This paper provides the results of numerical calculations of pressure drops and centerline velocities for laminar fully-developed flows of non-Newtonian fluids in circular ducts. The particular non-Newtonian fluid model considered is the Cross model, which has shown the ability to model the behavior of time-independent purely-viscous fluids over a wide range of shear rates. It is shown that the Cross model is equivalent to the more recently proposed extended modified power law (EMPL) model, and an alternative formulation of the nondimensional parameters arising from the use of these models is explored. Results are presented for friction factors and nondimensional centerline velocities over a wide range of fluid and flow conditions, and it is shown that simpler constitutive models can be used in cases where the ratios of the limiting Newtonian viscosities are extreme. The implications of the results to the design and analysis of piping systems is considered, and simple and accurate correlations are provided for engineering calculations.

References

References
1.
Irvine
,
T. F.
, and
Karni
,
J.
,
1987
, “
Non-Newtonian Flow and Heat Transfer
,”
Handbook of Single-Phase Convective Heat Transfer
,
S.
Kakaç
,
R. K.
Shah
, and
W.
Aung
, eds.,
Wiley
,
New York
, Chap. 20.
2.
Carreau
,
P. J.
,
1972
, “
Rheological Equations From Molecular Network Theories
,”
J. Rheol.
,
16
(
1
), pp.
99
127
.10.1122/1.549276
3.
Cross
,
M. M.
,
1965
, “
Rheology of Non-Newtonian Fluids: A New Flow Equation for Pseudoplastic Fluids
,”
J. Colloid Sci.
,
20
, pp.
417
438
.10.1016/0095-8522(65)90022-X
4.
Sisko
,
A. W.
,
1958
, “
The Flow of Lubricating Greases
,”
Ind. Eng. Chem.
,
50
(
12
), pp.
1789
1792
.10.1021/ie50588a042
5.
Reiner
,
M.
,
1960
,
Deformation, Strain and Flow
,
Wiley-Interscience
,
New York
.
6.
Sutterby
,
J. L.
,
1966
, “
Laminar Converging Flow of Dilute Polymer Solutions in Conical Sections – I. Viscosity Data, New Viscosity Model, Tube Flow Solution
,”
AIChE J.
,
12
, pp.
63
68
.10.1002/aic.690120114
7.
Brewster
,
R. A.
, and
Irvine
,
T. F.
,
1987
, “
Similitude Considerations in Laminar Flow of Modified Power Law Fluids in Circular Ducts
,”
Heat Mass Transfer
,
21
, pp.
83
86
.10.1007/BF01377563
8.
Capobianchi
,
M.
, and
Irvine
,
T. F.
,
1992
, “
Predictions of Pressure Drop and Heat Transfer in Concentric Annular Ducts With Modified Power Law Fluids
,”
Heat Mass Transfer
,
27
, pp.
209
215
. 10.1007/BF01589918
9.
Park
,
S.
,
Irvine
,
T. F.
, and
Capobianchi
,
M.
,
1994
, “
Experimental and Numerical Study of Friction Factor for a Modified Power Law Fluid in a Rectangular Duct
,”
Exp. Therm. Fluid Sci.
,
9
(
1
), pp.
61
68
.10.1016/0894-1777(94)90009-4
10.
Kim
,
S. C.
,
Irvine
,
T. F.
,
Lee
,
J. S.
,
Kim
,
C. H.
, and
Kim
,
T. H.
,
1995
, “
Graetz Problem Solutions for a Modified Power Law Fluid Over a Wide Range of Shear Rate
,”
Korean J. Rheol.
,
7
(
1
), pp.
35
41
.10.3348/kjr.2006.7.1.35
11.
Park
,
S.
, and
Lee
,
D.-R.
,
2001
, “
Anomalous Predictions of Pressure Drop and Heat Transfer in Ducts of Arbitrary Cross-Section With Modified Power Law Fluids
,”
Heat Mass Transfer
,
38
, pp.
141
149
.10.1007/s002310100198
12.
Davaa
,
G.
,
Shigechi
,
T.
, and
Momoki
,
S.
,
2002
, “
Fluid Flow for Modified Power Law Fluids in Concentric Annuli With Axially Moving Cores
,”
Rep. Faculty Eng. Nagasaki Univ.
,
32
(
58
), pp.
83
90
.
13.
Park
,
S.
, and
Lee
,
D.-R.
,
2003
, “
Investigations of Heat Transfer and Pressure Drop Between Parallel Channels With Pseudoplastic and Dilatant Fluids
,”
J. Appl. Polymer Sci.
,
89
, pp.
3601
3608
.10.1002/app.12641
14.
Park
,
S.
, and
Lee
,
D.-R.
,
2003
, “
Experimental and Numerical Investigations of Pressure Drop in a Rectangular Duct With Modified Power Law Fluids
,”
Heat Mass Transfer
,
39
, pp.
645
655
.10.1007/s00231-003-0445-9
15.
Capobianchi
,
M.
,
2008
, “
Pressure Drop Predictions for Laminar Flows of Extended Modified Power Law Fluids in Rectangular Ducts
,”
Int. J. Heat Mass Transfer
,
51
, pp.
1393
1401
.10.1016/j.ijheatmasstransfer.2007.11.019
16.
Capobianchi
,
M.
, and
Wagner
,
D.
,
2010
, “
Heat Transfer in Laminar Flows of Extended Modified Power Law Fluids in Rectangular Ducts
,”
Int. J. Heat Mass Transfer
,
53
, pp.
558
563
.10.1016/j.ijheatmasstransfer.2009.08.003
17.
Galindo-Rosales
,
F. J.
, and
Rubio-Hernandez
,
A.
,
2010
, “
Numerical Simulation in Steady Flow of Non-Newtonian Fluids in Pipes With Circular Cross-Section
,”
Numerical Simulation—Examples and Applications in Computational Fluid Dynamics
,
L.
Angermann
, ed.,
InTech
,
New York
, pp.
3
22
.
18.
CD-adapco
,
2012
, STAR-CCM+ v7.06 User Guide, Northville, MI.
19.
ASME V&V 20 Committee
,
2009
, “
Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer
,”
ASME
,
New York
.
20.
Fang
,
J.
, and
Owens
,
R. G.
,
2006
, “
Numerical Simulations of Pulsatile Blood Flow Using a New Constitutive Model
,”
Biorheology
,
43
, pp.
637
663
.
21.
Bodnár
,
T.
, and
Sequeira
,
A.
,
2008
, “
Numerical Simulation of the Coagulation Dynamics of Blood
,”
Comput. Math. Methods Med.
,
9
, pp.
83
104
.10.1080/17486700701852784
22.
Escudier
,
M. P.
, and
Smith
,
S.
,
2001
, “
Fully Developed Turbulent Flow of Non-Newtonian Liquids Through a Square Duct
,”
Proc. Roy. Soc. A
,
457
, pp.
911
936
.10.1098/rspa.2000.0698
23.
Escudier
,
M. P.
,
Gouldson
,
I. W.
,
Pereira
,
A. S.
,
Pinho
,
F. T.
, and
Poole
,
R. J.
,
2001
, “
On the Reproducibility of the Rheology of Shear-Thinning Liquids
,”
J. Non-Newtonian Fluid Mech.
,
97
, pp.
99
124
.10.1016/S0377-0257(00)00178-6
You do not currently have access to this content.