A critical review is made of recent studies of the modeling of viscous dissipation in a saturated porous medium, with applications to either forced convection or natural convection. Alternative forms of the viscous dissipation function are discussed. Limitations to the concept of fully developed convection are noted. Special attention is focused on the roles of viscous dissipation and work done by pressure forces (flow work) in natural convection in a two-dimensional box with either lateral or bottom heating.

1.
Nield
,
D. A.
, and
Bejan
,
A.
, 2006,
Convection in Porous Media
,
3rd ed.
,
Springer
,
New York
.
2.
Magyari
,
E.
, and
Keller
,
B.
, 2003, “
The Opposing Effect of Viscous Dissipation Allows for a Parallel Free Convection Boundary-Layer Flow Along a Cold Vertical Flat Plate
,”
Transp. Porous Media
0169-3913,
51
, pp.
227
230
.
3.
Magyari
,
E.
, and
Keller
,
B.
, 2003, “
Effect of Viscous Dissipation on a Quasi-Parallel Free Convection Boundary-Layer Flow Over a Vertical Plate in a Porous Medium
,”
Transp. Porous Media
0169-3913,
51
, pp.
231
236
.
4.
Magyari
,
E.
, and
Keller
,
B.
, 2003, “
Buoyancy Sustained by Viscous Dissipation
,”
Transp. Porous Media
0169-3913,
53
, pp.
105
115
.
5.
Magyari
,
E.
, and
Keller
,
B.
, 2004, “
Backward Free Convection Boundary Layers in Porous Media
,”
Transp. Porous Media
0169-3913,
55
, pp.
285
300
.
6.
Magyari
,
E.
, and
Rees
,
D. A. S.
, 2006, “
Effect of Viscous Dissipation on the Darcy Free Convection Boundary-Layer Flow Over a Vertical Plate With Exponential Distribution in a Porous Medium
,”
Fluid Dyn. Res.
0169-5983,
38
, pp.
405
429
.
7.
Magyari
,
E.
,
Pop
,
I.
, and
Keller
,
B.
, 2003, “
Effect of Viscous Dissipation on the Darcy Forced-Convection Flow Past a Plane Surface
,”
J. Porous Media
1091-028X,
6
, pp.
111
122
.
8.
Rees
,
D. A. S.
,
Magyari
,
E.
, and
Keller
,
B.
, 2003, “
The Development of the Asymptotic Viscous Dissipation Profile in a Vertical Free Convective Boundary Layer Flow in a Porous Medium
,”
Transp. Porous Media
0169-3913,
53
, pp.
347
355
.
9.
Rees
,
D. A. S.
,
Magyari
,
E.
, and
Keller
,
B.
, 2005, “
Vortex Instability of the Asymptotic Dissipation Profile in Porous Media
,”
Transp. Porous Media
0169-3913,
61
, pp.
1
14
.
10.
Nield
,
D. A.
,
Kuznetsov
,
A. V.
, and
Xiong
,
M.
, 2003, “
Thermally Developing Forced Convection in a Porous Medium: Parallel Plate Channel With Walls at Uniform Temperature, With Axial Conduction and Viscous Dissipation Effects
,”
Int. J. Heat Mass Transfer
0017-9310,
46
, pp.
643
651
.
11.
Kuznetsov
,
A. V.
,
Xiong
,
M.
, and
Nield
,
D. A.
, 2003, “
Thermally Developing Forced Convection in a Porous Medium: Circular Duct With Walls at Constant Temperature, With Longitudinal Conduction and Viscous Dissipation Effects
,”
Transp. Porous Media
0169-3913,
53
, pp.
331
345
.
12.
Nield
,
D. A.
,
Kuznetsov
,
A. V.
, and
Xiong
,
M.
, 2004, “
Effects of Viscous Dissipation and Flow Work on Forced Convection in a Channel Filled by a Saturated Porous Medium
,”
Transp. Porous Media
0169-3913,
56
, pp.
351
367
.
13.
Ranjbar-Kani
,
A. A.
, and
Hooman
,
K.
, 2004, “
Viscous Dissipation Effects on Thermally Developing Forced Convection in a Porous Medium: Circular Duct With Isothermal Wall
,”
Int. Commun. Heat Mass Transfer
0735-1933,
31
, pp.
897
907
.
14.
Hooman
,
K.
, and
Gorji-Bandry
,
M.
, 2005, “
Laminar Dissipative Flow in a Porous Channel Bounded by Isothermal Parallel Plates
,”
Appl. Math. Mech.
0253-4827,
26
, pp.
587
593
.
15.
Hooman
,
K.
,
Pourshaghaghy
,
A.
, and
Ejlali
,
A.
, 2006, “
Effects of Viscous Dissipation on Thermally Developing Forced Convection in a Porous Saturated Circular Tube With an Isoflux Wall
,”
Appl. Math. Mech.
0253-4827,
27
, pp.
683
694
.
16.
Hooman
,
K.
, and
Gurgenti
,
H.
