An integral approach of the boundary layer analysis is employed for the modeling of fluid flow around and heat transfer from infinite circular cylinders in power-law fluids. The Von Karman-Pohlhausenmethod is used to solve the momentum integral equation whereas the energy integral equation is solved for both isothermal and isoflux boundary conditions. A fourth-order velocity profile in the hydrodynamic boundary layer and a third-order temperature profile in the thermal boundary layer are used to solve both integral equations. Closed form expressions are obtained for the drag and heat transfer coefficients that can be used for a wide range of the power-law index, and generalized Reynolds and Prandtl numbers. It is found that pseudoplastic fluids offer less skin friction and higher heat transfer coefficients than dilatant fluids. As a result, the drag coefficients decrease and the heat transfer increases with the decrease in power-law index. Comparison of the analytical models with available experimental/numerical data proves the applicability of the integral approach for power-law fluids.

1.
Cho, Y. I. and Hartnett, J. P., 1985, “Non-Newtonian Fluids,” Handbook of Heat Transfer Applications, Second edition, Chapter 2, McGraw-Hill Book Company, New York.
2.
Chhabra, R. P. and Richardson, J. F., 1999, “Non-Newtonian Flow in the Process Industries: Fundamentals and Engineering Applications,” Butterworth-Heinemann, Great Britain.
3.
Khan, W. A., Culham, J. R., and Yovanovich, M. M., “Fluid Flow Around and Heat Transfer From an Infinite Circular Cylinder,” ASME Journal of Heat Transfer (in press).
4.
Acrivos
A.
,
Shah
M. J.
, and
Petersen
E. E.
,
1960
, “
Momentum and Heat Transfer in Laminar Boundary-Layer Flows of Non-Newtonian Fluids Past External Surfaces
,”
A.I.Ch.E. Journal
, Vol.
6
, No.
2
, pp.
312
317
.
5.
Schowalter
W. R.
,
1960
, “
Application of Boundary-Layer Theory to Power-Law Pseudo-Plastic Fluids: Similar Solutions
,”
A.I.Ch.E. Journal
, Vol.
6
, No.
1
, pp.
24
28
.
6.
Shah
M. J.
,
Petersen
E. E.
, and
Acrivos
A.
,
1962
, “
Heat Transfer from a Cylinder to a Power-Law Non-Newtonian Fluid
,”
A.I.Ch.E. Journal
, Vol.
8
, No.
4
, pp.
542
549
.
7.
Acrivos
A.
,
Shah
M. J.
, and
Petersen
E. E.
,
1965
, “
On Solution of Two-Dimensional Boundary-Layer Flow Equations for Non-Newtonian Power-Law Fluid
,”
Chemical Engineering Science
, Vol.
20
, No.
2
, pp.
101
105
.
8.
Lee
S. Y.
, and
Ames
W. F.
,
1966
, “
Similarity Solutions for Non-Newtonian Fluids
,”
A.I.Ch.E. Journal
, Vol.
12
, No.
4
, pp.
700
708
.
9.
Bizzle
G. D.
and
Slattery
J. C.
,
1962
, “
Non-Newtonian Boundary-Layer Flow
,”
Chemical Engineering Science
, Vol.
17
, pp.
777
782
.
10.
Wolf, C. J. and Szewczyk, A. A., 1966, “Laminar Heat Transfer to Non-Newtonian Fluids from Arbitrary Cylinders,” Proceedings of the Third IHTC, Chicago, Illinois, August 7–12, Volume 1.
11.
Serth
R. W.
, and
Kiser
K. M.
,
1967
, “
A Solution of the Two-Dimensional Boundary-Layer Equations for an Ostwald-de Waele Fluid
,”
Chemical Engineering Science
, Vol.
22
, pp.
945
956
.
12.
Lin
F. N.
and
Chern
S. Y.
,
1979
, “
Laminar Boundary Layer Flow of Non-Newtonian Fluid
,”
International Journal of Heat and Mass Transfer
, Vol.
22
, pp.
1323
1329
.
13.
Kim
H. W.
,
Jeng
D. R.
, and
DeWitt
K. J.
,
1983
, “
Momentum and Heat Transfer in Power-Law Fluid Flow Over Two-Dimensional or Axisymmetrical Bodies
,”
International Journal of Heat and Mass Transfer
, Vol.
