porous Media
,
78
, pp.
403
418
.10.1007/s11242-008-9314-9
81.
d'Hueppe
,
A.
,
Chandesris
,
M.
, and
Jamet
,
D.
,
2011
, “
Boundary Conditions at a Fluid-Porous Interface for a Convective Heat Transfer Problem: Analysis of the Jump Relations
,”
Int. J. Heat Mass. Transfer
,
54
, pp.
3683
3693
.10.1016/j.ijheatmasstransfer.2011.01.033
82.
d'Hueppe
,
M.
,
Chandesris
,
M.
,
Jamet
,
D.
, and
Goyeau
,
B.
,
2012
, “
Coupling a Two-Temperature Model and a One-Temperature Model at a Fluid-Porous Interface
,”
Int. J. Heat Mass Transfer
,
55
, pp.
2510
2523
.10.1016/j.ijheatmasstransfer.2012.01.009
83.
Kumari
,
M.
, and
Jayanthi
,
S.
,
2004
, “
Non-Darcy Non-Newtonian Free Convection Flow Over a Horizontal Cylinder in a Saturated Porous Medium
,”
Int. Commun. Heat Mass Transfer
,
31
, pp.
1219
1226
.10.1016/j.icheatmasstransfer.2004.08.019
84.
Kumari
,
M.
, and
Nath
,
G.
,
2004
, “
Non-Darcy Mixed Convection in Power-Law Fluids Along a Non-Isothermal Horizontal Surface in a Porous Medium
,”
Int. J. Eng. Sci.
,
42
, pp.
353
369
.10.1016/S0020-7225(03)00140-X
85.
Nield
,
D. A.
,
2009
, “
The Modeling of Form Drag in a Porous Medium Saturated by a Power-Law Fluid
,”
ASME J. Heat Trans.
,
131
(10), p.
104501
.10.1115/1.3180809
86.
Inoue
,
M.
, and
Nakayama
,
A.
,
1998
, “
Numerical Modeling of Non-Newtonian Fluid Flow in a Porous Medium Using a Three-Dimensional Periodic Array
,”
ASME J. Fluids Eng.
,
120
(1), pp.
131
135
.10.1115/1.2819636
87.
Nakayama
,
A.
, and
Shenoy
,
A. V.
,
1992
, “
A Unified Similarity Transformation for Darcy and Non-Darcy Forced-, Free- and Mixed-Convection Heat Transfer in Non-Newtonian Inelastic Fluid-Saturated Porous Media
,”
Chem. Eng. Sci.
,
50
, pp.
33
45
.10.1016/0300-9467(92)80004-T
88.
Nakayama
,
A.
, and
Shenoy
,
A. V.
,
1993
, “
Combined Forced and Free-Convection Heat-Transfer in Power-Law Fluid-Saturated Porous Media
,”
Appl. Sci. Res.
,
50
, pp.
83
85
.10.1007/BF01086454
89.
Nakayama
,
A.
, and
Shenoy
,
A. V.
,
1993
, “
Non-Darcy Forced Convective Heat Transfer in a Channel Embedded in a Non-Newtonian Inelastic Fluid-Saturated Porous Medium
,”
Can. J. Chem. Eng.
,
71
, pp.
168
173
.10.1002/cjce.5450710122
90.
Nield
,
D. A.
,
2011
, “
A Note on the Onset of Convection in a Layer of a Porous Medium Saturated by a Non-Newtonian Fluid of Power-Law Type
,”
Transp. Porous Media
,
87
, pp.
121
123
.10.1007/s11242-010-9671-z
91.
Nield
,
D. A.
,
2011
, “
A Further Note on the Onset of Convection in a Layer of a Porous Medium Saturated by a Non-Newtonian Fluid of Power-Law Type
,”
Transp. Porous Media
,
88
, pp.
187
191
.10.1007/s11242-011-9733-x
92.
Vadasz
,
P.
,
1998
, “
Free Convection in Rotating Porous Media
,”
Transport Phenomena in Porous Media
,
D. B.
Ingham
, and
I.
Pop
, eds.,
Elsevier
,
Oxford
, UK, pp.
285
312
.
93.
Vadasz
,
P.
,
1999
, “
Flow in Rotating Porous Media
,”
Fluid Transport in Porous Media
,
P.
du Plessis
, ed.,
Computational Mechanics
,
Southampton
, UK, pp.