, 2007, “
Effects of Viscous Dissipation and Boundary Conditions on Forced Convection in a Channel Occupied by a Saturated Porous Medium
,”
Transp. Porous Media
0169-3913, in press.
17.
Ene
,
H. J.
, and
Sanchez-Palencia
,
E.
, 1982, “
On Thermal Equation for Flow in Porous Media
,”
Int. J. Eng. Sci.
0020-7225,
20
, pp.
623
630
.
18.
Nield
,
D. A.
, 2000, “
Resolution of a Paradox Involving Viscous Dissipation and Nonlinear Drag in a Porous Medium
,”
Transp. Porous Media
0169-3913,
41
, pp.
349
357
.
19.
Narasimhan
,
A.
, and
Lage
,
J. L.
, 2005, “
Variable Viscosity Forced Convection in Porous Medium Channels
,”
Handbook of Porous Media
,
2nd ed.
,
K.
Vafai
, ed.,
Taylor & Francis
,
New York
, pp.
195
234
.
20.
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
0169-3913,
53
, pp.
117
122
.
21.
Nield
,
D. A.
, 2004, “
Comments on ‘A New Model for Viscous Dissipation in Porous Media Across a Range of Permeability Values’
,”
Transp. Porous Media
0169-3913,
55
, pp.
253
254
.
22.
Kuznetsov
,
A. V.
,
Xiong
,
M.
, and
Nield
,
D. A.
, 2003, “
Thermally Developing Forced Convection in a Porous Medium: Circular Duct With Walls at Constant Temperature, With Longitudinal Conduction and Viscous Dissipation Effects
,”
Transp. Porous Media
0169-3913,
53
, pp.
331
345
.
23.
Gerritsen
,
M. G.
,
Chen
,
T.
, and
Chen
,
Q.
, 2005, private communication.
24.
Bejan
,
A.
, 1984,
Convection Heat Transfer
,
Wiley
,
New York
.
25.
Nield
,
D. A.
, 2006, “
A Note on a Brinkman-Brinkman Forced Convection Problem
,”
Transp. Porous Media
0169-3913,
64
, pp.
185
188
.
26.
de Vahl Davis
,
G.
, 1983, “
Natural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution
,”
Int. J. Numer. Methods Fluids
0271-2091,
3
, pp.
249
264
.
27.
Costa
,
V. A. F.
, 2006, “
On Natural Convection in Enclosures Filled With Fluid-Saturated Porous Media Including Viscous Dissipation
,”
Int. J. Heat Mass Transfer
0017-9310,
49
, pp.
2215
2226
.
28.
Costa
,
V. A. F.
, 2005, “
Thermodynamics of Natural Convection in Enclosures With Viscous Dissipation
,”
Int. J. Heat Mass Transfer
0017-9310,
48
, pp.
2333
2341
.
29.
Pons
,
M.
, and
le Quéré
,
P.
, 2005, “
An Example of Entropy Balance in Natural Convection, Part 1: The Usual Boussinesq Equations
,”
C. R. Mec.
1631-0721,
333
, pp.
127
132
.
30.
Pons
,
M.
, and
le Quéré
,
P.
, 2005, “
An Example of Entropy Balance in Natural Convection, Part 2: The Thermodynamic Boussinesq Equations
,”
C. R. Mec.
1631-0721,
333
, pp.
133
138
.
31.
Gray
,
D. G.
, and
Giorgini
,
A.
, 1976, “
The Validity of the Boussinesq Approximation for Liquids and Gases
,”
Int. J. Heat Mass Transfer
0017-9310,
19
, pp.
545
551
.
32.
Breugem
,
W. P.
, and
Rees
,
D. A. S.
, 2006, “
A Derivation of the Volume-Averaged Boussinesq Equations for Flow in Porous Media With Viscous Dissipation
,”
Transp. Porous Media
0169-3913,
63
, pp.
1
12
.
33.
Chandrasekhar
,
S.
, 1961,
Hydrodynamic and Hydromagnetic Stability
,
Clarendon
,
Oxford
, p.
34
.
34.
Bejan
,
A.
, 1982,
Entropy Generation Though Heat and Fluid Flow
,
Wiley
,
New York
, pp.
35
36
.
35.
Bejan
,
A.
, 1988,
Advanced Engineering Thermodynamics
,
Wiley
,
New York
, p.
136
.
36.
Nield
,
D. A.
, 1982, “
Onset of Convection in a Porous Layer Saturated by an Ideal Gas
,”
Int. J. Heat Mass Transfer
0017-9310,
25
, pp.
1605
1606
.
37.
Mallinson
,
G.
,
Moyle
,
K.
, and
Norris
,
S.
, 2004, “
Volumetric Methods for Evaluating Irreversible Energy Losses and Entropy Production With Application to Bioengineering Flows
,”
Proceedings of the ICHMT International Symposium on Advances in Computational Heat Transfer
, Norway, Apr. 19–24, Paper No. CHT-04-262.
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