This work serves a two-fold purpose of briefly reviewing the currently existing literature on the scaling of thermal turbulent fields and, in addition, proposing a new scaling framework and testing its applicability. An extensive set of turbulent scalar transport data for turbulent flow in infinitely long channels is obtained using a Lagrangian scalar tracking approach combined with direct numerical simulation of turbulent flow. Two cases of Poiseuille channel flow, with friction Reynolds numbers 150 and 300, and different types of fluids with Prandtl number ranging from 0.7 to 50,000 are studied. Based on analysis of this database, it is argued that the value and the location of the maximum normal turbulent heat flux are important scaling parameters in turbulent heat transfer. Implementing such scaling on the mean temperature profile for different fluids and Reynolds number cases shows a collapse of the mean temperature profiles onto a single universal profile in the near wall region of the channel. In addition, the profiles of normal turbulent heat flux and the root mean square of the temperature fluctuations appear to collapse on one profile, respectively. The maximum normal turbulent heat flux is thus established as a turbulence thermal scaling parameter for both mean and fluctuating temperature statistics.

References

References
1.
Zagarola
,
M. V.
, and
Smits
,
A. J.
,
1998
, “
Mean-Flow Scaling in Turbulent Pipe Flow
,”
J. Fluid Mech.
,
373
, pp.
33
79
.10.1017/S0022112098002419
2.
Zagarola
,
M. V.
,
1996
, “
Mean Flow Scaling in Turbulent Pipe Flow
,” Ph.D. thesis, Princeton University, Princeton, NJ.
3.
Osterlund
,
J. M.
,
1999
, “
Experimental Studies of Zero Pressure-Gradient Turbulent Boundary Layer
,” Ph.D. thesis, KTH, Stockholm, Sweden.
4.
Hites
,
M. H.
,
1997
, “
Scaling of High-Reynolds Number Turbulent Boundary Layers in the National Diagnostic Facility
,” Ph.D. thesis, Illinois Institute of Technology, Chicago, IL.
5.
Nickels
,
T. B.
,
Marusic
,
I.
,
Hafez
,
S. M.
,
Hutchins
,
N.
, and
Chong
,
M. S.
,
2007
, “
Some Predictions of the Attached Model for a High Reynolds Number Boundary Layer
,”
Philos. Trans. R. Soc. Lond. A
,
365
, pp.
807
820
.10.1098/rsta.2006.1950
6.
Klewicki
,
J. C.
,
Foss
,
J. F.
, and
Wallace
,
J. M.
,
1998
,
Flow at Ultra-High Reynolds and Rayleigh Numbers
,
R. J.
Donnelly
and
K. R.
Sreenivasan
, eds.,
Springer
,
New York
.
7.
Marusic
,
I.
,
Mathis
,
R.
, and
Hutchins
,
N.
,
2010
, “
Predictive Model for Wall Bounded Turbulent Flow
,”
Science
,
329
, pp.
193
196
.10.1126/science.1188765
8.
Wei
,
T.
, and
Willmarth
,
W. W.
,
1989
, “
Reynolds-Number Effects on the Structure of a Turbulent Channel Flow
,”
J. Fluid Mech.
,
204
, pp.
57
95
.10.1017/S0022112089001667
9.
Shen
,
X.
, and
Warhaft
,
Z.
,
2000
, “
The Anisotropy of the Small Scale Structure in High Reynolds Number (Rë ∼ 1000) Turbulent Shear Flow
,”
Phys. Fluids
,
12
, pp.
2976
2989
.10.1063/1.1313552
10.
McKeon
,
B. J.
,
2010
, “
Controlling Turbulence
,”
Science
,
327
, pp.
1462
1463
.10.1126/science.1187607
11.
Smits
,
A. J.
,
McKeon
,
B. J.
, and
Marusic
, I
.
,
2011
, “
High-Reynolds Number Wall Turbulence
,”
Ann. Rev. Fluid Mech.
,
43
, pp.
353
375
.10.1146/annurev-fluid-122109-160753
12.
Kim
,
J.
,
Moin
,
P.
, and
Moser
,
R. D.
,
1987
, “
Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number
,”
J. Fluid Mech.
,
177
, pp.
133
166
.10.1017/S0022112087000892
13.