161
214
.
94.
Raptis
,
A.
, and
Perdikis
,
C.
,
1987
, “
Hydromagnetic Free-Convective Flow Through Porous Media
,”
Encyclopedia of Fluid Mechanics, and Modeling
,
N. P.
Cheremisinoff
, ed.,
Gulf
,
Houston
, TX, pp.
239
262
.
95.
Beavers
,
G. S.
, and
Sparrow
,
E. M.
,
1969
, “
Non-Darcy Flow Through Fibrous Porous Media
,”
ASME J. Appl. Mech.
,
36
(4), pp.
711
714
.10.1115/1.3564760
96.
Beavers
,
G. S.
,
Sparrow
,
E. M.
, and
Rodenz
,
D. E.
,
1973
, “
Influence of Bed Size on the Flow Characteristics and Porosity of Randomly Packed Beds of Spheres
,”
ASME J. Appl. Mech.
,
40
(3), pp.
655
660
.10.1115/1.3423067
97.
Bakhmeteff
,
B. A.
, and
Feodoroff
,
N. V.
,
1937
, “
Flow Through Granular Beds
,”
ASME J. Appl. Mech.
,
4
, pp.
A97
A104
.
98.
Fand
,
R. M.
,
Varahasamy
,
M.
, and
Yamamoto
,
L. M.
,
1994
, “
Heat Transfer by Natural Convection From Horizontal Cylinders Embedded in Porous Media Whose Matrices are Composed of Spheres: Viscous Dissipation
,”
Heat Transfer 1994, Proceedings of the 10th IHTC, Brighton, UK
,
G. F.
Hewitt
, ed.,
Institute of Chemical Engineers
,
Rugby, UK
, Vol. 5, pp.
237
242
.
99.
Al-Hadhrami
,
A. K.
,
Elliot
,
L.
, and
Ingham
,
D. B.
,
2003
, “
A New Model for Viscous Dissipation in Porous Media Across a Range of Permeability Values
,”
Transp. Porous Media
,
53
, pp.
117
122
.10.1023/A:1023557332542
100.
Nield
,
D. A.
,
2004
, “
Comments on ‘A New Model for Viscous Dissipation in Porous Media Across a Range of Permeability Values'
,”
Transp. Porous Media
,
55
, pp.
253
254
.10.1023/B:TIPM.0000010720.53847.1e
101.
Salama
,
A.
,
2011
, “
On the Brinkman Equation and the Concept of Viscous Dissipation in Porous Media
,”
Spec. Top. Rev. Porous Media
,
2
, pp.
83
89
.10.1615/SpecialTopicsRevPorousMedia.v2.i2.20
102.
Nakayama
,
A.
, and
Pop
,
I.
,
1989
, “
Free Convection Over a Non-Isothermal Body in a Porous Medium With Viscous Dissipation
,”
Int. Commun. Heat Mass Transfer
,
16
, pp.
173
180
.10.1016/0735-1933(89)90018-3
103.
Murthy
,
P. V. S. N.
, and
Singh
,
P.
,
1997
, “
Effect of Viscous Dissipation on a Non-Darcy Natural Convection Regime
,”
Int. J. Heat Mass Transfer
,
40
, pp.
1251
1260
.10.1016/S0017-9310(96)00181-0
104.
Costa
,
V. A.
,
2009
, “
Discussion: ‘The Modeling of Viscous Dissipation in a Saturated Porous Medium’ (Nield, D. A., 2007, ASME J. Heat Transfer, 129, pp. 1459–1463)
,”
ASME J. Heat Trans.
,
131
(2), p.
025501
.10.1115/1.2955478
105.
Costa
,
V. A. F.
,
2010
, “
Comment on the Paper by I. A. Badruddin, Z. A. Zainal, Z. A. Khan, and Z. Mallick ‘Effect of Viscous Dissipation and Radiation on Natural Convection in a Porous Medium Embedded Within Vertical Annulus,’ IJTS, 2007, 46(3), pp. 221–227
,”
Int. J. Therm. Sci.
,
49
, pp.
1874
1875
.10.1016/j.ijthermalsci.2010.04.021
106.
Nield
,
D. A.
,
2007
, “
The Modeling of Viscous Dissipation in a Saturated Porous Medium
,”
ASME J. Heat Trans.
,
129
(10), pp.
1459
1463
.10.1115/1.2755069
107.
