This paper proposes a numerical analysis of entropy generation during mixed convection inside a porous Poiseuille–Benard channel flow, where the Darcy–Brinkman model is used. Irreversibilities due to heat transfer and viscous dissipation have been derived, and then calculated by numerically solving mass, momentum, and energy conservation equations, by using a control volume finite element method (CVFEM). For a fixed value of the thermal Rayleigh (Ra = 104) and the modified Brinkman (Br* = 10−3) numbers, transient entropy generation exhibits a periodic behavior for the medium porosity ε ≥ 0.2, which is described by the onset of thermoconvective cells inside the porous channel. Highest irreversibility is obtained at ε = 0.5. More details about the effects of the Darcy, the Rayleigh, and the modified Brinkman numbers on entropy generation and heat transfer are discussed and graphically presented.

References

1.
Scheidegger
,
E.
,
1974
,
The Physics of Flow Through Porous Media
, 3rd ed.,
University of Toronto Press
,
Toronto, ON, Canada
.
2.
Bejan
,
A.
, and
Lage
,
J. L.
,
1991
, “
Heat Transfer From a Surface Covered With Hair
,”
Conv. Heat Mass Trans. Porous Media
,
196
, pp.
823
845
.
3.
Lucia
,
U.
,
2013
, “
Stationary Open Systems: A Brief Review on Contemporary Theories on Irreversibility
,”
Physica A
,
392
(
5
), pp.
1051
1062
.
4.
Nield
,
D. A.
, and
Bejan
,
A.
,
1999
,
Convection in Porous Media
, 2nd ed.,
Springer
,
New York
.
5.
Nield
,
D. A.
, and
Bejan
,
A.
,
2006
,
Convection in Porous Media
, 3rd ed.,
Springer-Verlag
,
New York
.
6.
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 Effects
,”
Int. J. Heat Mass Transfer
,
46
(
4
), pp.
643
651
.
7.
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
,”
Trans. Porous Media
,
56
(
3
), pp.
351
367
.
8.
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 Effects
,”
Trans. Porous Media
,
53
(
3
), pp.
331
345
.
9.
Saied
,
N. H.
, and
Pop
,
I.
,
2004
, “
Viscous Dissipation Effects on Free Convection in a Porous Cavity
,”
Int. Commun. Heat Mass Transfer
,
31
(
5
), pp.
723
732
.
10.
Ingham
,
D. B.
, and
Pop
,
I.
,
2005
,
Transport Phenomena in Porous Media III
,
Elsevier
,
Oxford, UK
.
11.
Shohel
,
M.
, and
Fraser
,
R. A.
,
2005
, “
Flow, Thermal, and Entropy Generation Characteristics Inside a Porous Channel With Viscous Dissipation
,”
Int. J. Therm. Sci.
,
44
(1), pp.
21
32
.
12.
Hooman
,
K.
,
Hooman
,
F.
, and
Mohebpour
,
S. R.
,
2008
, “
Entropy Generation for Forced Convection in a Porous Channel With Isoflux or Isothermal Walls
,”
Int. J. Exergy
,
5
(
1
), pp.
78
96
.
13.
Dwivedi
,
R.
,
Singh
,
S. P.
, and
Singh
,
B. B.
,
2010
, “
Analysis of Incompressible Viscous Laminar Flow Through a Channel Filled With Porous Media
,”
Int. J. Stab. Fluid Mech.
,
1
, pp.
127
134
.
14.
Abdulhassan
,
Dr.
,
Karamallah
,
A.
,
Wahid
,
Dr.
,
Mohammad
,
S.
, and
Wissam
,
H. K.
,
2011
, “
Numerical Study of Entropy Generation in a Vertical Square Channel Packed With Saturated Porous Media
,”
Eng. Tech. J.
,
29
, pp.
1721
1736
.
15.
Abbassi
,
H.
,
Magherbi
,
M.
, and
Ben Brahim
,
A.
,
2003
, “
Entropy Generation in Poiseuille–Benard Channel Flow
,”
Int. J. Therm. Sci.
,
42
(
12
), pp.
1081
1088
.
16.
Magherbi
,
M.
,
Abbassi
,
H.
, and
Ben Brahim
,
A.
,
2003
, “
Entropy Generation at the Onset of Natural Convection
,”
Int. J. Heat Mass Transfer
,
46
(
18
), pp.
3441
3450
.
17.
Mchirgui
,
A.
,
Hidouri
,
N.
,
Magherbi
,
M.
, and
Ben Brahim
,
A.
,
2012
, “
Entropy Generation in Double-Diffusive Convection in a Square Porous Cavity Using Darcy–Brinkman Formulation
,”
Trans. Porous Media
,
93
(
1
), pp.
223
240
.
18.
Oztop
,
H. F.
, and
Al-Salem
,
K.
,
2012
, “
A Review on Entropy Generation in Natural and Mixed Convection Heat Transfer for Energy Systems
,”
Renewable Sustainable Energy Rev.