Lyons
,
S. L.
,
Hanratty
,
T. J.
, and
McLaughlin
,
J. B.
,
1991
, “
Large-Scale Computer Simulation of Fully Developed Turbulent Channel Flow With Heat Transfer
,”
Int. J. Numer. Methods Fluids
,
13
, pp.
999
1028
.10.1002/fld.1650130805
14.
Kasagi
,
N.
,
Tomita
,
Y.
, and
Kuroda
,
A.
,
1992
, “
Direct Numerical Simulation of Passive Scalar Filed in a Turbulent Channel Flow
,”
ASME J. Heat Transfer
,
114
, pp.
598
606
.10.1115/1.2911323
15.
Moser
,
R. D.
,
Kim
,
J.
, and
Mansour
,
N. N.
,
1999
, “
Direct Numerical Simulation of Turbulent Channel Flow up to Reτ = 590
,”
Phys. Fluids
,
11
, pp.
943
945
.10.1063/1.869966
16.
Abe
,
H.
,
Kawamura
,
H.
, and
Choi
,
H.
,
2004
, “
Very Large-Scale Structures and their Effects on the Wall Shear-Stress Fluctuations in a Turbulent Channel Flow up to Reτ = 640
,”
ASME J. Fluid Eng.
,
126
, pp.
835
843
.10.1115/1.1789528
17.
Hu
,
Z. W.
,
Morfey
,
C. L.
, and
Sandham
,
N. D.
,
2006
, “
Wall Pressure and Shear Stress Spectra From Direct Numerical Simulations of Channel Flow
,”
AIAA J.
,
44
, pp.
1541
1549
.10.2514/1.17638
18.
Hoyas
,
S.
, and
Jimenez
,
J.
,
2006
, “
Scaling of the Velocity Fluctuations in Turbulent Channels up to Reτ = 2003
,”
Phys. Fluids
,
18
, p.
011702
.10.1063/1.2162185
19.
Abe
,
H.
,
Kawamura
,
H.
, and
Matsuo
,
Y.
,
2004
, “
Surface Heat-Flux Fluctuations in a Turbulent Channel Flow up to Reτ = 1020 With Pr = 0.025 and 0.71
,”
Int. J. Heat Fluid Flow
,
25
, pp.
401
419
.10.1016/j.ijheatfluidflow.2004.02.010
20.
Gad-el-Hak
,
M.
, and
Bandyopadhyay
,
H.
,
1994
, “
Reynolds Number Effects in Wall-Bounded Turbulent Flows
,”
Appl. Mech. Rev.
,
47
, pp.
307
365
.10.1115/1.3111083
21.
George
,
W. K.
, and
Castillo
,
L.
,
1997
, “
Zero-Pressure-Gradient Turbulent Boundary Layer
,”
Appl. Mech. Rev.
,
50
, pp.
689
729
.10.1115/1.3101858
22.
Degraaff
,
D. B.
, and
Eaton
,
J. K.
,
2000
, “
Reynolds-Number Scaling the Flat-Plate Turbulent Boundary Layer
,”
J. Fluid Mech.
,
422
, pp.
319
346
.10.1017/S0022112000001713
23.
Wei
,
T.
,
Fife
,
P.
,
Klewicki
,
J.
, and
McMurtry
,
P.
,
2005
, “
Properties of the Mean Momentum Balance in Turbulent Boundary Layer, Pipe and Channel Flows
,”
J. Fluid Mech.
,
522
, pp.
303
327
.10.1017/S0022112004001958
24.
Monkewitz
,
P. A.
,
Chauhan
,
K. A.
, and
Nagib
,
H. M.
,
2007
, “
Self-Consistent High-Reynolds Number Asymptotics for Zero-Pressure-Gradient Turbulent Boundary Layers
,”
Phys. Fluids
,
19
, p.
115101
.10.1063/1.2780196
25.
Barenblatt
,
G. I.
,
1993
, “
Scaling Laws for Fully Developed Shear Flows, Part 1: Basic Hypothesis and Analysis
,”
J. Fluid Mech.
,
248
, pp.
513
520
.10.1017/S0022112093000874
26.
Barenblatt
,
G. I.
,
1999
, “
Scaling Laws for Turbulent Wall Bounded Shear Flows at Very Large Reynolds Numbers
,”
J. Eng. Math.
,
36
, pp.
361
384
.10.1023/A:1004784331151
27.
