This paper presents a study of the thermal characteristics and entropy generation of a porous microchannel with thick walls featuring uneven thicknesses. Two sets of asymmetric boundary conditions are considered. The first includes constant temperatures at the surface of the outer walls, with the lower wall experiencing a higher temperature than the upper wall. The second case imposes a constant heat flux on the lower wall and a convection boundary condition on the upper wall. These set thermal models for microreactors featuring highly exothermic or endothermic reactions such as those encountered in fuel reforming processes. The porous system is considered to be under local thermal nonequilibrium (LTNE) condition. Analytical solutions are, primarily, developed for the temperature and local entropy fields and then are extended to the total entropy generation within the system. It is shown that the ratio of the solid to fluid effective thermal conductivity and the internal heat sources are the most influential parameters in the thermal and entropic behaviors of the system. In particular, the results demonstrate that the internal heat sources can affect the entropy generation in a nonmonotonic way and that the variation of the total entropy with internal heat sources may include extremum points.

References

References
1.
Kolb
,
G.
, and
Hessel
,
V.
,
2004
, “
Micro-Structured Reactors for Gas Phase Reactions
,”
Chem. Eng. J.
,
98
(1–2), pp.
1
38
.
2.
Wirth
,
T.
,
2013
,
Microreactors in Organic Synthesis and Catalysis
,
Wiley
, Weinheim, Germany.
3.
Chein
,
R. Y.
,
Chen
,
L. C.
,
Chen
,
Y. C.
, and
Chung
,
J. N.
,
2009
, “
Heat Transfer Effects on the Methanol-Steam Reforming With Partially Filled Catalyst Layers
,”
Int. J. Hydrogen Energy
,
34
(
13
), pp.
5398
5408
.
4.
Chein
,
R.-Y.
,
Chen
,
Y.-C.
, and
Chung
,
J. N.
,
2012
, “
Thermal Resistance Effect on Methanol-Steam Reforming Performance in Micro-Scale Reformers
,”
Int. J. Hydrogen Energy
,
37
(
1
), pp.
250
262
.
5.
Chein
,
R.
,
Chen
,
Y. C.
, and
Chung
,
J. N.
,
2012
, “
Axial Heat Conduction and Heat Supply Effects on Methanol-Steam Reforming Performance in Micro-Scale Reformers
,”
Int. J. Heat Mass Transfer
,
55
(11–12), pp.
3029
3042
.
6.
Som
,
S. K.
, and
Datta
,
A.
,
2008
, “
Thermodynamic Irreversibilities and Exergy Balance in Combustion Processes
,”
Prog. Energy Combust. Sci.
,
34
(
3
), pp.
351
376
.
7.
Namkung
,
H.
,
Yuan
,
X.
,
Lee
,
G.
,
Kim
,
D.
,
Kang
,
T. J.
, and
Kim
,
H. T.
,
2014
, “
Reaction Characteristics Through Catalytic Steam Gasification With Ultra Clean Coal Char and Coal
,”
J. Energy Inst.
,
87
(
3
), pp.
253
262
.
8.
Hooman
,
K.
, and
Ejlali
,
A.
,
2007
, “
Entropy Generation for Forced Convection in a Porous Saturated Circular Tube With Uniform Wall Temperature
,”
Int. Commun. Heat Mass Transfer
,
34
(
4
), pp.
408
419
.
9.
Hooman
,
K.
, and
Haji-Sheikh
,
A.
,
2007
, “
Analysis of Heat Transfer and Entropy Generation for a Thermally Developing Brinkman-Brinkman Forced Convection Problem in a Rectangular Duct With Isoflux Walls
,”
Int. J. Heat Mass Transfer
,
50
(21–22), pp.
4180
4194
.
10.
Hooman
,
K.
,
Gurgenci
,
H.
, and
Merrikh
,
A. A.
,
2007
, “
Heat Transfer and Entropy Generation Optimization of Forced Convection in Porous-Saturated Ducts of Rectangular Cross-Section
,”
Int. J. Heat Mass Transfer
,
50
(11–12), pp.
2051
2059
.
11.
Mahmud
,
S.
, 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.
Mahmud
,
S.
,
Tasnim
,
S. H.
,
Fraser
,
R. A.
, and
Pop
,
I.
,
2011
, “
Hydrodynamic and Thermal Interaction of a Periodically Oscillating Fluid With a Porous Medium Lying Over a Thick Solid Plate
,”
Int. J. Therm. Sci.
,
50
(
10
), pp.
1908
1919
.
13.
Siavashi
,
M.
,
Bahrami
,
H. R. T.
, and
Saffari
,
H.
,
2015
, “
Numerical Investigation of Flow Characteristics, Heat Transfer and Entropy Generation of Nanofluid Flow Inside an Annular Pipe Partially or Completely Filled With Porous Media Using Two-Phase Mixture Model
,”
Energy
,
93
(Part 2), pp.
2451
2466
.
14.
Karimi
,
N.
,
Agbo
,
D.