Nield
,
D. A.
,
2009
, “
Closure to ‘Discussion of ‘The Modeling of Viscous Dissipation in a Saturated Porous Medium’ (2009, ASME J. Heat Transfer, 131, p. 025501)
,”
ASME J. Heat Trans.
,
131
(2), p.
025502
.10.1115/1.2955480
108.
Barletta
,
A.
,
2008
, “
Comments on a Paradox of Viscous Dissipation in Relation to the Oberbeck-Boussinesq Approach
,”
Int. J. Heat Mass Transfer
,
51
, pp.
6312
6316
.10.1016/j.ijheatmasstransfer.2007.10.044
109.
Nield
,
D. A.
, and
Barletta
,
A.
,
2010
, “
Comment on the Comment by V. A. F. Costa, Int. J. Therm. Sci., 2010, 49(9), pp. 1874–1875, on the paper by I. A. Badruddin, Z. A. Zainal, Z. A. Khan, and Z. Mallick, ‘Effect of Viscous Dissipation and Radiation on Natural Convection in a Porous Medium Embedded Within Vertical Annulus' (Int. J. Therm. Sci., 2007, 46(3), pp. 221–227)
,”
Int. J. Therm. Sci.
,
49
, pp.
2491
2492
.10.1016/j.ijthermalsci.2010.07.020
110.
Magyari
,
E.
,
Rees
,
D. A. S.
, and
Keller
,
B.
,
2005
, “
Effect of Viscous Dissipation on the Flow in Fluid Saturated Porous Media
,”
Handbook of Porous Media
,
2nd ed.
,
K.
Vafai
, ed.,
Taylor and Francis
,
New York
, pp.
373
406
.
111.
Tiwari
,
R. K.
, and
Das
,
M. K.
,
2007
, “
Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids
,”
Int. J. Heat Mass Transfer
,
50
, pp.
2002
2018
.10.1016/j.ijheatmasstransfer.2006.09.034
112.
Brinkman
,
H. C.
,
1952
, “
The Viscosity of Concentrated Suspensions and Solutions
,”
Chem. Phys.
,
20
, pp.
571
581
.10.1063/1.1700493
113.
Maxwell
,
J. C.
,
1904
,
Treatise on Electricity and Magnetism
,
Oxford University Press
,
Oxford, UK
.
114.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Trans.
,
128
(3), pp.
240
250
.10.1115/1.2150834
115.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2009
, “
Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid
,”
Int. J. Heat Mass Transfer
,
52
, pp.
5796
5801
.10.1016/j.ijheatmasstransfer.2009.07.023
116.
Viskanta
,
R.
,
2009
, “
Overview of Radiative Transfer in Cellular Porous Materials
,” HT2009: Proceedings of the
ASME
Summer Heat Transfer Conference
, Vol.
1
, pp.
457
565
.10.1115/HT2009-88648
117.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2010
, “
The Onset of Convection in a Layer of Cellular Porous Material: Effect of Temperature-Dependent Conductivity Arising From Radiative Transfer
,”
ASME J. Heat Trans.
,
132
(7), p.
074503
.10.1115/1.4001125
118.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2010
, “
Forced Convection in Cellular Porous Materials: Effect of Temperature-Dependent Conductivity Arising From Radiative Transfer
,”
Int. J. Heat Mass Transfer
,
53
, pp.
2680
2684
.10.1016/j.ijheatmasstransfer.2010.02.041
119.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2010
, “
The Cheng-Minkowycz Problem for Cellular Porous Materials: Effect of Temperature-Dependent Conductivity Arising From Radiative Transfer
,”
Int. J. Heat Mass Transfer
,
53
, pp.
2676
2679
.10.1016/j.ijheatmasstransfer.2010.02.042
120.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2005
, “
A Two-Velocity Two-Temperature Model for a Bi-Dispersed Porous Medium: Forced Convection in a Channel
,”
Transp. Porous Media
,
59
, pp.
325
339
.10.1007/s11242-004-1685-y
121.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2004
, “
Forced Convection in a Bi-Disperse Porous Medium Channel: A Conjugate Problem
,”
Int. J. Heat Mass Transfer
,
47
, pp.
5375
5380
.10.1016/j.ijheatmasstransfer.2004.07.018
122.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2006
, “
Thermally Developing Forced Convection in a Bidisperse Porous Medium
,”
J. Porous Media
,
9
, pp.