Afzal
,
N.
,
2001
, “
Power Law and Log Law Velocity Profiles in Turbulent Boundary-Layer Flow: Equivalent Relations at Large Reynolds Numbers
,”
Acta Mech.
,
151
, pp.
195
216
.10.1007/BF01246918
28.
Afzal
,
N.
,
2009
, “
Analysis of Instantaneous Turbulent Velocity Vector and Temperature Profiles in Transitional Rough Channel Flow
,”
ASME J. Heat Transfer
,
131
, p.
064503
.10.1115/1.3085827
29.
Barenblatt
,
G. I.
, and
Chorin
,
A. J.
,
2004
, “
A Mathematical Model for the Scaling of Turbulence
,”
PNAS
,
101
, pp.
15023
15026
.10.1073/pnas.0406291101
30.
Barenblatt
,
G. I.
,
Chorin
,
A. J.
, and
Prostokishin
, V
. M.
,
2000
, “
A Note on the Intermediate Region in Turbulent Boundary Layers
,”
Phys. Fluids
,
12
, pp.
2159
2161
.10.1063/1.1287613
31.
Marusic
,
I.
,
Mckeon
,
B. J.
,
Monkewitz
,
P. A.
,
Nagib
,
H. M.
,
Smits
,
A. J.
, and
Sreenivasan
,
K. R.
,
2010
, “
Wall-Bounded Turbulent Flows at High Reynolds Numbers: Recent Advances and Key Issues
,”
Phys. Fluids
,
22
, p.
065103
.10.1063/1.3453711
32.
Warhaft
,
Z.
,
2000
, “
Passive Scalar in Turbulent Flow
,”
Ann. Rev. Flu. Mech.
,
32
, pp.
203
240
.10.1146/annurev.fluid.32.1.203
33.
Churchill
,
S. W.
,
1997
, “
Critique of the Classical Algebraic Analogies between Heat, Mass and Momentum Transfer
,”
Ind. Eng. Chem. Res.
,
36
, pp.
3866
3878
.10.1021/ie960750a
34.
Kader
,
B. A.
,
1981
, “
Temperature and Concentration Profiles in Fully Turbulent Boundary layers
,”
Int. J. Heat Mass Transfer
,
24
, pp.
1541
1544
.10.1016/0017-9310(81)90220-9
35.
Churchill
,
S. W.
,
1996
, “
A Critique of Predictive and Correlative Models for Turbulent Flow and Convection
,”
Ind. Eng. Chem. Res.
,
35
, pp.
3122
3140
.10.1021/ie960012m
36.
Churchill
,
S. W.
, and
Chan
,
C.
,
1994
, “
Improved Correlating Equations for the Friction Factor for Fully Turbulent Flow in Round Tubes and Between Identical Parallel Plates, Both Smooth and Naturally Rough
,”
Ind. Eng. Chem. Res.
,
33
, pp.
2016
2019
.10.1021/ie00032a018
37.
Churchill
,
S. W.
, and
Chan
,
C.
,
1995
, “
Theoretically Based Correlating Equations for the Local Characteristics of Fully Turbulent Flow in Round Tubes and between Parallel Plates
,”
Ind. Eng. Chem. Res.
,
34
, pp.
1332
1341
.10.1021/ie00043a039
38.
Churchill
,
S. W.
, and
Chan
,
C.
,
1995
, “
Turbulent Flow in Channels in Terms of the Turbulent Shear and Normal Stresses
,”
AIChE J.
,
41
, pp.
2513
2521
.10.1002/aic.690411202
39.
Churchill
,
S. W.
,
1997
, “
New Simplified Models and Formulations for Turbulent Flow and Convection
,”
AIChE J.
,
43
, pp.
1125
1140
.10.1002/aic.690430502
40.
Kader
,
B. A.
, and
Yaglom
,
A. M.
,
1972
, “
Heat and Mass Transfer Laws for Fully Turbulent Wall Flows
,”
Int. J. Heat Mass Transfer
,
15
, pp.
2329
2351
.10.1016/0017-9310(72)90131-7
41.
Churchill
,
S. W.
,
2002
, “
A reinterpretation of the Turbulent Prandtl Number
,”
Ind. Eng. Chem. Res.
,
41
, pp.
6393
6401
.10.1021/ie011021k
42.