,
16
(
1
), pp.
911
920
.
19.
Gilver
,
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
.
20.
Khaled
,
A. R. A.
, and
Vafai
,
K.
,
2003
, “
The Role of Porous Media in Modeling Flow and Heat Transfer in Biological Tissues
,”
Int. J. Heat Mass Transfer
,
46
(
26
), pp.
4989
5003
.
21.
Lundgren
,
T. S.
,
1972
, “
Slow Flow Through Stationary Random Beds and Suspensions Spheres
,”
J. Fluid Mech.
,
51
(
2
), pp.
273
299
.
22.
Sohankar
,
A.
,
Norberg
,
C.
, and
Davidson
,
L.
,
1998
, “
Low-Reynolds-Number Flow Around a Square Cylinder at Incidence: Study of Blockage, Onset of Vortex Shedding and Outlet Boundary Condition
,”
Int. J. Numer. Methods Fluids
,
26
(
1
), pp.
39
56
.
23.
Nicolas
,
X.
,
Traore
,
P.
,
Mojtabi
,
A.
, and
Caltagirone
,
J. P.
,
1997
, “
Augmented Lagrangian Method and Open Boundary Conditions in 2D Simulation of Poiseuille–Benard Channel Flow
,”
Int. J. Numer. Methods Fluids
,
25
(
3
), pp.
265
283
.
24.
Bejan
,
A.
,
1982
,
Entropy Generation Through Heat and Mass Flow
,
Wiley
,
New York
.
25.
Bejan
,
A.
,
1996
, “
Method of Entropy Generation Minimization, or Modeling and Optimization Based on Combined Heat Transfer and Thermodynamics
,”
Rev. Gén. Therm.
,
35
, pp.
637
646
.
26.
Bejan
,
A.
,
2006
,
Advances Engineering Thermodynamics
,
Wiley
,
New York
.
27.
Grazzini
,
G.
, and
Lucia
,
U.
,
1997
, “
Global Analysis of Dissipations Due to Irreversibility
,”
Rev. Gén. Therm.
,
36
(8), pp.
605
609
.
28.
Lucia
,
U.
,
2007
, “
Irreversibility Entropy Variation and the Problem of the Trend of Equilibrium
,”
Physica A
,
376
, pp.
289
292
.
29.
Lucia
,
U.
,
2012
, “
Maximum or Minimum Entropy Generation for Open Systems?
Physica A
,
391
(
12
), pp.
3392
3398
.
30.
Nield
,
D. A.
,
2000
, “
Resolution of a Paradox Involving Viscous Dissipation and Non Linear Drag in a Porous Medium
,”
Trans. Porous Media
,
41
(
3
), pp.
349
357
.
31.
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
,”
Trans. Porous Media
,
53
(
1
), pp.
117
122
.
32.
Bejan
,
A.
,
1996
,
Entropy Generation Minimization
,
CRC Press
,
New York
.
33.
Hidouri
,
N.
,
Magherbi
,
M.
, and
Ben Brahim
,
A.
,
2009
, “
Influence of a Magnetic Field on Entropy Generation in Poiseuille–Benard Channel Flow
,”
Adv. Appl. Fluid Mech.
,
5
(
2
), pp.
155
177
.
34.
Saabas
,
H. J.
, and
Baliga
,
B. R.
,
1994
, “
Co-Located Equal-Order Control-Volume Finite-Element Method for Multidimensional, Incompressible, Fluid Flow
,”
Numer. Heat Transfer, Part B
,
26
(
4
), pp.
381
407
.
35.
Prakash
,
C.
,
1986
, “
An Improved Control Volume Finite-Element Method for Heat and Mass Transfer and for Fluid Flow Using Equal Order Velocity–Pressure Interpolation
,”
Numer. Heat Transfer, Part B
,
9
(3), pp.
253
276
.
36.
Hookey
,
N. A.
,
1989
, “
A CVFEM for Two-Dimensional Viscous Compressible Fluid Flow
,” Ph.D. thesis, McGill University, Montreal, QC, Canada.
37.
Elkaim
,
D.
,
Reggio
,
M.
, and
Camarero
,
R.
,
1991
, “
Numerical Solution of Reactive Laminar Flow by a Control Volume Based Finite-Element Method and the Vorticity Stream Function Formulation
,”
Numer. Heat Transfer, Part B
,
20
(
2
), pp.
223
240
.
38.
Abbassi
,
H.
,
Turki
,
S.
, and
Ben Nasrallah
,
S.
,
2001
, “
Mixed Convection in a Plane Channel With a Built-Intriangular Prison
,”
Numer. Heat Transfer, Part A
,
39
, pp.
307
320
.
39.
Abbassi
,
H.
,
Turki
,
S.
, and
Ben Nasrallah
,
S.
,
2001
, “
Numerical Investigation of Forced Convection in a Plane Channel With a Built-In Triangular Prism
,”
Int. J. Therm. Sci.
,
40
(
7
), pp.
649
658
.
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