Developing and fully developed laminar flows of power law fluid with forced convection heat transfer through a concentric annular duct are numerically analyzed. The results are presented for the following ranges: 0.2 ≤ n ≤ 1.8 (power law index), 10 ≤ Re ≤ 1000 (Reynolds number), and r* = 0.2, 0.5, 0.8 (aspect ratio). In addition, the influences of different thermal boundary conditions on the thermal performance are delineated. The effects of rheological parameter on the developing length, friction factor, temperature distribution, velocity profile, and Nusselt number along the channel length are investigated. The results are compared with earlier research and excellent agreement was observed.

References

References
1.
Fredrickson
,
A. G.
, and
Bird
,
R. B.
,
1958
, “
Non-Newtonian Flow in Annuli
,”
Indust. Eng. Chem.
,
50
(
3
), pp.
347
352
.10.1021/ie50579a035
2.
Fredrickson
,
A. G.
, and
Bird
,
R. B.
,
1958
, “
Friction Factors for Axial Non-Newtonian Annular Flow
,”
Indust. Eng. Chem.
,
50
(
10
), pp.
1599
1600
.10.1021/ie50586a050
3.
Hanks
,
R. W.
, and
Larsen
,
K. M.
,
1979
, “
Flow of Power-Law Non-Newtonian Fluids in Concentric Annuli
,”
Indust. Eng. Chem. Fundamentals
,
18
(
1
), pp.
33
35
.10.1021/i160069a008
4.
Prasanth
,
N.
, and
Shenoy
,
U. V.
,
1992
, “
Poiseuille Flow of a Power-Law Fluid Between Coaxial Cylinders
,”
J. Appl. Polym. Sci.
,
46
(
7
), pp.
1189
1194
.10.1002/app.1992.070460708
5.
David
,
J.
, and
Filip
,
P.
,
1996
, “
Explicit Pressure Drop-Flow Rate Relation for Laminar Axial Flow of Power-Law Fluids in Concentric Annuli
,”
J. Petrol. Sci. Eng.
,
16
(
4
), pp.
203
208
.10.1016/S0920-4105(96)00039-3
6.
Kozicki
,
W.
,
Chou
,
C. H.
, and
Tiu
,
C.
,
1966
, “
Non-Newtonian Flow in Ducts of Arbitrary Cross-Sectional Area
,”
Chem. Eng. Sci.
,
21
(
8
), pp.
665
679
.10.1016/0009-2509(66)80016-7
7.
Tuoc
,
T. K.
, and
Mcgiven
,
J. M.
,
1994
, “
Laminar Flow of Non-Newtonian Fluids in Annuli
,”
Chem. Eng. Res. Des.
,
72
(A
5
), pp.
669
676
.
8.
Liu
,
J.
, and
Shah
, V
. L.
,
1975
, “
Numerical Solution of a Casson Fluid Flow in the Entrance of Annular Tubes
,”
Appl. Sci. Res.
,
31
, pp.
213
222
.10.1007/BF02116159
9.
Round
,
G. F.
, and
Yu
,
S.
,
1993
, “
Entrance Laminar Flows of Viscoplastic Fluids in Concentric Annuli
,”
Can. J. Chem. Eng.
,
71
, pp.
642
645
.10.1002/cjce.5450710417
10.
Maia
,
M. C. A.
, and
Gasparetto
,
C. A.
,
2003
, “
A Numerical Solution for the Entrance Region of Non-Newtonian Flow in Annuli
,”
Brazilian J. Chem. Eng.
,
20
(
2
), pp.
201
211
.10.1590/S0104-66322003000200014
11.
Mishra
, I
. M.
, and
Mishra
,
P.
,
1977
, “
Linearized Approach for Predicting Loss Coefficients in Entrance Region Flows of Purely Viscous Non-Newtonian Fluids in an Annular Duct
,”
Chem. Eng. J.
,
14
, pp.
41
47
.10.1016/0300-9467(77)80021-X
12.
Coelho
,
P. M.
,
Pinho
,
F. T.
, and
Oliveira
,
P. J.
,
2003
, “
Thermal Entry Flow for a Viscoelastic Fluid: The Graetz Problem for PTT Model
,”
Int. J. Heat Mass Tran.
,
46
(
20
), pp.
3865
3880
.10.1016/S0017-9310(03)00179-0
13.
Oliveira
,
P. J.
,
Coelho
,
P. M.
, and
Pinho
,
F. T.
,
2004
, “
The Graetz Problem With Viscous Dissipation for FENE-P Fluids
,”
J. Non Newt. Fluid. Mech.
,
121
(
1
), pp.
69
72
.10.1016/j.jnnfm.2004.04.005
14.
Pinho
,
F. T.
and
Oliveira
,
P. J.
,
2000
, “
Axial Annular Flow of a Nonlinear Viscoelastic Fluid-an Analytical Solution
,”
J. Non Newt. Fluid. Mech.
,
93
, pp.