393
402
.10.1615/JPorMedia.v9.i5.10
123.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2010
, “
Forced Convection in a Channel Partly Occupied by a Bidisperse Porous Medium: Asymmetric Case
,”
Int. J. Heat Mass Transfer
,
53
, pp.
5167
5175
.10.1016/j.ijheatmasstransfer.2010.07.046
124.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2011
, “
Forced Convection in a Channel Partly Occupied by a Bidisperse Porous Medium: Symmetric Case
,”
ASME J. Heat Trans
.,
133
(7), p.
072601
.10.1115/1.4003667
125.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2005
, “
Heat Transfer in Bidisperse Porous Media
,”
Transport Phenomena in Porous Media III
,
D. B.
Ingham
, and
I.
Pop
, eds.,
Elsevier
,
Oxford, UK
, pp.
34
59
.
126.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2006
, “
The Onset of Convection in a Bidisperse Porous Medium
,”
Int. J. Heat Mass Transfer
,
49
, pp.
3068
3074
.10.1016/j.ijheatmasstransfer.2006.02.008
127.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2007
, “
The Effects of Combined Horizontal and Vertical Heterogeneity on the Onset of Convection in a Bidisperse Porous Medium
,”
Int. J. Heat Mass Transfer
,
50
, pp.
3329
3339
.10.1016/j.ijheatmasstransfer.2007.01.027
128.
Straughan
,
B.
,
2009
, “
On the Nield-Kuznetsov Theory for Convection in Bidisperse Porous Media
,”
Transp. Porous Media
,
77
, pp.
159
168
.10.1007/s11242-008-9307-8
129.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2011
, “
The Onset of Convection in a Tridisperse Porous Medium
,”
Int. J. Heat Mass Transfer
,
54
, pp.
3120
3127
.10.1016/j.ijheatmasstransfer.2011.04.021
130.
Narasimhan
,
A.
, and
Reddy
,
B. V. K.
,
2010
, “
Natural Convection Inside a Bidisperse Porous Medium Enclosure
,”
ASME J. Heat Trans.
,
132
(1)
, p.
012502
.10.1115/1.3192134
131.
Narasimhan
,
A.
, and
Reddy
,
B. V. K.
,
2011
, “
Laminar Forced Convection in a Heat Generating Bi-Disperse Porous Medium Channel
,”
Int. J. Heat Mass Transfer
,
54
, pp.
636
644
.10.1016/j.ijheatmasstransfer.2010.08.022
132.
Narasimhan
,
A.
, and
Reddy
,
B. V. K.
,
2011
, “
Resonance of Natural Convection Inside a Bidisperse Porous Medium Enclosure
,”
ASME J. Heat Trans.
,
133
(4), p.
042601
.10.1115/1.4001316
133.
Narasimhan
,
A.
,
Reddy
,
B. V. K.
, and
Dutta
,
P.
,
2012
, “
Thermal Management Using the Bi-Disperse Porous Medium Approach
,”
Int. J. Heat Mass Transfer
,
55
, pp.
538
546
.10.1016/j.ijheatmasstransfer.2011.11.006
134.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2008
, “
Natural Convection About a Vertical Plate Embedded in a Bidisperse Porous Medium
,”
Int. J. Heat Mass Transfer
,
51
, pp.
1658
1664
.10.1016/j.ijheatmasstransfer.2007.07.011
135.
Rees
,
D. A. S.
,
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2008
, “
Vertical Free Convective Boundary-Layer Flow in a Bidisperse Porous Medium
,”
ASME J. Heat Trans.
,
130
(9), p.
092601
.10.1115/1.2943304
136.
Kumari
,
M.
, and
Pop
,
I.
,
2009
, “
Mixed Convection Boundary Layer Flow Past a Horizontal Circular Cylinder Embedded in a Bidisperse Porous Medium
,”
Transp. Porous Media
,
77
, pp.
287
308
.10.1007/s11242-008-9293-x
137.
Revnic
,
C.
,
Grosan
,
Y.
,
Pop
,
I.
, and
Ingham
,
D. B.
,
2009
, “
Free Convection in a Square Cavity Filled With a Bidisperse Porous Medium
,”
Int. J. Therm. Sci.
,
48
, pp.
1876
1883
.10.1016/j.ijthermalsci.2009.02.016
You do not currently have access to this content.