,
Khan
,
A. T.
, and
Younger
,
P. L.
,
2015
, “
On the Effects of Exothermicity and Endothermicity Upon the Temperature Fields in a Partially-Filled Porous Channel
,”
Int. J. Therm. Sci.
,
96
, pp.
128
148
.
15.
Buonomo
,
B.
,
Manca
,
O.
, and
Lauriat
,
G.
,
2014
, “
Forced Convection in Micro-Channels Filled With Porous Media in Local Thermal Non-Equilibrium Conditions
,”
Int. J. Therm. Sci.
,
77
, pp.
206
222
.
16.
Torabi
,
M.
,
Zhang
,
K.
,
Yang
,
G.
,
Wang
,
J.
, and
Wu
,
P.
,
2015
, “
Heat Transfer and Entropy Generation Analyses in a Channel Partially Filled With Porous Media Using Local Thermal Non-Equilibrium Model
,”
Energy
,
82
, pp.
922
938
.
17.
Torabi
,
M.
,
Karimi
,
N.
, and
Zhang
,
K.
,
2015
, “
Heat Transfer and Second Law Analyses of Forced Convection in a Channel Partially Filled by Porous Media and Featuring Internal Heat Sources
,”
Energy
,
93
(Part 1), pp.
106
127
.
18.
Torabi
,
M.
,
Karimi
,
N.
,
Zhang
,
K.
, and
Peterson
,
G. P.
,
2016
, “
Generation of Entropy and Forced Convection of Heat in a Conduit Partially Filled With Porous Media—Local Thermal Non-Equilibrium and Exothermicity Effects
,”
Appl. Therm. Eng.
,
106
, pp.
518
536
.
19.
Chee
,
Y. S.
,
Ting
,
T. W.
, and
Hung
,
Y. M.
,
2015
, “
Entropy Generation of Viscous Dissipative Flow in Thermal Non-Equilibrium Porous Media With Thermal Asymmetries
,”
Energy
,
89
, pp.
382
401
.
20.
Ting
,
T. W.
,
Hung
,
Y. M.
, and
Guo
,
N.
,
2015
, “
Entropy Generation of Viscous Dissipative Nanofluid Convection in Asymmetrically Heated Porous Microchannels With Solid-Phase Heat Generation
,”
Energy Convers. Manage.
,
105
, pp.
731
745
.
21.
Dickson
,
C.
,
Torabi
,
M.
, and
Karimi
,
N.
,
2016
, “
First and Second Law Analyses of Nanofluid Forced Convection in a Partially-Filled Porous Channel—The Effects of Local Thermal Non-Equilibrium and Internal Heat Sources
,”
Appl. Therm. Eng.
,
103
, pp.
459
480
.
22.
Torabi
,
M.
,
Dickson
,
C.
, and
Karimi
,
N.
,
2016
, “
Theoretical Investigation of Entropy Generation and Heat Transfer by Forced Convection of Copper–Water Nanofluid in a Porous Channel—Local Thermal Non-Equilibrium and Partial Filling Effects
,”
Powder Technol.
,
301
, pp.
234
254
.
23.
Elliott
,
A.
,
Torabi
,
M.
,
Karimi
,
N.
, and
Cunningham
,
S.
,
2016
, “
On the Effects of Internal Heat Sources Upon Forced Convection in Porous Channels With Asymmetric Thick Walls
,”
Int. Commun. Heat Mass Transfer
,
73
, pp.
100
110
.
24.
Torabi
,
M.
,
Zhang
,
K.
,
Karimi
,
N.
, and
Peterson
,
G. P.
,
2016
, “
Entropy Generation in Thermal Systems With Solid Structures—A Concise Review
,”
Int. J. Heat Mass Transfer
,
97
, pp.
917
931
.
25.
Chen
,
W. H.
,
Cheng
,
T. C.
, and
Hung
,
C. I.
,
2011
, “
Modeling and Simulation of Microwave Double Absorption on Methanol Steam Reforming for Hydrogen Production
,”
Int. J. Hydrogen Energy
,
36
(
1
), pp.
333
344
.
26.
Chen
,
W. H.
,
Cheng
,
T. C.
, and
Hung
,
C. I.
,
2011
, “
Numerical Predictions on Thermal Characteristic and Performance of Methanol Steam Reforming With Microwave-Assisted Heating
,”
Int. J. Hydrogen Energy
,
36
(
14
), pp.
8279
8291
.
27.
Civan
,
F.
,
2011
,
Porous Media Transport Phenomena
,
Wiley
, Hoboken, NJ.
28.
Torabi
,
M.
,
Peterson
,
G. P.
,
Torabi
,
M.
, and
Karimi
,
N.
,
2016
, “
A Thermodynamic Analysis of Forced Convection Through Porous Media Using Pore Scale Modeling
,”
Int. J. Heat Mass Transfer
,
99
, pp.
303
316
.
29.
Torabi
,
M.
,
Torabi
,
M.
