The steady-state fully developed laminar flow of non-Newtonian power-law fluids is analytically studied in a circular microchannel under an imposed uniform and constant wall heat flux. Increasing the flow behavior index results in broadening the dimensionless temperature distribution, i.e., in enlarging the wall and bulk fluid temperature difference. Similar behavior may also be observed when heating or cooling flux is reduced. For any particular value of the flow behavior index, a critical Brinkman number exists in which the bulk mean fluid temperature equals the wall temperature; in this special case of surface cooling, the Nusselt number tends to infinity. Dilatants (shear-thickening fluids) demonstrate more tangible reactions than pseudoplastics (shear-thinning fluids) to changes in the Brinkman number. Entropy generation increases with the flow behavior index as well as the Brinkman number. For shear-thickening fluids, the entropy generation rate from heat transfer is more than the entropy generation rate from fluid friction, while an opposite trend is observed for shear-thinning fluids.

References

References
1.
Chhabra
,
R. P.
, and
Richardson
,
J. F.
,
2008
,
Non-Newtonian Flow and Applied Rheology
,
Butterworth-Heinemann
,
Oxford, UK
.
2.
Karniadakis
,
G.
,
Beskok
,
A.
, and
Aluru
,
N.
,
2005
,
Microflows and Nanoflows
,
Springer
,
New York
.
3.
Moghadam
,
A. J.
,
2015
, “
Thermal Characteristics of Time-Periodic Electroosmotic Flow in a Circular Microchannel
,”
Heat Mass Transfer
,
51
(
10
), pp.
1461
1473
.
4.
Moghadam
,
A. J.
,
2016
, “
Exact Solution of Electroviscous Flow and Heat Transfer in a Semi-Annular Microcapillary
,”
ASME J. Heat Transfer
,
138
(
1
), p.
011702
.
5.
Moghadam
,
A. J.
,
2013
, “
Electrokinetic-Driven Flow and Heat Transfer of a Non-Newtonian Fluid in a Circular Microchannel
,”
ASME J. Heat Transfer
,
135
(
2
), p.
021705
.
6.
Morini
,
G. L.
,
2005
, “
Viscous Heating in Liquid Flows in Micro-Channels
,”
Int. J. Heat Mass Transfer
,
48
(
17
), pp.
3637
3647
.
7.
Koo
,
J.
, and
Kleinstreuer
,
C.
,
2004
, “
Viscous Dissipation Effects in Microtubes and Microchannels
,”
Int. J. Heat Mass Transfer
,
47
(14–16), pp.
3159
3169
.
8.
Tyagi
,
V. P.
,
1966
, “
Laminar Forced Convection of a Dissipative Fluid in a Channel
,”
ASME J. Heat Transfer
,
88
(
2
), pp.
161
167
.
9.
Aydin
,
O.
,
2005
, “
Effects of Viscous Dissipation on the Heat Transfer in Forced Pipe Flow
,”
Energy Convers. Manage.
,
46
(
5
), pp.
757
769
.
10.
Mehendal
,
S. S.
,
Jacobo
,
A. M.
, and
Shah
,
R. K.
,
2000
, “
Fluid Flow and Heat Transfer at Micro- and Meso-Scales With Application to Heat Exchanger Design
,”
ASME Appl. Mech. Rev.
,
53
(
7
), pp.
175
193
.
11.
Herwig
,
H.
, and
Hausner
,
O.
,
2003
, “
Critical View on ‘New Results in Micro-Fluid Mechanics': An Example
,”
Int. J. Heat Mass Transfer
,
46
(
5
), pp.
935
937
.
12.
Bharti
,
R. P.
,
Harvie
,
D. J. E.
, and
Davidson
,
M. R.
,
2009
, “
Electroviscous Effects in Steady Fully Developed Flow of a Power-Law Liquid Through a Cylindrical Microchannel
,”
Int. J. Heat Fluid Flow
,
30
(
4
), pp.
804
811
.
13.
Dehkordi
,
A. M.
, and
Mohammadi
,
A. A.
,
2009
, “
Transient Forced Convection With Viscous Dissipation to Power-Law Fluids in Thermal Entrance Region of Circular Ducts With Constant Wall Heat Flux
,”
Energy Convers. Manage.
,
50
(
4
), pp.
1062
1068
.
14.
Chen
,
G. M.
, and
Tso
,
C. P.
,
2011
, “
Effects of Viscous Dissipation on Forced Convective Heat Transfer in a Channel Embedded in a Power-Law Fluid Saturated Porous Medium
,”
Int. Commun. Heat Mass Transfer
,
38
(
1
), pp.
57
62
.
15.
Bharti
,
R. P.
,
Chhabra
,
R. P.
, and
Eswaran
,
V.
,
2007
, “
Steady Forced Convection Heat Transfer From a Heated Circular Cylinder to Power-Law Fluids
,”
Int. J. Heat Mass Transfer
,
50
(5–6), pp.
977
990
.
16.
Tso
,
C. P.
,
Sheela-Francisca
,
J.
, and
Hung
,
Y. M.
,
2010
, “
Viscous Dissipation Effects of Power-Law Fluid Flow Within Parallel Plates With Constant Heat Fluxes
,”
J. Non-Newtonian Fluid Mech.
,
165
(11–12), pp.