Churchill
,
S. W.
,
Yu
,
B.
, and
Kawaguchi
,
Y.
,
2005
, “
The Accuracy and Parametric Sensitivity of Algebraic Models for Turbulent Flow and Convection
,”
Int. J. Heat Mass Transfer
,
48
, pp.
5488
5503
.10.1016/j.ijheatmasstransfer.2005.06.023
43.
Mitrovic
,
B. M.
,
Le
,
P. M.
, and
Papavassiliou
,
D. V.
,
2004
, “
On the Prandtl or Schmidt Number Dependence of the Turbulent Heat or Mass Transfer Coefficient
,”
Chem. Eng. Sci.
,
59
(
3
), pp.
543
555
.10.1016/j.ces.2003.09.039
44.
Le
,
P. M.
, and
Papavassiliou
,
D. V.
,
2006
, “
On Temperature Prediction at Low Re Turbulent Flows Using the Churchill Turbulent Heat Flux Correlation
,”
Int. J. Heat Mass Transfer
,
49
, pp.
3681
3690
.10.1016/j.ijheatmasstransfer.2006.02.022
45.
Danov
,
S. N.
,
Arai
,
N.
, and
Churchill
,
S. W.
,
2000
, “
Exact Formulations and nearly Exact Numerical Solutions for Convection in Turbulent Flow between Parallel Plates
,”
Int. J. Heat Mass Transfer
,
43
, pp.
2767
2777
.10.1016/S0017-9310(99)00254-9
46.
Kays
,
W. M.
,
1994
, “
Turbulent Prandtl Number—Where are We?
Trans. ASME J. Heat Transfer
,
116
, pp.
284
295
.10.1115/1.2911398
47.
Srinivasan
,
C.
, and
Papavassiliou
,
D. V.
,
2011
, “
Prediction of Turbulent Prandtl Number in Wall Flows With Lagrangian Simulations
,”
Ind. Eng. Chem. Res.
,
50
(
15
), pp.
8881
8891
.10.1021/ie1019497
48.
Afzal
,
N.
,
1976
, “
Millikan's Argument at Moderately Large Reynolds Number
,”
Phys. Fluids
,
19
, pp.
600
602
.10.1063/1.861498
49.
Afzal
,
N.
,
1984
, “
Mesolayer Theory for Turbulent Flows
,”
AIAA J.
,
22
, pp.
437
439
.10.2514/3.8414
50.
Afzal
,
N.
,
1984
, “
Periods Between Bursting in Turbulent Shear Flow: An Intermediate Layer
,”
Curr. Sci.
,
53
, pp.
640
642
.
51.
Panton
,
R. L.
,
2007
, “
Composite Asymptotic Expansions and Scaling Wall Turbulence
,”
Philos. Trans. R. Soc. London, Ser. A
,
365
, pp.
733
754
.10.1098/rsta.2006.1951
52.
Klewicki
,
J.
,
McMurtry
,
P.
,
Fife
,
P.
, and
Wei
,
T.
,
2004
, “
A Physical Model of the Turbulent Boundary Layer Consonant With the Structure of Mean Momentum Balance
,”
Proceedings of the 15th Australasian Fluid Mechanics Conference, University of Sydney
,
Sydney, Australia
.
53.
Wei
,
T.
,
Fife
,
P.
,
Klewicki
,
J.
, and
McMurtry
,
P.
,
2005
, “
Scaling Heat Transfer in Fully Developed Turbulent Channel Flow
,”
Int. J. Heat Mass Transf.
,
48
, pp.
5284
5296
.10.1016/j.ijheatmasstransfer.2005.07.035
54.
Kawamura
,
H.
,
Abe
,
H.
, and
Shingai
,
K.
,
2000
, “
DNS of Turbulence and Heat Transport in a Channel Flow With Different Reynolds and Prandtl Numbers and Boundary Conditions
,”
Proceedings of the 3rd International Symposium on Turbulence, Heat and Mass Transfer
,
Aichi Shuppan, Japan
, p.
15
.
55.
Klewicki
,
J.
,
Fife
,
P.
,
Wei
,
T.
, and
McMurtry
,
P.
,
2006
, “
Overview of the Methodology for Scaling the Intermediate Equations of Wall Turbulence
,”
AIAA J.
,
44
, pp.