325
337
.10.1016/S0377-0257(00)00113-0
15.
Uzun
, I
.
, and
Unsal
,
M.
,
1997
, “
A Numerical Study of Laminar Heat Convection in Ducts of Irregular Cross-Sections
,”
Int. Commun. Heat Mass Transfer
,
24
(
6
), pp.
835
848
.10.1016/S0735-1933(97)00070-5
16.
Lin
,
C. X.
,
Zhang
,
P.
, and
Ebadian
,
M. A.
,
1997
, “
Laminar Forced Convection in the Entrance Region of Helical Pipes
,”
Int. J. Heat Mass Tran.
,
40
(
14
), pp.
3293
3304
.10.1016/S0017-9310(96)00381-X
17.
Lin
,
M. J.
,
Wang
,
Q. W.
, and
Tao
,
W. Q.
,
2000
, “
Developing Laminar Flow and Heat Transfer in Annular-Sector Ducts
,”
Heat Transf. Eng.
,
21
, pp.
53
61
.10.1080/014576300271022
18.
Escudier
,
M. P.
,
Oliveira
,
P. J.
,
Pinho
,
F. T.
, and
Smith
,
S.
,
2002
, “
Fully Developed Laminar Flow of Non-Newtonian Liquids Through Annuli: Comparison of Numerical Calculations With Experiments
,”
Experiment. Fluid.
,
33
(
1
), pp.
101
111
.10.1007/S00348-002-0429-4
19.
Viana
,
M. J. G.
,
Nascimento
,
U. C. S.
,
Quaresma
,
J. N. N.
, and
Macedo
,
E. N.
,
2001
, “
Integral Transform Method for Laminar Heat Transfer Convection of Herschel–Bulkley Fluids Within Concentric Annular Ducts
,”
Braz. J. Chem. Eng.
,
18
(
4
), pp.
337
358
.10.1590/S0104-66322001000400001
20.
Nouar
,
C.
,
Benaouda-Zouaoui
,
B.
, and
Desaubry
,
C.
,
2000
, “
Laminar Mixed Convection in a Horizontal Annular Duct. Case of Thermodependent Non-Newtonian Fluid
,”
Eur. J. Mechan. B
,
19
(
3
), pp.
423
452
.10.1016/S0997-7546(00)00120-5
21.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2005
, “
Thermally Developing Forced Convection in a Channel Occupied by a Porous Medium Saturated by a Non-Newtonian Fluid
,”
Int. J. Heat Mass Tran.
,
48
, pp.
1214
1218
.10.1016/j.ijheatmasstransfer.2004.09.040
22.
Manglik
,
R. M.
, and
Fang
,
P.
,
2002
, “
Thermal Processing of Viscous Non-Newtonian Fluids in Annular Ducts: Effects of Power-Law Rheology, Duct Eccentricity and Thermal Boundary Conditions
,”
Int. J. Heat Mass Tran.
,
45
(
4
), pp.
803
814
.10.1016/S0017-9310(01)00186-7
23.
Soares
,
E. J.
,
Naccache
,
M. F.
, and
Mendes
,
P. R. S.
,
2003
, “
Heat Transfer to Viscoplastic Materials Flowing Axially Through Concentric Annuli
,”
Int. J. Heat Fluid Flow
,
24
(
5
), pp.
762
773
.10.1016/S0142-727X(03)00066-3
24.
Nascimento
,
U. C. S.
,
Macedo
,
E. N.
, and
Quaresma
,
J.N.N.
,
2002
, “
Thermal Entry Region Analysis Through the Finite Integral Transform Technique in Laminar Flow of Bingham Fluids Within Concentric Annular Ducts
,”
Int. J. Heat Mass Tran.
,
45
, pp.
923
929
.10.1016/S0017-9310(01)00187-9
25.
Ait Messaoudene
,
N.
,
Horimek
,
A.
,
Nouar
,
C.
, and
Benaouda-Zouaoui
,
B.
,
2011
, “
Laminar Mixed Convection in an Eccentric Annular Horizontal Duct for a Thermodependent Non-Newtonian Fluid
,”
Int. J. Heat Mass Tran.
,
54
(
19–20
), pp.
4220
4234
.10.1016/j.ijheatmasstransfer.2011.05.022
26.
Davidson
,
L.
, and
Farhanieh
,
B.
,
1992
, “
CALC-BFC: A Finite-Volume Code Employing Collocated Variable Arrangement and Cartesian Velocity Components for Components for Computation of Fluid Flow and Heat Transfer in Complex Three-Dimensional Geometries
,” Rept. 92/4, Thermo and Fluid Dynamics, Chalmers University of Technology, Gothenburg, Sweden.
27.
Kakac
,
S.
,
Shah
,
R. K.
,
Aung
,
W.
, eds.,
1987
,
Handbook of Single-Phase Convective Heat Transfer
, Wiley, New York, Chapter 3.
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