625
630
.
17.
Lawal
,
A.
,
Nigeria
,
P. H.
, and
Mujumdar
,
A. S.
,
1992
, “
The Effects of Viscous Dissipation on Heat Transfer to Power Law Fluids in Arbitrary Cross-Sectional Ducts
,”
Warme- Stoffübertragung
,
27
(
7
), pp.
437
446
.
18.
Guo
,
J. F.
,
Xu
,
M.
,
Cai
,
J.
, and
Huai
,
X.
,
2011
, “
Viscous Dissipation Effect on Entropy Generation in Curved Square Microchannels
,”
Energy
,
36
(
8
), pp.
5416
5423
.
19.
Hung
,
Y. M.
,
2010
, “
Analytical Study on Forced Convection of Nanofluids With Viscous Dissipation in Microchannel
,”
Heat Transfer Eng.
,
31
(
14
), pp.
1184
1192
.
20.
Hung
,
Y. M.
,
2009
, “
A Comparative Study of Viscous Dissipation Effect on Entropy Generation in Single-Phase Liquid Flow in Microchannels
,”
Int. J. Therm. Sci.
,
48
(
5
), pp.
1026
1035
.
21.
Bejan
,
A.
,
1996
,
Entropy Generation Minimization
,
CRC Press
,
New York
.
22.
Bejan
,
A.
,
1979
, “
A Study of Entropy Generation in Fundamental Convective Heat Transfer
,”
ASME J. Heat Transfer
,
101
(
4
), pp.
718
725
.
23.
Shamshiri
,
M.
,
Khazaeli
,
R.
,
Ashrafizaadeh
,
M.
, and
Mortazavi
,
S.
,
2012
, “
Heat Transfer and Entropy Generation Analyses Associated With Mixed Electrokinetically Induced and Pressure-Driven Power-Law Microflows
,”
Energy
,
42
(
1
), pp.
157
169
.
24.
Mah
,
W. H.
,
Hung
,
Y. M.
, and
Guo
,
N.
,
2012
, “
Entropy Generation of Viscous Dissipative Nanofluid Flow in Microchannels
,”
Int. J. Heat Mass Transfer
,
55
(15–16), pp.
4169
4182
.
25.
Hung
,
Y. M.
,
2008
, “
Viscous Dissipation Effect on Entropy Generation for Non-Newtonian Fluids in Microchannels
,”
Int. Commun. Heat Mass Transfer
,
35
(
9
), pp.
1125
1129
.
26.
Mahmud
,
S.
, and
Fraser
,
R. A.
,
2006
, “
Second Law Analysis of Forced Convection in a Circular Duct for Non-Newtonian Fluids
,”
Energy
,
31
(
12
), pp.
2226
2244
.
27.
Mahmud
,
S.
, and
Fraser
,
R. A.
,
2002
, “
Inherent Irreversibility of Channel and Pipe Flows for Non-Newtonian Fluids
,”
Int. Commun. Heat Mass Transfer
,
29
(
5
), pp.
577
587
.
28.
Tan
,
L. Y.
, and
Chen
,
G. M.
,
2013
, “
Analysis of Entropy Generation for a Power-Law Fluid in Microchannels
,”
ASME
Paper No. MNHMT2013-22159.
29.
Mahmud
,
S.
, and
Fraser
,
R. A.
,
2003
, “
The Second Law Analysis in Fundamental Convective Heat Transfer Problems
,”
Int. J. Therm. Sci.
,
42
(
2
), pp.
177
186
.
30.
Mohammadi
,
M. R.
, and
Moghadam
,
A. J.
,
2015
, “
Heat Transfer and Entropy Generation Analysis of Bingham Plastic Fluids in Circular Microchannels
,”
ASME J. Therm. Sci. Eng. Appl.
,
7
(
4
), p.
041019
.
31.
Moghadam
,
A. J.
, and
Akbarzadeh
,
P.
,
2016
, “
Time-Periodic Electroosmotic Flow of Non-Newtonian Fluids in Microchannels
,”
IJE
,
29
(
5
), pp.
706
714
.
32.
Tan
,
D. K.
, and
Liu
,
Y.
,
2014
, “
Combined Effects of Streaming Potential and Wall Slip on Flow and Heat Transfer in Microchannels
,”
Int. Commun. Heat Mass Transfer
,
53
, pp.
39
42
.
33.
Bird
,
R. B.
,
Stewart
,
W. E.
, and
Lightfoot
,
E. N.
,
2002
,
Transport Phenomena
,
Wiley
,
New York
.
34.
Barkhordari
,
M.
, and
Etemad
,
S. G.
,
2007
, “
Numerical Study of Slip Flow Heat Transfer of Non-Newtonian Fluids in Circular Microchannels
,”
Int. J. Heat Fluid Flow
,
28
(
5
), pp.
1027
1033
.
35.
Hooman
,
K.
,
2007
, “
Entropy Generation for Microscale Forced Convection: Effects of Different Thermal Boundary Conditions, Velocity Slip, Temperature Jump, Viscous Dissipation, and Duct Geometry
,”
Int. Commun. Heat Mass Transfer
,
34
(
8
), pp.
945
957
.
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