2475
2481
.10.2514/1.18911
56.
Le
,
P. M.
, and
Papavassiliou
,
D. V.
,
2008
, “
On the Scaling of Heat Transfer Using Thermal Flux Gradients for Fully Developed Turbulent Channel and Couette Flows
,”
Int. Comm. Heat Mass Transfer
,
35
(
4
), pp.
404
412
.10.1016/j.icheatmasstransfer.2007.09.006
57.
George
,
W. K.
,
Wosnik
,
M.
, and
Castillo
,
L.
,
1997
, “
Similarity Analysis for Forced Convection Turbulent Boundary Layer
,”
Proceedings of the 10th International Symposium on Transport Phenomena in Thermal Sciences and Process Engineering
,
Kyoto, Japan
, p.
239
.
58.
Wang
,
X.
, and
Castillo
,
L.
,
2003
, “
Asymptotic Solutions in Forced Convection Turbulent Boundary Layers
,”
J. Turbul.
,
4
, pp.
1
18
.10.1088/1468-5248/4/1/006
59.
Blackwell
,
B. F.
,
Kays
,
W. M.
, and
Moffat
,
R. J.
,
1972
, “
The Turbulent Boundary Layer on a Porous Plate: An Experimental Study of Heat Transfer Behavior With Adverse Pressure Gradients
,” Department of Mechanical Engineering, Stanford University Thermosciences Division Report No. HMT-16.
60.
Blom
,
J.
,
1970
, “
An Experimental Determination of the Turbulent Prandtl Number in a Developing Temperature Boundary Layer
,” Ph.D. thesis, Technishe Hogeschool, Eindhoven, The Netherlands.
61.
Orlando
,
A. F.
,
Kays
,
W. M.
, and
Moffat
,
R. J.
,
1974
, “
Turbulent Transport of Heat and Momentum in a Boundary Layer Subject to Deceleration, Suction and Variable Wall Temperature
,” Department of Mechanical Engineering, Stanford University Thermosciences Division, Report No. HMT-17.
62.
Thielbahr
,
W. H.
,
Kays
,
W. M.
, and
Moffact
,
R. J.
,
1969
, “
The Turbulent Boundary Layer: Experimental Heat Transfer With Strong Favorable Pressure Gradients and Blowing
,” Department of Mechanical Engineering, Stanford University Thermosciences Division Report No HMT-5.
63.
Wang
,
X.
,
Castillo
,
L.
, and
Araya
,
G.
,
2008
, “
Temperature Scalings and Profiles in Forced Convection Turbulent Boundary Layers
,”
Trans. ASME J. Heat Transfer
,
130
, p.
021701
.10.1115/1.2813781
64.
Finnicum
,
D. S.
, and
Hanratty
,
T. J.
,
1988
, “
Effect of Favorable Pressure Gradients on Turbulent Boundary Layers
,”
AIChE J.
,
34
, pp.
529
540
.10.1002/aic.690340402
65.
Gunther
,
A.
,
Papavassiliou
,
D. V.
,
Warholic
,
M. D.
, and
Hanratty
,
T. J.
,
1998
, “
Turbulent Flow in a Channel in Low Reynolds Number
,”
Exp. Fluids
,
25
, pp.
503
511
.10.1007/s003480050256
66.
Kontomaris
,
K.
,
Hanratty
,
T. J.
, and
McLaughlin
,
J. B.
,
1993
, “
An Algoritm for Tracking Fluid Particles in a Spectral Simulation of Turbulent Channel Flow
,”
J. Comput. Phys.
,
103
, pp.
231
242
.10.1016/0021-9991(92)90398-I
67.
Papavassiliou
,
D. V.
, and
Hanratty
,
T. J.
,
1995
, “
The Use of Lagrangian Methods to Describe Transport of Heat From the Wall
,”
Ind. Eng. Chem. Res.
,
34
, pp.
3359
3367
.10.1021/ie00037a023
68.
Papavassiliou
,
D. V.
,
2002
, “
Turbulent Transport From Continuous Sources at the Wall of a Channel
,”
Int. J. Heat Mass Transfer
,
45
(
17
), pp.
3571
3583
.10.1016/S0017-9310(02)00065-0
69.
Kim
,
J.
, and
Moin
,
P.