26
, No.
2
, pp.
245
259
.
14.
Mizushina
T.
and
Usui
H.
,
1978
, “
Approximate Solution of the Boundary Layer Equations for the Flow of a Non-Newtonian Fluid Around a Cylinder
,”
Heat Transfer: Japanese Research
, Vol.
7
, No.
2
, pp.
83
92
.
15.
Nakayama
A.
,
Shenoy
A. V.
, and
Koyama
H.
,
1986
, “
An Analysis for Forced Convection Heat Transfer from External Surfaces to Non-Newtonian Fluids
,”
Warme-und Stoffubertragung
, Vol.
20
, pp.
219
227
.
16.
Shenoy
A. V.
, and
Nakayam
A.
,
1986
, “
Forced Convection Heat Transfer fro Axisymmetric Bodies to Non-Newtonian Fluids
,”
Canadian Journal of Chemical Engineering
, Vol.
64
, pp.
680
686
.
17.
Nakayama, A., 1986, “Integral Methods for Forced Convection Heat Transfer in Power-Law Non-Newtonian Fluids,” Encyclopedia of Fluid Mechanics: Rheology and Non-Newtonian Flows, Vol. 7, pp. 305–339, Houston, USA:Gulf.
18.
Anderson
H. I.
,
1988
, “
The Nakayama-Koyama Approach to Laminar Forced Convection Heat Transfer to Power-Law Fluids
,”
International Journal of Heat and Fluid Flow
, Vol.
9
, No.
3
, pp.
343
346
.
19.
Luikov, A. V., Schulman, Z. P., and Berkovsky, B. M., 1966, “Heat and Mass Transfer in a Boundary Layer of Non-Newtonian Fluids,” Proceedings of the Third IHTC, Chicago, Illinois, August 7–12, Volume 1.
20.
Luikov
A. V.
,
Schulman
Z. P.
, and
Puris
B. I.
,
1969
a, “
Mass Transfer of Cylinder in Forced Flow of Non-Newtonian Viscoelastic Fluid
,”
Heat Transfer-Soviet Research
, Vol.
1
, No.
1
, pp.
121
32
.
21.
Luikov
A. V.
,
Schulman
Z. P.
, and
Puris
B. I.
,
1969
b, “
External Convective Mass Transfer in Non-Newtonian Fluid
,”
International Journal of Heat and Mass Transfer
, Vol.
12
, pp.
377
391
.
22.
James
D. F.
, and
Acosta
A. J.
,
1970
, “
The Laminar Flow of Dilute Polymer Solutions Around Circular Cylinders
,”
Journal of Fluid Mechanics
, Vol.
42
, Part
2
, pp.
269
288
.
23.
Takashi
K.
,
Maeda
M.
, and
Ikai
S.
,
1977
, “
Experimental Study of Heat Transfer from a Cylinder Submerged in a Non-Newtonian Fluid
,” die dem Nahenungsansatz von K. Pohlhausen genugen,
Lilenthal Bericht
510
, p.
335
339
.
24.
Mizushina
T.
,
Usui
H.
,
Veno
K.
, and
Kato
T.
,
1978
, “
Experiments of Pseudoplastic Fluid Cross Flow Around a Circular Cylinder
,”
Heat Transfer: Japanese Research
, Vol.
7
, No.
3
, pp.
92
101
.
25.
Kumar
S.
,
Mall
B. K.
, and
Upadhyay
S. N.
,
1980
, “
On the Mass Transfer in Non-Newtonian Fluids: II Transfer fro Cylinders to Power-Law Fluids
,”
Letters in Heat and Mass Transfer
, Vol.
7
, pp.
55
64
.
26.
Ghosh
U. K.
,
Gupta
S. N.
,
Kumar
S.
, and
Upadhay
S. N.
,
1986
, “
Mass Transfer in Cross Flow of Non-Newtonian Fluid Around a Circular Cylinder
,”
International Journal of Heat and Mass Transfer
, Vol.
29
, No.
6
, pp.
955
960
.
27.
Rao
B. K.
,
2000
, “
Heat Transfer to Non-Newtonian Flows Over a Cylinder in Cross Flow
,”
International Journal of Heat and Fluid Flow
, Vol.
21
, pp.
693
700
.
28.