, and
Peterson
,
G. P.
,
2016
, “
Heat Transfer and Entropy Generation Analyses of Forced Convection Through Porous Media Using Pore Scale Modeling
,”
ASME J. Heat Transfer
,
139
(
1
), p.
012601
.
30.
Coutinho
,
J. E. A.
, and
de Lemos
,
M. J. S.
,
2012
, “
Laminar Flow With Combustion in Inert Porous Media
,”
Int. Commun. Heat Mass Transfer
,
39
(
7
), pp.
896
903
.
31.
Gaffar
,
S. A.
,
Prasad
,
V. R.
,
Reddy
,
E. K.
, and
Bég
,
O. A.
,
2015
, “
Thermal Radiation and Heat Generation/Absorption Effects on Viscoelastic Double-Diffusive Convection From an Isothermal Sphere in Porous Media
,”
Ain Shams Eng. J.
,
6
(
3
), pp.
1009
1030
.
32.
Dada
,
M. S.
, and
Disu
,
A. B.
,
2015
, “
Heat Transfer With Radiation and Temperature Dependent Heat Source in MHD Free Convection Flow in a Porous Medium Between Two Vertical Wavy Walls
,”
J. Niger. Math. Soc.
,
34
(
2
), pp.
200
215
.
33.
Chen
,
J.
,
Song
,
W.
,
Gao
,
X.
, and
Xu
,
D.
,
2016
, “
Hetero-/Homogeneous Combustion and Flame Stability of Fuel-Lean Propane–Air Mixtures Over Platinum in Catalytic Micro-Combustors
,”
Appl. Therm. Eng.
,
100
, pp.
932
943
.
34.
Yao
,
X.
,
Zhang
,
Y.
,
Du
,
L.
,
Liu
,
J.
, and
Yao
,
J.
,
2015
, “
Review of the Applications of Microreactors
,”
Renewable Sustainable Energy Rev.
,
47
, pp.
519
539
.
35.
Torabi
,
M.
, and
Peterson
,
G. P.
,
2016
, “
Effects of Velocity Slip and Temperature Jump on the Heat Transfer and Entropy Generation in Micro Porous Channels Under Magnetic Field
,”
Int. J. Heat Mass Transfer
,
102
, pp.
585
595
.
36.
Ibáñez
,
G.
,
López
,
A.
,
Pantoja
,
J.
, and
Moreira
,
J.
,
2014
, “
Combined Effects of Uniform Heat Flux Boundary Conditions and Hydrodynamic Slip on Entropy Generation in a Microchannel
,”
Int. J. Heat Mass Transfer
,
73
, pp.
201
206
.
37.
Ibáñez
,
G.
,
2015
, “
Entropy Generation in MHD Porous Channel With Hydrodynamic Slip and Convective Boundary Conditions
,”
Int. J. Heat Mass Transfer
,
80
, pp.
274
280
.
38.
Ibáñez
,
G.
,
López
,
A.
,
Pantoja
,
J.
, and
Moreira
,
J.
,
2016
, “
Entropy Generation Analysis of a Nanofluid Flow in MHD Porous Microchannel With Hydrodynamic Slip and Thermal Radiation
,”
Int. J. Heat Mass Transfer
,
100
, pp.
89
97
.
39.
Torabi
,
M.
, and
Zhang
,
K.
,
2015
, “
Temperature Distribution, Local and Total Entropy Generation Analyses in MHD Porous Channels With Thick Walls
,”
Energy
,
87
, pp.
540
554
.
40.
Kumar
,
V.
,
Paraschivoiu
,
M.
, and
Nigam
,
K. D. P.
,
2011
, “
Single-Phase Fluid Flow and Mixing in Microchannels
,”
Chem. Eng. Sci.
,
66
(
7
), pp.
1329
1373
.
41.
Kaisare
,
N. S.
, and
Vlachos
,
D. G.
,
2012
, “
A Review on Microcombustion: Fundamentals, Devices and Applications
,”
Prog. Energy Combust. Sci.
,
38
(
3
), pp.
321
359
.
42.
Yang
,
K.
, and
Vafai
,
K.
,
2010
, “
Analysis of Temperature Gradient Bifurcation in Porous Media—An Exact Solution
,”
Int. J. Heat Mass Transfer
,
53
(19–20), pp.
4316
4325
.
43.
Vafai
,
K.
,
2005
,
Handbook of Porous Media
,
2nd ed.
,
CRC Press
, Boca Raton, FL.
44.
Gavriilidis
,
A.
,
Angeli
,
P.
,
Cao
,
E.
,
Yeong
,
K. K.
, and
Wan
,
Y. S. S.
,
2002
, “
Technology and Applications of Microengineered Reactors
,”
Chem. Eng. Res. Des.
,
80
(
1
), pp.
3
30
.
45.
Iliuta
,
I.
,
Hamidipour
,
M.
,
Schweich
,
D.
, and
Larachi
,
F.
,
2012
, “
Two-Phase Flow in Packed-Bed Microreactors: Experiments, Model and Simulations
,”
Chem. Eng. Sci.
,
73
, pp.
299
313
.
You do not currently have access to this content.