,
1989
, “
Transport of Passive Scalars in a Turbulent Channel Flow
,”
Transport of Passive Scalars in a Turbulent Channel Flow (Turbulent Shear Flows
, Vol.
6
),
J. C.
Andre
,
J.
Cousteix
,
F.
Durst
,
B. E.
Launder
,
F. W.
Schmidt
,
J. H.
Whitelaw
, eds.,
Springer
,
Berlin
.
70.
Kawamura
,
H.
,
Abe
,
H.
, and
Matsuo
,
Y.
,
1999
, “
DNS of Turbulent Heat Transfer in Channel Flow With Respect to Reynolds and Prandtl Number Effects
,”
Int. J. Heat Fluid Flow
,
20
, pp.
196
207
.10.1016/S0142-727X(99)00014-4
71.
Shaw
,
D. A.
, and
Hanratty
,
T. J.
,
1977
, “
Influence of Schmidt Number on the Fluctuations of Turbulent Mass Transfer of a Wall
,”
AIChE J.
,
23
, pp.
160
169
.10.1002/aic.690230204
72.
Hasegawa
,
Y.
, and
Kasagi
,
N.
,
2009
, “
Low-Pass Filtering Effects of Viscous Sublayer on High Schmidt Number Mass Transfer Close to a Solid Wall
,”
Int. J. Heat Fluid Flow
,
30
, pp.
525
533
.10.1016/j.ijheatfluidflow.2009.02.011
73.
Na
,
Y.
, and
Hanratty
,
T. J.
,
2000
, “
Limiting Behavior of Turbulent Scalar Transport Close to a Wall
,”
Int. J. Heat Mass Transf.
,
43
, pp.
1749
1758
.10.1016/S0017-9310(99)00258-6
74.
Teital
,
M.
, and
Antonia
,
R. A.
,
1993
, “
Heat Transfer in Fully Developed Turbulent Channel Flow: Comparison Between Experiment and Direct Numerical Simulations
,”
Int. J. Heat Mass Transfer
,
36
, pp.
1701
1706
.10.1016/S0017-9310(05)80080-8
75.
Churchill
,
S. W.
,
2000
, “
Progress in Thermal Science: AICHE Institute Lecture
,”
AIChE J.
,
46
, pp.
1704
1722
.10.1002/aic.690460903
76.
Schwertfirm
,
F.
, and
Manhart
,
M.
,
2001
, “
DNS of Passive Scalar Transport in Turbulent Channel Flow at High Schmidt Numbers
,”
Int. J. Heat Fluid Flow
,
28
, pp.
1204
1214
.10.1016/j.ijheatfluidflow.2007.05.012
77.
Dong
,
Y. H.
,
Lu
,
X. Y.
, and
Zhuang
,
L. X.
,
2003
, “
Large Eddy Simulation of Turbulent Channel Flow With Mass Transfer at High-Schmidt Numbers
,”
Int. J. Heat Mass Transf.
,
46
, pp.
1529
1539
.10.1016/S0017-9310(02)00456-8
78.
Wang
,
L. Y.
,
Dong
,
Y. H.
, and
Lu
,
X. Y.
,
2004
, “
Larger Eddy Simulation of Turbulent Open Channel Flow With Heat Transfer at High Prandtl Numbers
,”
Acta Mech.
,
170
, pp.
227
246
.10.1007/s00707-004-0115-0
79.
Papavassiliou
,
D. V.
, and
Hanratty
,
T. J.
,
1997
, “
Transport of a Passive Scalar in a Turbulent Channel Flow
,”
Int. J. Heat Mass Transfer
,
40
(
6
), pp.
1303
1311
.10.1016/S0017-9310(96)00202-5
80.
Ponoth
,
S. S.
, and
McLaughlin
,
J. B.
,
2000
, “
Numerical Simulation of a Mass Transfer for Bubbles in Water
,”
Chem. Eng. Sci.
,
55
, pp.
1237
1255
.10.1016/S0009-2509(99)00412-1
81.
Mito
,
Y.
, and
Hanratty
,
T. J.
,
2003
, “
Lagrangian Stochastic Simulation of Turbulent Dispersion of Heat Markers in a Channel Flow
,”
Int. J. Heat Mass Transfer
,
46
(
6
), pp.
1063
1073
.10.1016/S0017-9310(02)00362-9
You do not currently have access to this content.