Coelho
P. M.
, and
Pinho
F. T.
,
2003
, “
Vortex Shedding in Cylinder Flow of Shear-Thinning Fluids: I. Identification and Demarcation of Flow Regimes
,”
Journal of Non-Newtonian Fluid Mechanics
, Vol.
110
, pp.
143
176
.
29.
Coelho
P. M.
, and
Pinho
F. T.
,
2003
, “
Vortex Shedding in Cylinder Flow of Shear-Thinning Fluids: II. Flow Characteristics
,”
Journal of Non-Newtonian Fluid Mechanics
, Vol.
110
, pp.
177
193
.
30.
Coelho
P. M.
, and
Pinho
F. T.
,
2004
, “
Vortex Shedding in Cylinder Flow of Shear-Thinning Fluids: III. Pressure Characteristics
,”
Journal of Non-Newtonian Fluid Mechanics
, Vol.
121
, pp.
55
68
.
31.
D’Alessio
S. J. D.
, and
Pascal
J. P.
,
1996
, “
Steady Flow of a Power-Law Fluid Past a Cylinder
,”
Acta Mechanica
, Vol.
117
, pp.
87
100
.
32.
Chhabra
R. P.
,
Soares
A. A.
, and
Ferreira
J. M.
,
2004
, “
Steady Non-Newtonian Flow Past a Circular Cylinder: A Numerical Study
,”
Acta Mechanica
, Vol.
172
, pp.
1
16
.
33.
Agarwal
M.
,
Chhabra
R. P.
, and
Eswaran
V.
,
2002
, “
Laminar Momentum and Thermal Boundary Layers of Power-Law Fluids Over a Slender Cylinder
,”
Chemical Engineering Science
, Vol.
57
, pp.
1331
1341
.
34.
Khan, W. A., 2004, “Modeling of Fluid Flow and Heat Transfer for Optimization of Pin-Fin Heat Sinks,” Ph. D. Thesis, Department of Mechanical Engineering, University of Waterloo, Canada.
35.
Pohlhausen
K.
,
1921
, “
Zur Na¨ aherungsweise Integration der Differential Gleichung der Laminaren Reibungschicht
,”
Zeitschrift fu¨r angewandte Mathematic und Mechanic
, Vol.
1
, pp.
252
268
.
36.
Schlichting, H., 1979, Boundary Layer Theory, 7th Edition., McGraw-Hill, New York.
37.
Walz, A., 1941, “Ein neuer Ansatz fu¨r das Greschwindligkeitsprofil der laminaren Reibungsschicht,” Lilienthal-Bericht 141, p. 8.
38.
Shibu
S.
,
Chhabra
R. P.
, and
Eswaran
V.
,
2001
, “
Power-Law Fluid Flow Over a Bundle of Cylinders at Intermediate Reynolds Numbers
,”
Chemical Engineering Science
, Vol.
56
, pp.
5545
5554
.
39.
Zˇukauskas, A. and ZˇiugZˇzda, J., 1985, Heat Transfer of a Cylinder in Crossflow, Hemisphere Publishing Corporation, New York.
40.
Fand
R. M.
, and
Keswani
K. K.
,
1972
, “
A Continuous Correlation Equation for Heat Transfer From Cylinders to Air in Crossflow for Reynolds Numbers From 10−2 to 2 × 105
,”
International Journal of Heat and Mass Transfer
, Vol.
15
, pp.
559
562
.
41.
Nakamura
H.
, and
Igarashi
T.
,
2004
, “
Variation of Nusselt Number with Flow Regimes Behind a Circular Cylinder for Reynolds Numbers from 70 30000
,”
International Journal of Heat and Mass Transfer
, Vol.
47
, pp.
5169
5173
.
42.
Van der Hegge Zijnen
B. G.
,
1956
, “
Modified Correlation Formulae for Heat Transfer by Natural and Forced Convection from Horizontal Cylinders
,”
Applied Scientific Research-A
, Vol.
6
, No.
2–3
, pp.
129
140
.
43.
Scho¨nauer
W.
,
1964
, “
Ein Differenzenverfahren zur Lo¨sung der Grenzschichtgleichung fu¨ur stationa¨re, laminare, inkompressible Stro¨mung
,”
Ing.-Arch.
, Vol.
33
, p.
173
173
.
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